Correlating Time-Domain Noise to Detect Fraudulent Credit Cards

Size: px
Start display at page:

Download "Correlating Time-Domain Noise to Detect Fraudulent Credit Cards"

Transcription

1 School of Engineering and Applied Science Electrical and Systems Engineering Department ESE 498 Correlating Time-Domain Noise to Detect Fraudulent Credit Cards By Wenyuan Liu Andrew Wiens Supervisor Robert Morley Submitted in Partial Fulfillment of the Requirement for the BSEE Degree, Electrical and Systems Engineering Department, School of Engineering and Applied Science, Washington University in St. Louis May 2013

2 Table of Contents List of Figures and Tables 2 Student Statement 3 Abstract 3 Acknowledgment 3 Problem Statement 4 Problem Formulation 4 Project Specification 4 Concept Synthesis 4 Detailed Engineering Analysis and Design Presentation 6 Conclusions 21 References 22 1

3 List of Figures and Tables Figure 1 Noise region in the data track 5 Figure 2 Mean smoothing filter 5 Figure 3 Output from mean smoother 6 Figure 4 Our LabView design 7 Figure 5 Raw, unprocessed waveform 8 Figure 6 Find Peaks sub-vi 8 Figure 7 Accept distribution before and after adding false peak discrimination 9 Figure 8 FSM sub-vi that finds the swipe direction 10 Figure 9 State diagram of the FSM sub-vi 10 Figure 10 Normalize block 11 Figure 11 Example normalized waveform 12 Figure 12 Filter block 13 Figure 13 Filtered waveform 13 Figure 14 Trim edges sub-vi 14 Figure 15 Normalized and filtered waveform with data peaks trimmed 14 Figure 16 Decimate and sample subset 15 Figure 17 Example waveform after decimation 16 Figure 18 Quantization 17 Figure 1 Example magneprint 17 Figure 20 Correlation block sub-vi 18 Figure 21 Accept and reject distributions generated from Dr. Morley s card database 19 Figure 22 Block diagram of live mode VI 19 Figure 23 Accept and reject distributions generated in live mode 20 Figure 24 Optimizer VI 21 Table 1 Best M, B, filter half-width, and spacing (delta) parameters 22 2

4 Student Statement We, the designers, have applied ethics to the design process and in the selection of the final proposed design. We have complied with the WUSTL Honor Code. Abstract In this project, we developed using Labview a system that detects fraudulent credit cards using the noise in-between the data on the credit cards. First, we determined the direction of the card swipe and normalized all swipes to be forwards. Then the amplitudes of the peaks were normalized to one, as well as the number of samples between adjacent data peaks to 266(zeros) and 133(ones). The normalized waveform is then high pass filtered with a FIR moving average filter and then broken up from peak to peak. 64 samples were taken in-between the peaks among the 266 samples (only from zeroes). Then we formed a Magneprint of the card by decimating, quantizing, and choosing a subset of the samples. We found the best parameters for the filter, decimation, samples taken, and sample spacing for Magneprint sizes of 384, 768, 1024, 2048 bits that minimized the rate of false positive and false negative swipes. In the end our system was excellent in determining fraudulent cards. Acknowledgment Thanks to Dr. Morley and Ed Richter for their help in this project. 3

5 Problem Statement Today s market is dominated by credit card transactions. There are many ways to counterfeit credit cards, which creates problems in credit card security. A system to detect fraudulent credit cards is needed, and the system must be robust, consistent, and reliable as well as taking cost into consideration. Problem Formulation We have proposed a credit card security system where the task is to create a unique fingerprint of each individual card called a Magneprint. Fraudulent counterfeits can then be identified when their Magneprints are compared to the authentic card. For the system to be robust, consistent, costefficient and reliable, it must have minimal rates of false positives and false negatives as well as small Magneprint sizes. Project Specifications The Magneprint sizes allowed for performance testing are 384, 768, 1024, 2048 bits. The rate of false positives and false rejects must be minimized and for our scope and initial stages of testing it must be less than 0.5%. Concept Synthesis Literature Review The Magneprint patents provide much information about the nature of the noise found on magnetic cards as well as implementations to generate a fingerprint from the noise. Figure 1 appears in U.S. patent no. 7,478,751 and shows an example of magnetic noise on a credit card as captured by an analog to digital converter while swiping a card through a card reader. High frequency noise can be found between the data peaks. 4

6 Figure 1 Noise region in the data track In order to isolate the high frequency noise to create a fingerprint of the credit card, the low frequency components of the waveform have to be removed. The same patent describes a method to remove low frequencies from the waveform using a mean smoother (moving average filter). The mean smoother subtracts the average of n neighboring samples from each sample. This filter is useful for creating Magneprints because it has a steep response in the frequency domain. Also, because the filter has a finite impulse response, energy from data peaks in the waveform do not affect the noise region. A block diagram of the filter and an example of a waveform filtered with the mean smoother are shown below as they appear in the patent. Figure 2 shows the block diagram for the mean smoother and Figure 3 shows an example waveform produced by the mean smoother. Figure 2 Mean smoothing filter 5

7 Figure 3 Output from mean smoother Concept Generation and Reduction Another way to process the noise in between the data peaks instead of using a moving average filter is to linearly normalize the slope of the noise by dividing every sample by the slope calculated from the first and last sample. We thought about this alternative and decided that the moving average provided greater simplicity and it is easier to optimize via sweeping the filter length. Detailed Engineering Analysis and Design Presentation We have chosen LabView 2012 as our tool to build the Magneprint system for its utility and popularity in academia as well as per recommendations from our advisor Dr. Morley. The scheme of the system is to capture unique fingerprints made of noise from individual cards and build a database. Known authentic and inauthentic cards are correlated and the results displayed on histograms to check for system performance, the details of which will be discussed later in this section. Top The general mechanism of our system is to first capture a waveform of a card, which will present with data and noise. Since our database will contain only forward containing Magneprints, we will flip the 6

8 waveforms from all backwards swipes. Then we normalize the waveforms so that they can be properly correlated. The waveform is then put through various signal processing techniques such as taking only specified chunks of the whole waveform, a moving average filter, decimation, taking subsamples, and quantization to create the Magneprint. The parameters for the Filter, Decimate (and subsample), and Quantize VIs are determined with another optimization VI explained later in this section. In the end each card is correlated with the rest and the results are displayed on histograms. The top-level LabView VI is shown in Figure 4 below. It shows our implementation at the highest level, a pipeline architecture of 1D array of waveforms. Part of the credit goes to Dr. Morley for his code in acquiring a raw waveform from DAT files. Figure 4 Our LabView design Figure 5 shows a raw waveform captured by swiping a Washington University student ID thru a Magtek card reader provided by Dr. Morley. The waveform is not processed in any way; as depicted, it contains around 85k samples. 7

