# Time series analysis Matlab tutorial. Joachim Gross

Size: px
Start display at page:

## Transcription

1 Time series analysis Matlab tutorial Joachim Gross

2 Outline Terminology Sampling theorem Plotting Baseline correction Detrending Smoothing Filtering Decimation

3 Remarks Focus on practical aspects, exercises, getting experience (not on equations, theory) Focus on How to do Learn some basic skills for TS analysis Note: Usually there is not a single perfectly correct way of doing a TS operation! => learn the limitations!

4 What is a time series? A sequence of measurements over time

5 Terminology Continuous TS: continuous observations Discrete TS: observations at specific times usually equally spaced Deterministic TS: future values can be exactly predicted from past values Stochastic TS: exact prediction not possible

6 Objectives of TS analysis Description Explanation Prediction Control

7 Simple descriptive analysis Summary statistics (mean, std) is not always meaningful for TS

8 Sampling Converting a continuous signal into a discrete time series Reconstruction is possible if sampling frequency is greater than twice the signal bandwidth Time (s) Hz sampling

9 Sampling Nyquist frequency: half of sampling frequency Hz sampling Hz reconstruction

10 Sampling Aliasing: Frequencies above Nyquist frequency are reconstructed below Nyquist frequency Hz sampling

11 Sampling Aliasing: Frequencies above Nyquist frequency are reconstructed below Nyquist frequency Power Spectrum Magnitude (db) Frequency 4 Hz sampling Power Spectrum Magnitude (db) Frequency 8 Hz sampling

12 Simple operations on TS Plotting Removing a baseline Removing a trend Smoothing Filtering Decimation

13 Plotting in Matlab For visual inspection of TS For publications/talks plot sptool

14 Data preprocessing I Removing offset ts=ts-mean(ts);

15 Data preprocessing I Removing a baseline basel=find(t<=); ts=ts-mean(ts(basel));

16 Data preprocessing II Removing a trend ts=detrend(ts); subtracts best fitting line detrend can be used to subtract mean: detrend(ts, constant ) data linear data

17 Data preprocessing III Smoothing ts=filter(ones(,3)/3,,ts); %mean filter, moving average uses zeros at beginning! => baseline correction or do not use first 3 samples

18 Data preprocessing III introduces a shift! => either correct for it or ts=filtfilt(ones(,5)/5,,ts); %mean filter, forward and reverse no shift! filter can take any smoothing kernel (gaussian, etc) 7 shifted by 5 samples 4 filtfilt

19 Data preprocessing III Smoothing ts=medfilt(ts,3); %median filter, takes into account the shift uses at beginning and end!

20 Data preprocessing III Smoothing ts=sgolayfilt(ts,3,4); %Savitzky-Golay filter fits 3 rd order polynomial to frames of size 4 good at preserving high frequencies in the data

21 Data preprocessing III Smoothing compare unsmoothed and smoothed data check for shift check beginning (and end) of the smoothed time series

22 Exercise

23 Data preprocessing IV Filtering FIR-Filter (finite impulse response) stable high filter order usually have linear phase (phase change is proportional to frequency) IIR-Filter (infinite impulse response) potentially unstable low filter order non-linear phase distortion computationally efficient

24 Data preprocessing IV IIR-Filter: Butterworth Elliptic Chebychev Typ Chebychev Typ 2 Bessel FIR-Filter: fir

25 Data preprocessing IV lowpass highpass bandpass bandstop Magnitude (db) Magnitude Response (db) db is logarithmic unit db = factor of 3dB = factor of 2 db= factor of Frequency (Hz) 5 Hz lowpass

26 Data preprocessing IV lowpass highpass bandpass bandstop Magnitude (db) Magnitude Response (db) -7-8 db is logarithmic unit db = factor of 3dB = factor of 2 db= factor of Frequency (Hz) 3 Hz highpass

27 Data preprocessing IV lowpass highpass bandpass bandstop Magnitude (db) Magnitude Response (db) db is logarithmic unit db = factor of 3dB = factor of 2 db= factor of Frequency (Hz) 2-3 Hz bandpass