9 Figure 5 Raw, unprocessed waveform Find Peaks Below is a figure of the sub VI we created to find the peaks in the raw waveform. It uses a peak detector block to find all peaks in the waveform. Figure 6 Find Peaks sub-vi At first we used the raw peaks from the peak detector. However, we found that the peak detector found not only the data peaks, but also picked false peaks due to noise as well. This was a problem for the accept distribution because the Magneprints must line up correctly. This sub VI we designed tries to detect and discard false peaks. It does by checking both the number of samples between the peaks and the amplitude of the peaks. 1. First, the Find Peaks sub-vi determines the number of samples between each consecutive pair of peaks. 8

10 a. If the percent difference in the number of samples between two peaks is within +/- 15 percent compared to the previous two samples, then the peak is considered true and the data bit is a zero. b. Otherwise: i. If the percent difference is between -35 and -70 percent, that is, there are 35 to 70 percent fewer samples between the two peaks less than the last zero bit, then: 1. If the percent difference in amplitude since the last peak is within +/- 60 percent, then the peak is considered true and the data bit is a one 2. Otherwise the peak is considered noise and discarded. ii. Otherwise the peak is considered noise and discarded. To find the percentages above, we made a few swipes and plotted histograms of the peak-to-peak change in the separation and change in amplitude between peaks. The histograms revealed that the user is not generally capable of a bit-to-bit change in speed greater than about 15 percent. After implementing our Find Peaks sub-vi, our accept distribution was much improved. Since the number of false peaks was reduced, the Magneprints lined up better than before. The diagram below shows the improved accept distribution before and after implementing false peak discrimination. Figure 7 Accept distribution before and after adding false peak discrimination FSM We designed a sub VI called FSM that determines the direction the card was swiped. It determines the direction bit-by-bit using a finite state machine that detects the start sentinel. The LabView code is shown in Figure 8, and the state diagram is shown in Figure 9. 9

11 Figure 8 FSM sub-vi that finds the swipe direction backward forward Figure 9 State diagram of the FSM sub-vi 10

12 Normalize In order to correlate the time-domain signal, each swipe s waveform must be normalized, otherwise the speed of the swipe will change the correlation. The normalize block uses the Find Peaks block to split the waveform into pieces correcponding to peaks in the data. It throws out ones, keeping only zero bits. This is because ones have a higher frequency than zeros, and the noise section is too small to be very useful for building Magneprints. After splitting the waveform, it resamples each sub array to 266 samples. Then, it normalizes the amplitude of the entire waveform so that the data peaks are 1. It does this by comparing the absolute amplitude of the data peaks, linearly interpolating between the data peaks, and dividing each sample by that number. Figure 10 shows the VI for the normalize block and Figure 11 shows a sample waveform of a normalized swipe. Figure 10 Normalize block 11

13 Figure 11 Example normalized waveform Filter This block implements the mean smoothing filter described in the patent. The sub-vi pads the beginning of the input waveform with n zeros, where n is the half-width of the moving average filter. It then filters the original input waveform with a moving average block, subtracts the filtered waveform from the padded waveform, and then removes n samples from the beginning. Figure 12 shows the block diagram and Figure 13 shows a sample waveform filtered with the mean smoother. 12

14 Figure 12 Filter block Figure 13 Filtered waveform Trim Edges This sub-vi removes the data portion of the waveform leaving the noise portion. Our implementation removes the first and last 101 samples from each 266-sample data bit leaving 64 samples of Magneprint per bit. Figure 14 shows the block diagram and Figure 15 shows a sample Magneprint waveform. 13

15 Figure 14 Trim edges sub-vi Figure 15 Normalized and filtered waveform with data peaks trimmed 14

16 Decimate and sample subset Here is our Decimate and sample subset subvi. The input waveform is first converted to an array. Then based on separation, the array is effectively decimated by taking only the nth element and building a new array containing those n elements. When the desired number of samples is reached, the inside loop which builds new array stops. In addition, if a large enough separation (delta) is chosen so that the end of the input array is reached before taking the desired amount of samples (signified by the greater than or equal to comparison block), the loop also stops. That further ensures robustness of the whole system. Figure 16 Decimate and sample subset 15

17 Figure 17 shows a resulting waveform after having a sample separation of 67 samples and taking 96 total samples. As you can clearly see when compared to the previous waveform (Figure 15), the number of samples has greatly decreased from around 11k samples down to 96 samples. Quantize Figure 17 Example waveform after decimation Here is our Quantization sub-vi. The input waveform is quantized based on B, the number of bits. Quantization represents a waveform in discrete levels based on the number of bits desired. So if B is 4, the number of levels a waveform can be represented in is 2 4 = 16. The higher the number of bits, the more levels the waveform can be represented in and so the resolution is higher. But one drawback of having a high number of bits is that it increases the size of the Magneprint, and that is why we want to optimize B and get the smallest B possible while still maintaining system performance. Part of this quantization sub-vi came from Dr. Morley. 16

18 Figure 18 Quantization Here our waveform is quantized into 16 levels since B is 4. As you can see there are some flat portions of the wave form which is representative of quantization, where the samples having amplitudes near that level all got rounded to that level (shown by the circles). Correlate Figure 2 Example magneprint The correlate block shown in Figure 20 finds the correlation between every pair of cards in the input 1D array of waveforms. Each waveform has attributes telling the card number, swipe number, swipe direction, and average speed. The accept distribution is populated with correlation coefficients from pairs of cards that share the same card number but different swipe numbers. The reject distribution is 17

19 populated with correlation coefficients from pairs of cards that have different card numbers. A distribution of average speeds is also populated, using the average speed attribute that was added to each waveform by the normalize block. Figure 20 Correlation block sub-vi Figure 21 shows the results after running the top level VI using a database of swipes provided by Dr. Morley. There were a total of 264 swipes in the database containing 75 different cards and around 3 reswipes for each card, with some additional swipes swiped backwards. The parameters used were: Filter=17, Delta=89, M(subsamples to take)=96. B(number of bits)=4. As you can see for the reject distribution the histogram is a near perfect Gaussian distribution centered around 0. The histogram is also fairly tight, meaning the standard deviation is small, with the range above and below -0.4 to 0.4. The accept distribution also looks excellent, with no correlations below 0.9. This means that the two distributions do not overlap, and so there are no false positive swipes (a card deemed authentic when it is not) and no false negatives (a card deemed inauthentic when it is). This further demonstrates the robustness and accuracy of our system. 18