28 Data preprocessing IV lowpass highpass bandpass bandstop Magnitude (db) -5 - Magnitude Response (db) -5-2 db is logarithmic unit db = factor of 3dB = factor of 2 db= factor of Frequency (Hz) 3-4 Hz bandstop

29 Simple design: FIR [b]=fir(4,2*4/sf); %4 Hz lowpass [b]=fir(4,2*4/sf, high ); %4 Hz highpass [b]=fir(4,2*[4 ]/sf); %4- Hz bandpass [b]=fir(4,2*[4 ]/sf, stop ); %4- Hz bandstop tsf=filter(b,,ts); tsf=filtfilt(b,,ts); %forward and reverse

30 Simple design: IIR [b,a]=butter(4,2*4/sf); %4 Hz lowpass [b,a]=butter(4,2*4/sf, high ); %4 Hz highpass [b,a]=butter(4,2*[4 ]/sf); %4- Hz bandpass [b,a]=butter(4,2*[4 ]/sf, stop ); %4- Hz bandstop tsf=filter(b,a,ts); tsf=filtfilt(b,a,ts); %forward and reverse

31 Simple Inspection freqz(b,a,,); sf number of frequencies Magnitude (db) - -2 Phase (degrees) Frequency (Hz) Frequency (Hz)

32 Complex design fdatool magnitude response phase response impulse response compare filters effect of changing filter order

33 Filter artifacts onset transients filter 2 x Hz lowpass (4th order Butterworth) x filtfilt

34 Filter artifacts ringing 2 x -3 with artifact 2 x -3 without artifact

35 Filter artifacts ringing filter, 2 Hz lowpass (2 th order Butterworth) filtfilt 2 x x

36 Filter artifacts beginning and end of filtered ts is distorted filtering artifacts is dangerous filtering may change the latency of effects! filtering may change the phase

37 Suggestions be careful with low frequencies use low order butterworth forward and reverse (to avoid phase distortions) carefully check beginning and end of filtered ts make sure you don t have artifacts in the data use surrogate data (filtered noise)

38 Data preprocessing V Decimation ts=decimate(ts,4); decimate uses a lowpass filter to avoid aliasing artifacts

39 Exercises 2-4

### Digital filter design for electrophysiological data a practical approach

NOTICE: this is the author s version of a work that was accepted for publication in the Journal of Neuroscience Methods following peer review. Changes resulting from the publishing process, such as editing,

### Em bedded DSP : I ntroduction to Digital Filters

Embedded DSP : Introduction to Digital Filters 1 Em bedded DSP : I ntroduction to Digital Filters Digital filters are a important part of DSP. In fact their extraordinary performance is one of the keys

### Analog Filters. A common instrumentation filter application is the attenuation of high frequencies to avoid frequency aliasing in the sampled data.

Analog Filters Filters can be used to attenuate unwanted signals such as interference or noise or to isolate desired signals from unwanted. They use the frequency response of a measuring system to alter

### SGN-1158 Introduction to Signal Processing Test. Solutions

SGN-1158 Introduction to Signal Processing Test. Solutions 1. Convolve the function ( ) with itself and show that the Fourier transform of the result is the square of the Fourier transform of ( ). (Hints:

### SECTION 6 DIGITAL FILTERS

SECTION 6 DIGITAL FILTERS Finite Impulse Response (FIR) Filters Infinite Impulse Response (IIR) Filters Multirate Filters Adaptive Filters 6.a 6.b SECTION 6 DIGITAL FILTERS Walt Kester INTRODUCTION Digital

### Digital Signal Processing IIR Filter Design via Impulse Invariance

Digital Signal Processing IIR Filter Design via Impulse Invariance D. Richard Brown III D. Richard Brown III 1 / 11 Basic Procedure We assume here that we ve already decided to use an IIR filter. The basic

### 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

### chapter Introduction to Digital Signal Processing and Digital Filtering 1.1 Introduction 1.2 Historical Perspective

Introduction to Digital Signal Processing and Digital Filtering chapter 1 Introduction to Digital Signal Processing and Digital Filtering 1.1 Introduction Digital signal processing (DSP) refers to anything

### CHAPTER 6 Frequency Response, Bode Plots, and Resonance

ELECTRICAL CHAPTER 6 Frequency Response, Bode Plots, and Resonance 1. State the fundamental concepts of Fourier analysis. 2. Determine the output of a filter for a given input consisting of sinusoidal

### ELEN E4810: Digital Signal Processing Topic 8: Filter Design: IIR

ELEN E48: Digital Signal Processing Topic 8: Filter Design: IIR. Filter Design Specifications 2. Analog Filter Design 3. Digital Filters from Analog Prototypes . Filter Design Specifications The filter

### PRACTICAL GUIDE TO DATA SMOOTHING AND FILTERING

PRACTICAL GUIDE TO DATA SMOOTHING AND FILTERING Ton van den Bogert October 3, 996 Summary: This guide presents an overview of filtering methods and the software which is available in the HPL.. What is

### Analog and Digital Filters Anthony Garvert November 13, 2015

Analog and Digital Filters Anthony Garvert November 13, 2015 Abstract In circuit analysis and performance, a signal transmits some form of information, such as a voltage or current. However, over a range

### Lecture 1-6: Noise and Filters

Lecture 1-6: Noise and Filters Overview 1. Periodic and Aperiodic Signals Review: by periodic signals, we mean signals that have a waveform shape that repeats. The time taken for the waveform to repeat

### Transition Bandwidth Analysis of Infinite Impulse Response Filters

Transition Bandwidth Analysis of Infinite Impulse Response Filters Sujata Prabhakar Department of Electronics and Communication UCOE Punjabi University, Patiala Dr. Amandeep Singh Sappal Associate Professor

### Frequency Response of Filters

School of Engineering Department of Electrical and Computer Engineering 332:224 Principles of Electrical Engineering II Laboratory Experiment 2 Frequency Response of Filters 1 Introduction Objectives To

### 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

### Introduction to Digital Filters

CHAPTER 14 Introduction to Digital Filters Digital filters are used for two general purposes: (1) separation of signals that have been combined, and (2) restoration of signals that have been distorted

### Implementation of the LMS Algorithm for Noise Cancellation on Speech Using the ARM LPC2378 Processor.

School of Mathematics and Systems Engineering Reports from MSI - Rapporter från MSI Implementation of the LMS Algorithm for Noise Cancellation on Speech Using the ARM LPC2378 Processor. Cesar Augusto Azurdia

### Introduction to IQ-demodulation of RF-data

Introduction to IQ-demodulation of RF-data by Johan Kirkhorn, IFBT, NTNU September 15, 1999 Table of Contents 1 INTRODUCTION...3 1.1 Abstract...3 1.2 Definitions/Abbreviations/Nomenclature...3 1.3 Referenced

### CHAPTER 8 ANALOG FILTERS

ANALOG FILTERS CHAPTER 8 ANALOG FILTERS SECTION 8.: INTRODUCTION 8. SECTION 8.2: THE TRANSFER FUNCTION 8.5 THE SPLANE 8.5 F O and Q 8.7 HIGHPASS FILTER 8.8 BANDPASS FILTER 8.9 BANDREJECT (NOTCH) FILTER

### SUMMARY. Additional Digital/Software filters are included in Chart and filter the data after it has been sampled and recorded by the PowerLab.

This technique note was compiled by ADInstruments Pty Ltd. It includes figures and tables from S.S. Young (2001): Computerized data acquisition and analysis for the life sciences. For further information

### Probability and Random Variables. Generation of random variables (r.v.)

Probability and Random Variables Method for generating random variables with a specified probability distribution function. Gaussian And Markov Processes Characterization of Stationary Random Process Linearly

### NAPIER University School of Engineering. Electronic Systems Module : SE32102 Analogue Filters Design And Simulation. 4 th order Butterworth response

NAPIER University School of Engineering Electronic Systems Module : SE32102 Analogue Filters Design And Simulation. 4 th order Butterworth response In R1 R2 C2 C1 + Opamp A - R1 R2 C2 C1 + Opamp B - Out

### Design of Efficient Digital Interpolation Filters for Integer Upsampling. Daniel B. Turek

Design of Efficient Digital Interpolation Filters for Integer Upsampling by Daniel B. Turek Submitted to the Department of Electrical Engineering and Computer Science in partial fulfillment of the requirements