20 Figure 21 Accept and reject distributions generated from Dr. Morley s card database Live Mode Figure 22 shows the top level VI for live mode operation. The user is able to swipe cards using the card reader and in real-time, the program is able to build the accept and reject histograms. Pressing the Authentic button will put the next swipe into the accept histogram and un-pressing it will put the swipe into the reject. The save button saves all the current swipes in memory into a directory marked by Save Directory. The DAQ assistant helps acquire the waveform with the sampling rate of 500kHz. The VI is broken up into 3 sections which and are run sequentially to avoid timing issues. It is not much different from the file mode VI. Figure 22 Block diagram of live mode VI Figure 23 shows our results. The parameters used are shown on the top. We used 11 different cards to build the reject histogram and 8 swipes of a Washington University ID to build the accept histogram. As you can see for the reject distribution, even though it does not look as symmetric as the previous 19

21 reject histogram taken from the database, it is still centered about 0 and is still fairly tight. It is because there are only 11 swipes that it does not look perfectly Gaussian. For the accept histogram, it looks just like the one taken using the database. Every swipe correlation looks to have a correlation coefficient of above 0.9, meaning a fairly perfect match. As explained before, the rate of false positives and false negatives is still minimal. Figure 23 Accept and reject distributions generated in live mode Optimize VI Separation is defined as: Where μ A = mean of the accept distribution σ A = standard deviation of the accept distribution 20

22 σ R = standard deviation of the reject distribution Separation S is used as a rating of performance for our system. The higher the separation, the smaller the rates of false positives and false negatives, because the accept and reject distributions have less overlap. That way we can pick a threshold that determines if a card is authentic or not that does not touch the tails of the accept and reject distributions. Figure 24 shows the optimizer VI, a VI that sweeps the parameter values and calculates separation for each parameter combination. The combination of parameters that give the largest S is chosen and displayed on the LabView front panel for M*B sizes of 384, 768, 1024, and Delta can take on any value that does not overflow the smallest Magneprint in the database, while Filter can take these values: 17, 22, 27, 32, 37. M and B can be any factor combinations of 384, 768, 1024, and 2048 for each M*B. Figure 24 Optimizer VI This VI is run using swipes from the database. The results containing parameters achieving highest separation is shown in Table 1 below. 21

23 Table 1 Best M, B, filter half-width, and spacing (delta) parameters This optimization program is very computationally intensive and it took around 2 hours to complete on a quad core PC. Cost Analysis Since this project is almost purely software, we will discuss the cost associated with running our code. To run our code efficiently in LabView, especially the optimization VI, at least a mid-tier quad core PC is required and that costs around $500. Making further improvements to our code will require programmer man-hours and that can cost at least $15/hr spent on our code. Bill of materials Where applicable, we have estimated the cost to program and test our project: Magtek card reader $75 LabView 2012 $2700 NI ELVIS II $3625 PC workstation $600 Hazards and Failure Analysis Our software implementation poses no threat to the public and the environment. Conclusions We were able to determine various parameters for the best separation for each M*B size as detailed in Figure 20, with the separation being at least 0.642, which is excellent in reducing the rate of false 22

24 positives and false negatives. The live swiping of cards confirmed our working system, which was able to identify authentic and fraudulent cards base on setting a correlation threshold of 0.8; our system is very robust and reliable and is an accurate way to distinguish authentic cards from copied cards. Future areas of exploration include hardware implementation of the system, optimizing cost vs. robustness for commercial use, and after that commercial testing. In addition, our implementation could use less computing time and memory by processing the cards on the fly. References Method and apparatus for authenticating a magnetic fingerprint signal using a filter capable of isolating a remanent noise related signal component, with R. E. Morley, R. S. DeLand, E. C. Limtao, E. J. Richter, and S. R. Wood U.S. Patent No. 7,478,751, January 20, 2009 "Magnetic stripe card verification system," with T. C. McGeary and R. S. DeLand, Jr. U.S. Patent No. 6,098,881, August 8,

Jitter Measurements in Serial Data Signals

Jitter Measurements in Serial Data Signals Jitter Measurements in Serial Data Signals Michael Schnecker, Product Manager LeCroy Corporation Introduction The increasing speed of serial data transmission systems places greater importance on measuring

More information

Data Acquisition Using NI-DAQmx

Data Acquisition Using NI-DAQmx Instructor s Portion Data Acquisition Using NI-DAQmx Wei Lin Department of Biomedical Engineering Stony Brook University Summary This experiment requires the student to use NI-DAQmx to acquire voltage

More information

PCM Encoding and Decoding:

PCM Encoding and Decoding: PCM Encoding and Decoding: Aim: Introduction to PCM encoding and decoding. Introduction: PCM Encoding: The input to the PCM ENCODER module is an analog message. This must be constrained to a defined bandwidth

More information

ESE498. Intruder Detection System

ESE498. Intruder Detection System 0 Washington University in St. Louis School of Engineering and Applied Science Electrical and Systems Engineering Department ESE498 Intruder Detection System By Allen Chiang, Jonathan Chu, Siwei Su Supervisor

More information

Department of Electrical and Computer Engineering Ben-Gurion University of the Negev. LAB 1 - Introduction to USRP

Department of Electrical and Computer Engineering Ben-Gurion University of the Negev. LAB 1 - Introduction to USRP Department of Electrical and Computer Engineering Ben-Gurion University of the Negev LAB 1 - Introduction to USRP - 1-1 Introduction In this lab you will use software reconfigurable RF hardware from National

More information

Lab 1: The Digital Oscilloscope

Lab 1: The Digital Oscilloscope PHYSICS 220 Physical Electronics Lab 1: The Digital Oscilloscope Object: To become familiar with the oscilloscope, a ubiquitous instrument for observing and measuring electronic signals. Apparatus: Tektronix

More information

A Design of a PID Self-Tuning Controller Using LabVIEW

A Design of a PID Self-Tuning Controller Using LabVIEW Journal of Software Engineering and Applications, 2011, 4, 161-171 doi:10.4236/jsea.2011.43018 Published Online March 2011 (http://www.scirp.org/journal/jsea) 161 A Design of a PID Self-Tuning Controller