### How To Understand The Nyquist Sampling Theorem

Nyquist Sampling Theorem By: Arnold Evia Table of Contents What is the Nyquist Sampling Theorem? Bandwidth Sampling Impulse Response Train Fourier Transform of Impulse Response Train Sampling in the Fourier

### Introduction to time series analysis

Introduction to time series analysis Margherita Gerolimetto November 3, 2010 1 What is a time series? A time series is a collection of observations ordered following a parameter that for us is time. Examples

### Frequency response. Chapter 1. 1.1 Introduction

Chapter Frequency response. Introduction The frequency response of a system is a frequency dependent function which expresses how a sinusoidal signal of a given frequency on the system input is transferred

### Short-time FFT, Multi-taper analysis & Filtering in SPM12

Short-time FFT, Multi-taper analysis & Filtering in SPM12 Computational Psychiatry Seminar, FS 2015 Daniel Renz, Translational Neuromodeling Unit, ETHZ & UZH 20.03.2015 Overview Refresher Short-time Fourier

ECSE 4440 Control System Engineering Fall 2001 Project 3 Controller Design in Frequency Domain TA 1. Abstract 2. Introduction 3. Controller design in Frequency domain 4. Experiment 5. Colclusion 1. Abstract

### FAST Fourier Transform (FFT) and Digital Filtering Using LabVIEW

FAST Fourier Transform (FFT) and Digital Filtering Using LabVIEW Wei Lin Department of Biomedical Engineering Stony Brook University Instructor s Portion Summary This experiment requires the student to

### Experimental validation of loudspeaker equalization inside car cockpits

Experimental validation of loudspeaker equalization inside car cockpits G. Cibelli, A. Bellini, E. Ugolotti, A. Farina, C. Morandi ASK Industries S.p.A. Via F.lli Cervi, 79, I-421 Reggio Emilia - ITALY

### Lecture 9. Poles, Zeros & Filters (Lathi 4.10) Effects of Poles & Zeros on Frequency Response (1) Effects of Poles & Zeros on Frequency Response (3)

Effects of Poles & Zeros on Frequency Response (1) Consider a general system transfer function: zeros at z1, z2,..., zn Lecture 9 Poles, Zeros & Filters (Lathi 4.10) The value of the transfer function

### Predictive Indicators for Effective Trading Strategies By John Ehlers

Predictive Indicators for Effective Trading Strategies By John Ehlers INTRODUCTION Technical traders understand that indicators need to smooth market data to be useful, and that smoothing introduces lag

### Aliasing, Image Sampling and Reconstruction

Aliasing, Image Sampling and Reconstruction Recall: a pixel is a point It is NOT a box, disc or teeny wee light It has no dimension It occupies no area It can have a coordinate More than a point, it is

### Spike-Based Sensing and Processing: What are spikes good for? John G. Harris Electrical and Computer Engineering Dept

Spike-Based Sensing and Processing: What are spikes good for? John G. Harris Electrical and Computer Engineering Dept ONR NEURO-SILICON WORKSHOP, AUG 1-2, 2006 Take Home Messages Introduce integrate-and-fire

### 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

### MODULATION Systems (part 1)

Technologies and Services on Digital Broadcasting (8) MODULATION Systems (part ) "Technologies and Services of Digital Broadcasting" (in Japanese, ISBN4-339-62-2) is published by CORONA publishing co.,

### ANALYZER BASICS WHAT IS AN FFT SPECTRUM ANALYZER? 2-1

WHAT IS AN FFT SPECTRUM ANALYZER? ANALYZER BASICS The SR760 FFT Spectrum Analyzer takes a time varying input signal, like you would see on an oscilloscope trace, and computes its frequency spectrum. Fourier's

### Laboratory #5: RF Filter Design

EEE 194 RF Laboratory Exercise 5 1 Laboratory #5: RF Filter Design I. OBJECTIVES A. Design a third order low-pass Chebyshev filter with a cutoff frequency of 330 MHz and 3 db ripple with equal terminations

### PYKC Jan-7-10. Lecture 1 Slide 1

Aims and Objectives E 2.5 Signals & Linear Systems Peter Cheung Department of Electrical & Electronic Engineering Imperial College London! By the end of the course, you would have understood: Basic signal