More information

Signal to Noise Instrumental Excel Assignment

Signal to Noise Instrumental Excel Assignment Signal to Noise Instrumental Excel Assignment Instrumental methods, as all techniques involved in physical measurements, are limited by both the precision and accuracy. The precision and accuracy of a

More information

DIGITAL-TO-ANALOGUE AND ANALOGUE-TO-DIGITAL CONVERSION

DIGITAL-TO-ANALOGUE AND ANALOGUE-TO-DIGITAL CONVERSION DIGITAL-TO-ANALOGUE AND ANALOGUE-TO-DIGITAL CONVERSION Introduction The outputs from sensors and communications receivers are analogue signals that have continuously varying amplitudes. In many systems

More information

Lab 4 - Data Acquisition

Lab 4 - Data Acquisition Spring 11 Lab 4 - Data Acquisition Lab 4-1 Lab 4 - Data Acquisition Format This lab will be conducted during your regularly scheduled lab time in a group format. Each student is responsible for learning

More information

GETTING STARTED WITH LABVIEW POINT-BY-POINT VIS

GETTING STARTED WITH LABVIEW POINT-BY-POINT VIS USER GUIDE GETTING STARTED WITH LABVIEW POINT-BY-POINT VIS Contents Using the LabVIEW Point-By-Point VI Libraries... 2 Initializing Point-By-Point VIs... 3 Frequently Asked Questions... 5 What Are the

More information

LabVIEW Day 1 Basics. Vern Lindberg. 1 The Look of LabVIEW

LabVIEW Day 1 Basics. Vern Lindberg. 1 The Look of LabVIEW LabVIEW Day 1 Basics Vern Lindberg LabVIEW first shipped in 1986, with very basic objects in place. As it has grown (currently to Version 10.0) higher level objects such as Express VIs have entered, additional

More information

Lab 3: Introduction to Data Acquisition Cards

Lab 3: Introduction to Data Acquisition Cards Lab 3: Introduction to Data Acquisition Cards INTRODUCTION: In this lab, you will be building a VI to display the input measured on a channel. However, within your own VI you will use LabVIEW supplied

More information

Digital Transmission of Analog Data: PCM and Delta Modulation

Digital Transmission of Analog Data: PCM and Delta Modulation Digital Transmission of Analog Data: PCM and Delta Modulation Required reading: Garcia 3.3.2 and 3.3.3 CSE 323, Fall 200 Instructor: N. Vlajic Digital Transmission of Analog Data 2 Digitization process

More information

1) Write the following as an algebraic expression using x as the variable: Triple a number subtracted from the number

1) Write the following as an algebraic expression using x as the variable: Triple a number subtracted from the number 1) Write the following as an algebraic expression using x as the variable: Triple a number subtracted from the number A. 3(x - x) B. x 3 x C. 3x - x D. x - 3x 2) Write the following as an algebraic expression

More information

Optical Fibres. Introduction. Safety precautions. For your safety. For the safety of the apparatus

Optical Fibres. Introduction. Safety precautions. For your safety. For the safety of the apparatus Please do not remove this manual from from the lab. It is available at www.cm.ph.bham.ac.uk/y2lab Optics Introduction Optical fibres are widely used for transmitting data at high speeds. In this experiment,

More information

EXPERIMENT NUMBER 5 BASIC OSCILLOSCOPE OPERATIONS

EXPERIMENT NUMBER 5 BASIC OSCILLOSCOPE OPERATIONS 1 EXPERIMENT NUMBER 5 BASIC OSCILLOSCOPE OPERATIONS The oscilloscope is the most versatile and most important tool in this lab and is probably the best tool an electrical engineer uses. This outline guides

More information

Integrating the Internet into Your Measurement System. DataSocket Technical Overview

Integrating the Internet into Your Measurement System. DataSocket Technical Overview Integrating the Internet into Your Measurement System DataSocket Technical Overview Introduction The Internet continues to become more integrated into our daily lives. This is particularly true for scientists

More information

Clock Jitter Definitions and Measurement Methods

Clock Jitter Definitions and Measurement Methods January 2014 Clock Jitter Definitions and Measurement Methods 1 Introduction Jitter is the timing variations of a set of signal edges from their ideal values. Jitters in clock signals are typically caused

More information

AC Measurements Using the Oscilloscope and Multimeter by Mr. David Fritz

AC Measurements Using the Oscilloscope and Multimeter by Mr. David Fritz AC Measurements Using the Oscilloscope and Multimeter by Mr. David Fritz 1 Sine wave with a DC offset f = frequency in Hz A = DC offset voltage (average voltage) B = Sine amplitude Vpp = 2B Vmax = A +

More information

Impedance 50 (75 connectors via adapters)

Impedance 50 (75 connectors via adapters) VECTOR NETWORK ANALYZER PLANAR TR1300/1 DATA SHEET Frequency range: 300 khz to 1.3 GHz Measured parameters: S11, S21 Dynamic range of transmission measurement magnitude: 130 db Measurement time per point:

More information

LabVIEW Day 6: Saving Files and Making Sub vis

LabVIEW Day 6: Saving Files and Making Sub vis LabVIEW Day 6: Saving Files and Making Sub vis Vern Lindberg You have written various vis that do computations, make 1D and 2D arrays, and plot graphs. In practice we also want to save that data. We will

More information

EET 310 Programming Tools

EET 310 Programming Tools Introduction EET 310 Programming Tools LabVIEW Part 1 (LabVIEW Environment) LabVIEW (short for Laboratory Virtual Instrumentation Engineering Workbench) is a graphical programming environment from National

More information

Cell Phone Vibration Experiment

Cell Phone Vibration Experiment Objective Cell Phone Vibration Experiment Most cell phones are designed to vibrate. But at what frequency do they vibrate? With an accelerometer, data acquisition and signal analysis the vibration frequency

More information

MICROPROCESSOR AND MICROCOMPUTER BASICS

MICROPROCESSOR AND MICROCOMPUTER BASICS Introduction MICROPROCESSOR AND MICROCOMPUTER BASICS At present there are many types and sizes of computers available. These computers are designed and constructed based on digital and Integrated Circuit

More information

DDX 7000 & 8003. Digital Partial Discharge Detectors FEATURES APPLICATIONS

DDX 7000 & 8003. Digital Partial Discharge Detectors FEATURES APPLICATIONS DDX 7000 & 8003 Digital Partial Discharge Detectors The HAEFELY HIPOTRONICS DDX Digital Partial Discharge Detector offers the high accuracy and flexibility of digital technology, plus the real-time display