### Frequency Response of FIR Filters

Frequency Response of FIR Filters Chapter 6 This chapter continues the study of FIR filters from Chapter 5, but the emphasis is frequency response, which relates to how the filter responds to an input

DSP First Laboratory Exercise #9 Sampling and Zooming of Images In this lab we study the application of FIR ltering to the image zooming problem, where lowpass lters are used to do the interpolation needed

### Analog signals are those which are naturally occurring. Any analog signal can be converted to a digital signal.

3.3 Analog to Digital Conversion (ADC) Analog signals are those which are naturally occurring. Any analog signal can be converted to a digital signal. 1 3.3 Analog to Digital Conversion (ADC) WCB/McGraw-Hill

### 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

### 2.161 Signal Processing: Continuous and Discrete Fall 2008

MT OpenCourseWare http://ocw.mit.edu.6 Signal Processing: Continuous and Discrete Fall 00 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms. MASSACHUSETTS

### Agilent Creating Multi-tone Signals With the N7509A Waveform Generation Toolbox. Application Note

Agilent Creating Multi-tone Signals With the N7509A Waveform Generation Toolbox Application Note Introduction Of all the signal engines in the N7509A, the most complex is the multi-tone engine. This application

### AN-837 APPLICATION NOTE

APPLICATION NOTE One Technology Way P.O. Box 916 Norwood, MA 262-916, U.S.A. Tel: 781.329.47 Fax: 781.461.3113 www.analog.com DDS-Based Clock Jitter Performance vs. DAC Reconstruction Filter Performance

### Lectures 6&7: Image Enhancement

Lectures 6&7: Image Enhancement Leena Ikonen Pattern Recognition (MVPR) Lappeenranta University of Technology (LUT) leena.ikonen@lut.fi http://www.it.lut.fi/ip/research/mvpr/ 1 Content Background Spatial

### Understanding CIC Compensation Filters

Understanding CIC Compensation Filters April 2007, ver. 1.0 Application Note 455 Introduction f The cascaded integrator-comb (CIC) filter is a class of hardware-efficient linear phase finite impulse response

### Implementation of Digital Signal Processing: Some Background on GFSK Modulation

Implementation of Digital Signal Processing: Some Background on GFSK Modulation Sabih H. Gerez University of Twente, Department of Electrical Engineering s.h.gerez@utwente.nl Version 4 (February 7, 2013)

### TDA2040. 20W Hi-Fi AUDIO POWER AMPLIFIER

20W Hi-Fi AUDIO POWER AMPLIFIER DESCRIPTION The TDA2040 is a monolithic integrated circuit in Pentawatt package, intended for use as an audio class AB amplifier. Typically it provides 22W output power

### LAB 12: ACTIVE FILTERS

A. INTRODUCTION LAB 12: ACTIVE FILTERS After last week s encounter with op- amps we will use them to build active filters. B. ABOUT FILTERS An electric filter is a frequency-selecting circuit designed

### T = 1 f. Phase. Measure of relative position in time within a single period of a signal For a periodic signal f(t), phase is fractional part t p

Data Transmission Concepts and terminology Transmission terminology Transmission from transmitter to receiver goes over some transmission medium using electromagnetic waves Guided media. Waves are guided

### Voice---is analog in character and moves in the form of waves. 3-important wave-characteristics:

Voice Transmission --Basic Concepts-- Voice---is analog in character and moves in the form of waves. 3-important wave-characteristics: Amplitude Frequency Phase Voice Digitization in the POTS Traditional

### Duobinary Modulation For Optical Systems

Introduction Duobinary Modulation For Optical Systems Hari Shanar Inphi Corporation Optical systems by and large use NRZ modulation. While NRZ modulation is suitable for long haul systems in which the

### 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

### CHAPTER 3: DIGITAL IMAGING IN DIAGNOSTIC RADIOLOGY. 3.1 Basic Concepts of Digital Imaging

Physics of Medical X-Ray Imaging (1) Chapter 3 CHAPTER 3: DIGITAL IMAGING IN DIAGNOSTIC RADIOLOGY 3.1 Basic Concepts of Digital Imaging Unlike conventional radiography that generates images on film through