More information

Best Practises for LabVIEW FPGA Design Flow. uk.ni.com ireland.ni.com

Best Practises for LabVIEW FPGA Design Flow. uk.ni.com ireland.ni.com Best Practises for LabVIEW FPGA Design Flow 1 Agenda Overall Application Design Flow Host, Real-Time and FPGA LabVIEW FPGA Architecture Development FPGA Design Flow Common FPGA Architectures Testing and

More information

Understanding Dynamic Range in Acceleration Measurement Systems. February 2013 By: Bruce Lent

Understanding Dynamic Range in Acceleration Measurement Systems. February 2013 By: Bruce Lent in Acceleration Measurement Systems February 2013 By: Bruce Lent Topics to discuss Definition of dynamic range The effective range Making full use of the high level Using filters to improve dynamic range

More information

MICROPHONE SPECIFICATIONS EXPLAINED

MICROPHONE SPECIFICATIONS EXPLAINED Application Note AN-1112 MICROPHONE SPECIFICATIONS EXPLAINED INTRODUCTION A MEMS microphone IC is unique among InvenSense, Inc., products in that its input is an acoustic pressure wave. For this reason,

More information

Counters and Decoders

Counters and Decoders Physics 3330 Experiment #10 Fall 1999 Purpose Counters and Decoders In this experiment, you will design and construct a 4-bit ripple-through decade counter with a decimal read-out display. Such a counter

More information

Filter Comparison. Match #1: Analog vs. Digital Filters

Filter Comparison. Match #1: Analog vs. Digital Filters CHAPTER 21 Filter Comparison Decisions, decisions, decisions! With all these filters to choose from, how do you know which to use? This chapter is a head-to-head competition between filters; we'll select

More information

Section 3. Sensor to ADC Design Example

Section 3. Sensor to ADC Design Example Section 3 Sensor to ADC Design Example 3-1 This section describes the design of a sensor to ADC system. The sensor measures temperature, and the measurement is interfaced into an ADC selected by the systems

More information

Sampling and Interpolation. Yao Wang Polytechnic University, Brooklyn, NY11201

Sampling and Interpolation. Yao Wang Polytechnic University, Brooklyn, NY11201 Sampling and Interpolation Yao Wang Polytechnic University, Brooklyn, NY1121 http://eeweb.poly.edu/~yao Outline Basics of sampling and quantization A/D and D/A converters Sampling Nyquist sampling theorem

More information

Lecture 2. Binary and Hexadecimal Numbers

Lecture 2. Binary and Hexadecimal Numbers Lecture 2 Binary and Hexadecimal Numbers Purpose: Review binary and hexadecimal number representations Convert directly from one base to another base Review addition and subtraction in binary representations

More information

Lecture 14. Point Spread Function (PSF)

Lecture 14. Point Spread Function (PSF) Lecture 14 Point Spread Function (PSF), Modulation Transfer Function (MTF), Signal-to-noise Ratio (SNR), Contrast-to-noise Ratio (CNR), and Receiver Operating Curves (ROC) Point Spread Function (PSF) Recollect

More information

6.025J Medical Device Design Lecture 3: Analog-to-Digital Conversion Prof. Joel L. Dawson

6.025J Medical Device Design Lecture 3: Analog-to-Digital Conversion Prof. Joel L. Dawson Let s go back briefly to lecture 1, and look at where ADC s and DAC s fit into our overall picture. I m going in a little extra detail now since this is our eighth lecture on electronics and we are more

More information

Lab 5 Getting started with analog-digital conversion

Lab 5 Getting started with analog-digital conversion Lab 5 Getting started with analog-digital conversion Achievements in this experiment Practical knowledge of coding of an analog signal into a train of digital codewords in binary format using pulse code

More information

Selecting RJ Bandwidth in EZJIT Plus Software

Selecting RJ Bandwidth in EZJIT Plus Software Selecting RJ Bandwidth in EZJIT Plus Software Application Note 1577 Introduction Separating jitter into its random and deterministic components (called RJ/DJ separation ) is a relatively new technique

More information

SAS Analyst for Windows Tutorial

SAS Analyst for Windows Tutorial Updated: August 2012 Table of Contents Section 1: Introduction... 3 1.1 About this Document... 3 1.2 Introduction to Version 8 of SAS... 3 Section 2: An Overview of SAS V.8 for Windows... 3 2.1 Navigating

More information

The front end of the receiver performs the frequency translation, channel selection and amplification of the signal.

The front end of the receiver performs the frequency translation, channel selection and amplification of the signal. Many receivers must be capable of handling a very wide range of signal powers at the input while still producing the correct output. This must be done in the presence of noise and interference which occasionally

More information

DDX 7000 & 8003. Digital Partial Discharge Detectors FEATURES APPLICATIONS

DDX 7000 & 8003. Digital Partial Discharge Detectors FEATURES APPLICATIONS DDX 7000 & 8003 Digital Partial Discharge Detectors The HAEFELY HIPOTRONICS DDX Digital Partial Discharge Detector offers the high accuracy and flexibility of digital technology, plus the real-time display

More information

Electronic Communications Committee (ECC) within the European Conference of Postal and Telecommunications Administrations (CEPT)

Electronic Communications Committee (ECC) within the European Conference of Postal and Telecommunications Administrations (CEPT) Page 1 Electronic Communications Committee (ECC) within the European Conference of Postal and Telecommunications Administrations (CEPT) ECC RECOMMENDATION (06)01 Bandwidth measurements using FFT techniques

More information

Digital Systems Based on Principles and Applications of Electrical Engineering/Rizzoni (McGraw Hill

Digital Systems Based on Principles and Applications of Electrical Engineering/Rizzoni (McGraw Hill Digital Systems Based on Principles and Applications of Electrical Engineering/Rizzoni (McGraw Hill Objectives: Analyze the operation of sequential logic circuits. Understand the operation of digital counters.

More information

The Development of a Pressure-based Typing Biometrics User Authentication System

The Development of a Pressure-based Typing Biometrics User Authentication System The Development of a Pressure-based Typing Biometrics User Authentication System Chen Change Loy Adv. Informatics Research Group MIMOS Berhad by Assoc. Prof. Dr. Chee Peng Lim Associate Professor Sch.

More information

Analog Representations of Sound

Analog Representations of Sound Analog Representations of Sound Magnified phonograph grooves, viewed from above: The shape of the grooves encodes the continuously varying audio signal. Analog to Digital Recording Chain ADC Microphone

More information

Measuring Temperature withthermistors a Tutorial David Potter

Measuring Temperature withthermistors a Tutorial David Potter NATIONAL INSTRUMENTS The Software is the Instrument Application Note 065 Measuring Temperature withthermistors a Tutorial David Potter Introduction Thermistors are thermally sensitive resistors used in

More information

Electrical Resonance

Electrical Resonance Electrical Resonance (R-L-C series circuit) APPARATUS 1. R-L-C Circuit board 2. Signal generator 3. Oscilloscope Tektronix TDS1002 with two sets of leads (see Introduction to the Oscilloscope ) INTRODUCTION

More information

MP3 Player CSEE 4840 SPRING 2010 PROJECT DESIGN. zl2211@columbia.edu. ml3088@columbia.edu

MP3 Player CSEE 4840 SPRING 2010 PROJECT DESIGN. zl2211@columbia.edu. ml3088@columbia.edu MP3 Player CSEE 4840 SPRING 2010 PROJECT DESIGN Zheng Lai Zhao Liu Meng Li Quan Yuan zl2215@columbia.edu zl2211@columbia.edu ml3088@columbia.edu qy2123@columbia.edu I. Overview Architecture The purpose

More information

Digital Imaging and Multimedia. Filters. Ahmed Elgammal Dept. of Computer Science Rutgers University

Digital Imaging and Multimedia. Filters. Ahmed Elgammal Dept. of Computer Science Rutgers University Digital Imaging and Multimedia Filters Ahmed Elgammal Dept. of Computer Science Rutgers University Outlines What are Filters Linear Filters Convolution operation Properties of Linear Filters Application

More information

Normality Testing in Excel

Normality Testing in Excel Normality Testing in Excel By Mark Harmon Copyright 2011 Mark Harmon No part of this publication may be reproduced or distributed without the express permission of the author. mark@excelmasterseries.com

More information

Clock Recovery in Serial-Data Systems Ransom Stephens, Ph.D.

Clock Recovery in Serial-Data Systems Ransom Stephens, Ph.D. Clock Recovery in Serial-Data Systems Ransom Stephens, Ph.D. Abstract: The definition of a bit period, or unit interval, is much more complicated than it looks. If it were just the reciprocal of the data

More information

Abstract. Cycle Domain Simulator for Phase-Locked Loops

Abstract. Cycle Domain Simulator for Phase-Locked Loops Abstract Cycle Domain Simulator for Phase-Locked Loops Norman James December 1999 As computers become faster and more complex, clock synthesis becomes critical. Due to the relatively slower bus clocks

More information

Exercise 10: Basic LabVIEW Programming

Exercise 10: Basic LabVIEW Programming Exercise 10: Basic LabVIEW Programming In this exercise we will learn the basic principles in LabVIEW. LabVIEW will be used in later exercises and in the project part, as well in other courses later, so

More information

User s Guide DDS-3X25 USB ARBITRARY FUNCTION GENERATOR

User s Guide DDS-3X25 USB ARBITRARY FUNCTION GENERATOR User s Guide DDS-3X25 USB ARBITRARY FUNCTION GENERATOR Content General safety summary...1 Introduction...2 Chapter 1 Getting started...3 System Requirements...4 Installing Hardware...5 Installing Software...8

More information

FREQUENCY RESPONSE ANALYZERS

FREQUENCY RESPONSE ANALYZERS FREQUENCY RESPONSE ANALYZERS Dynamic Response Analyzers Servo analyzers When you need to stabilize feedback loops to measure hardware characteristics to measure system response BAFCO, INC. 717 Mearns Road

More information

Introduction to Digital Audio

Introduction to Digital Audio Introduction to Digital Audio Before the development of high-speed, low-cost digital computers and analog-to-digital conversion circuits, all recording and manipulation of sound was done using analog techniques.

More information

Siemens and National Instruments Deliver Integrated Automation and Measurement Solutions

Siemens and National Instruments Deliver Integrated Automation and Measurement Solutions Siemens and National Instruments Deliver Integrated Automation and Measurement Solutions The Need for Integrated Automation and Measurement Manufacturing lines consist of numerous decoupled systems for

More information

Software Defined Radio

Software Defined Radio Software Defined Radio GNU Radio and the USRP Overview What is Software Defined Radio? Advantages of Software Defined Radio Traditional versus SDR Receivers SDR and the USRP Using GNU Radio Introduction

More information

ELECTRON SPIN RESONANCE Last Revised: July 2007

ELECTRON SPIN RESONANCE Last Revised: July 2007 QUESTION TO BE INVESTIGATED ELECTRON SPIN RESONANCE Last Revised: July 2007 How can we measure the Landé g factor for the free electron in DPPH as predicted by quantum mechanics? INTRODUCTION Electron

More information

Statistics, Probability and Noise

Statistics, Probability and Noise CHAPTER Statistics, Probability and Noise Statistics and probability are used in Digital Signal Processing to characterize signals and the processes that generate them. For example, a primary use of DSP

More information

(Refer Slide Time: 2:10)

(Refer Slide Time: 2:10) Data Communications Prof. A. Pal Department of Computer Science & Engineering Indian Institute of Technology, Kharagpur Lecture-12 Multiplexer Applications-1 Hello and welcome to today s lecture on multiplexer

More information

Shear :: Blocks (Video and Image Processing Blockset )

Shear :: Blocks (Video and Image Processing Blockset ) 1 of 6 15/12/2009 11:15 Shear Shift rows or columns of image by linearly varying offset Library Geometric Transformations Description The Shear block shifts the rows or columns of an image by a gradually

More information

How To Counter Noise Noise From A Low Voltage Differential Signaling Circuit

How To Counter Noise Noise From A Low Voltage Differential Signaling Circuit TDK EMC Technology Practice Section EMC Countermeasures of Low Voltage Differential Signaling Circuits TDK Corporation Magnetics Business Group Toshio Tomonari 1 Introduction Low Voltage Differential Signaling

More information

Hands On ECG. Sean Hubber and Crystal Lu

Hands On ECG. Sean Hubber and Crystal Lu Hands On ECG Sean Hubber and Crystal Lu The device. The black box contains the circuit and microcontroller, the mini tv is set on top, the bars on the sides are for holding it and reading hand voltage,

More information

GnuRadio CONTACT INFORMATION: phone: +1.301.527.1629 fax: +1.301.527.1690 email: whitepaper@hsc.com web: www.hsc.com

GnuRadio CONTACT INFORMATION: phone: +1.301.527.1629 fax: +1.301.527.1690 email: whitepaper@hsc.com web: www.hsc.com GnuRadio CONTACT INFORMATION: phone: +1.301.527.1629 fax: +1.301.527.1690 email: whitepaper@hsc.com web: www.hsc.com PROPRIETARY NOTICE All rights reserved. This publication and its contents are proprietary

More information

INTRODUCTION. The principles of which are to:

INTRODUCTION. The principles of which are to: Taking the Pain Out of Chromatographic Peak Integration Shaun Quinn, 1 Peter Sauter, 1 Andreas Brunner, 1 Shawn Anderson, 2 Fraser McLeod 1 1 Dionex Corporation, Germering, Germany; 2 Dionex Corporation,

More information

Manual for the sound card oscilloscope V1.24 C. Zeitnitz english translation by P. van Gemmeren and K. Grady

Manual for the sound card oscilloscope V1.24 C. Zeitnitz english translation by P. van Gemmeren and K. Grady Manual for the sound card oscilloscope V1.24 C. Zeitnitz english translation by P. van Gemmeren and K. Grady C. Zeitnitz 04/2008 This Software and all previous versions are NO Freeware! The use of the

More information

Switch Mode Power Supply Topologies

Switch Mode Power Supply Topologies Switch Mode Power Supply Topologies The Buck Converter 2008 Microchip Technology Incorporated. All Rights Reserved. WebSeminar Title Slide 1 Welcome to this Web seminar on Switch Mode Power Supply Topologies.

More information

The Scientific Data Mining Process

The Scientific Data Mining Process Chapter 4 The Scientific Data Mining Process When I use a word, Humpty Dumpty said, in rather a scornful tone, it means just what I choose it to mean neither more nor less. Lewis Carroll [87, p. 214] In

More information

SignalPad Data Logging and Analysis Software

SignalPad Data Logging and Analysis Software SignalPad Data Logging and Analysis Software Overview SignalPad is a data logging and analysis application developed with National Instruments LabVIEW. The configuration-based user interface provides ready-to-run

More information

Simple SDR Receiver. Looking for some hardware to learn about SDR? This project may be just what you need to explore this hot topic!

Simple SDR Receiver. Looking for some hardware to learn about SDR? This project may be just what you need to explore this hot topic! Michael Hightower, KF6SJ 13620 White Rock Station Rd, Poway, CA 92064; kf6sj@arrl.net Simple SDR Receiver Looking for some hardware to learn about SDR? This project may be just what you need to explore

More information

Signal Processing in So.ware and Electric Field Sensing

Signal Processing in So.ware and Electric Field Sensing Signal Processing in So.ware and Electric Field Sensing CSE 466: So.ware for Embedded Systems Winter 2009 B. Mayton University of Washington CSE & Intel Research SeaMle CSE

More information

Homework 11. Part 1. Name: Score: / null

Homework 11. Part 1. Name: Score: / null Name: Score: / Homework 11 Part 1 null 1 For which of the following correlations would the data points be clustered most closely around a straight line? A. r = 0.50 B. r = -0.80 C. r = 0.10 D. There is

More information

Harmonics and Noise in Photovoltaic (PV) Inverter and the Mitigation Strategies

Harmonics and Noise in Photovoltaic (PV) Inverter and the Mitigation Strategies Soonwook Hong, Ph. D. Michael Zuercher Martinson Harmonics and Noise in Photovoltaic (PV) Inverter and the Mitigation Strategies 1. Introduction PV inverters use semiconductor devices to transform the

More information

Chapter 4. LLC Resonant Converter

Chapter 4. LLC Resonant Converter Chapter 4 LLC Resonant Converter 4.1 Introduction In previous chapters, the trends and technical challenges for front end DC/DC converter were discussed. High power density, high efficiency and high power

More information

Digital Audio. Fig. 1 Binary numbers

Digital Audio. Fig. 1 Binary numbers Digital Audio Prior to the advent of computers, sound recordings were made using exclusively analog systems, where the instantaneous signal amplitude was continuously conveyed by a voltage we could measure

More information

User guide for the Error & Warning LabVIEW toolset

User guide for the Error & Warning LabVIEW toolset User guide for the Error & Warning LabVIEW toolset Rev. 2014 December 2 nd 2014 1 INTRODUCTION... 1 2 THE LABVIEW ERROR CLUSTER... 2 2.1 The error description... 3 2.2 Custom error descriptions... 4 3

More information

Sampling Theorem Notes. Recall: That a time sampled signal is like taking a snap shot or picture of signal periodically.

Sampling Theorem Notes. Recall: That a time sampled signal is like taking a snap shot or picture of signal periodically. Sampling Theorem We will show that a band limited signal can be reconstructed exactly from its discrete time samples. Recall: That a time sampled signal is like taking a snap shot or picture of signal

More information

Command-induced Tracking Jitter Study I D. Clark November 24, 2009

Command-induced Tracking Jitter Study I D. Clark November 24, 2009 Command-induced Tracking Jitter Study I D. Clark November 24, 2009 Introduction Reports of excessive tracking jitter on the MMT elevation axis have lately been theorized to be caused by the input command

More information

Petrel TIPS&TRICKS from SCM

Petrel TIPS&TRICKS from SCM Petrel TIPS&TRICKS from SCM Knowledge Worth Sharing Histograms and SGS Modeling Histograms are used daily for interpretation, quality control, and modeling in Petrel. This TIPS&TRICKS document briefly

More information

The Phase Modulator In NBFM Voice Communication Systems

The Phase Modulator In NBFM Voice Communication Systems The Phase Modulator In NBFM Voice Communication Systems Virgil Leenerts 8 March 5 The phase modulator has been a point of discussion as to why it is used and not a frequency modulator in what are called

More information

DAC Digital To Analog Converter

DAC Digital To Analog Converter DAC Digital To Analog Converter DAC Digital To Analog Converter Highlights XMC4000 provides two digital to analog converters. Each can output one analog value. Additional multiple analog waves can be generated

More information

HYBRID FIR-IIR FILTERS By John F. Ehlers

HYBRID FIR-IIR FILTERS By John F. Ehlers HYBRID FIR-IIR FILTERS By John F. Ehlers Many traders have come to me, asking me to make their indicators act just one day sooner. They are convinced that this is just the edge they need to make a zillion

More information

Transmitter Interface Program

Transmitter Interface Program Transmitter Interface Program Operational Manual Version 3.0.4 1 Overview The transmitter interface software allows you to adjust configuration settings of your Max solid state transmitters. The following

More information

Lab 11 Digital Dice. Figure 11.0. Digital Dice Circuit on NI ELVIS II Workstation

Lab 11 Digital Dice. Figure 11.0. Digital Dice Circuit on NI ELVIS II Workstation Lab 11 Digital Dice Figure 11.0. Digital Dice Circuit on NI ELVIS II Workstation From the beginning of time, dice have been used for games of chance. Cubic dice similar to modern dice date back to before

More information

AVR127: Understanding ADC Parameters. Introduction. Features. Atmel 8-bit and 32-bit Microcontrollers APPLICATION NOTE

AVR127: Understanding ADC Parameters. Introduction. Features. Atmel 8-bit and 32-bit Microcontrollers APPLICATION NOTE Atmel 8-bit and 32-bit Microcontrollers AVR127: Understanding ADC Parameters APPLICATION NOTE Introduction This application note explains the basic concepts of analog-to-digital converter (ADC) and the

More information

QUICK START GUIDE FOR DEMONSTRATION CIRCUIT 956 24-BIT DIFFERENTIAL ADC WITH I2C LTC2485 DESCRIPTION

QUICK START GUIDE FOR DEMONSTRATION CIRCUIT 956 24-BIT DIFFERENTIAL ADC WITH I2C LTC2485 DESCRIPTION LTC2485 DESCRIPTION Demonstration circuit 956 features the LTC2485, a 24-Bit high performance Σ analog-to-digital converter (ADC). The LTC2485 features 2ppm linearity, 0.5µV offset, and 600nV RMS noise.

More information

10EaZy SW White Paper Choosing the right hardware

10EaZy SW White Paper Choosing the right hardware 10EaZy SW White Paper Choosing the right hardware Selecting proper hardware for the 10EaZy SW This white paper describes important elements to consider before purchasing hardware intended for sound level

More information

EECS 556 Image Processing W 09. Interpolation. Interpolation techniques B splines

EECS 556 Image Processing W 09. Interpolation. Interpolation techniques B splines EECS 556 Image Processing W 09 Interpolation Interpolation techniques B splines What is image processing? Image processing is the application of 2D signal processing methods to images Image representation

More information

DATA LOGGING SYSTEM FOR PRESSURE MONITORING

DATA LOGGING SYSTEM FOR PRESSURE MONITORING DATA LOGGING SYSTEM FOR PRESSURE MONITORING Georgi Todorov Nikolov, Boyanka Marinova Nikolova, Marin Berov Marinov Department of Electronics, Technical University of Sofia, Studenstki Grad, TU-Sofia, block

More information

A Guide to Calibrating Your Spectrum Analyzer

A Guide to Calibrating Your Spectrum Analyzer A Guide to Calibrating Your Application Note Introduction As a technician or engineer who works with electronics, you rely on your spectrum analyzer to verify that the devices you design, manufacture,

More information

Positive Feedback and Oscillators

Positive Feedback and Oscillators Physics 3330 Experiment #6 Fall 1999 Positive Feedback and Oscillators Purpose In this experiment we will study how spontaneous oscillations may be caused by positive feedback. You will construct an active

More information

Data Storage 3.1. Foundations of Computer Science Cengage Learning

Data Storage 3.1. Foundations of Computer Science Cengage Learning 3 Data Storage 3.1 Foundations of Computer Science Cengage Learning Objectives After studying this chapter, the student should be able to: List five different data types used in a computer. Describe how

More information

Agilent AN 1316 Optimizing Spectrum Analyzer Amplitude Accuracy

Agilent AN 1316 Optimizing Spectrum Analyzer Amplitude Accuracy Agilent AN 1316 Optimizing Spectrum Analyzer Amplitude Accuracy Application Note RF & Microwave Spectrum Analyzers Table of Contents 3 3 4 4 5 7 8 8 13 13 14 16 16 Introduction Absolute versus relative

More information

ECEN 1400, Introduction to Analog and Digital Electronics

ECEN 1400, Introduction to Analog and Digital Electronics ECEN 1400, Introduction to Analog and Digital Electronics Lab 4: Power supply 1 INTRODUCTION This lab will span two lab periods. In this lab, you will create the power supply that transforms the AC wall

More information

Making OSNR Measurements In a Modulated DWDM Signal Environment

Making OSNR Measurements In a Modulated DWDM Signal Environment Making OSNR Measurements In a Modulated DWDM Signal Environment Jack Dupre Jim Stimple Making OSNR measurements in a modulated DWDM signal environment May 2001 In a DWDM spectrum, it is desirable to measure

More information

Time-Correlated Multi-domain RF Analysis with the MSO70000 Series Oscilloscope and SignalVu Software

Time-Correlated Multi-domain RF Analysis with the MSO70000 Series Oscilloscope and SignalVu Software Time-Correlated Multi-domain RF Analysis with the MSO70000 Series Oscilloscope and SignalVu Software Technical Brief Introduction The MSO70000 Series Mixed Oscilloscope, when coupled with SignalVu Spectrum

More information

Power Supplies. 1.0 Power Supply Basics. www.learnabout-electronics.org. Module

Power Supplies. 1.0 Power Supply Basics. www.learnabout-electronics.org. Module Module 1 www.learnabout-electronics.org Power Supplies 1.0 Power Supply Basics What you ll learn in Module 1 Section 1.0 Power Supply Basics. Basic functions of a power supply. Safety aspects of working

More information

Data Analysis on the ABI PRISM 7700 Sequence Detection System: Setting Baselines and Thresholds. Overview. Data Analysis Tutorial

Data Analysis on the ABI PRISM 7700 Sequence Detection System: Setting Baselines and Thresholds. Overview. Data Analysis Tutorial Data Analysis on the ABI PRISM 7700 Sequence Detection System: Setting Baselines and Thresholds Overview In order for accuracy and precision to be optimal, the assay must be properly evaluated and a few

More information

SR2000 FREQUENCY MONITOR

SR2000 FREQUENCY MONITOR SR2000 FREQUENCY MONITOR THE FFT SEARCH FUNCTION IN DETAILS FFT Search is a signal search using FFT (Fast Fourier Transform) technology. The FFT search function first appeared with the SR2000 Frequency

More information