### Digital Signal Processing Complete Bandpass Filter Design Example

Digital Signal Processing Complete Bandpass Filter Design Example D. Richard Brown III D. Richard Brown III 1 / 10 General Filter Design Procedure discrete-time filter specifications prewarp DT frequency

### (Refer Slide Time: 01:11-01:27)

Digital Signal Processing Prof. S. C. Dutta Roy Department of Electrical Engineering Indian Institute of Technology, Delhi Lecture - 6 Digital systems (contd.); inverse systems, stability, FIR and IIR,

### Linear Filtering Part II

Linear Filtering Part II Selim Aksoy Department of Computer Engineering Bilkent University saksoy@cs.bilkent.edu.tr Fourier theory Jean Baptiste Joseph Fourier had a crazy idea: Any periodic function can

### Sampling: What Nyquist Didn t Say, and What to Do About It

Sampling: What Nyquist Didn t Say, and What to Do About It Tim Wescott, Wescott Design Services The Nyquist-Shannon sampling theorem is useful, but often misused when engineers establish sampling rates

### Clutter Filter Design for Ultrasound Color Flow Imaging

Clutter Filter Design for Ultrasound Color Flow Imaging by Steinar Bjærum (Corresponding author) Department of Physiology and Biomedical Engineering Norwegian University of Science and Technology Trondheim,

### 1995 Mixed-Signal Products SLAA013

Application Report 995 Mixed-Signal Products SLAA03 IMPORTANT NOTICE Texas Instruments and its subsidiaries (TI) reserve the right to make changes to their products or to discontinue any product or service

### NONLINEAR TIME SERIES ANALYSIS

NONLINEAR TIME SERIES ANALYSIS HOLGER KANTZ AND THOMAS SCHREIBER Max Planck Institute for the Physics of Complex Sy stems, Dresden I CAMBRIDGE UNIVERSITY PRESS Preface to the first edition pug e xi Preface

### Time Series Analysis: Introduction to Signal Processing Concepts. Liam Kilmartin Discipline of Electrical & Electronic Engineering, NUI, Galway

Time Series Analysis: Introduction to Signal Processing Concepts Liam Kilmartin Discipline of Electrical & Electronic Engineering, NUI, Galway Aims of Course To introduce some of the basic concepts of

### Time-series filtering techniques in Stata

Time-series filtering techniques in Stata Christopher F Baum Department of Economics, Boston College July 2006 Christopher F Baum Time-series filtering techniques in Stata 1 Introduction There are several

### LM833,LMF100,MF10. Application Note 779 A Basic Introduction to Filters - Active, Passive,and. Switched Capacitor. Literature Number: SNOA224A

LM833,LMF100,MF10 Application Note 779 A Basic Introduction to Filters - Active, Passive,and Switched Capacitor Literature Number: SNOA224A A Basic Introduction to Filters Active, Passive, and Switched-Capacitor

### COURSE DESCRIPTOR Signal Processing II Signalbehandling II 7.5 ECTS credit points (7,5 högskolepoäng)

Blekinge Institute of Technology School of Engineering, ASB Andhra University College of Engineering (A) TWO YEAR DOUBLE DEGREE MASTERS PROGRAM MS (SIGNAL PROCESSING) FIRST YEAR I SEMESTER CODE Name of

### Bandwidth-dependent transformation of noise data from frequency into time domain and vice versa

Topic Bandwidth-dependent transformation of noise data from frequency into time domain and vice versa Authors Peter Bormann (formerly GeoForschungsZentrum Potsdam, Telegrafenberg, D-14473 Potsdam, Germany),

### 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:

### UNIVERSITY OF CALIFORNIA, SAN DIEGO Electrical & Computer Engineering Department ECE 101 - Fall 2010 Linear Systems Fundamentals

UNIVERSITY OF CALIFORNIA, SAN DIEGO Electrical & Computer Engineering Department ECE 101 - Fall 2010 Linear Systems Fundamentals FINAL EXAM WITH SOLUTIONS (YOURS!) You are allowed one 2-sided sheet of

### MATRIX TECHNICAL NOTES

200 WOOD AVENUE, MIDDLESEX, NJ 08846 PHONE (732) 469-9510 FAX (732) 469-0418 MATRIX TECHNICAL NOTES MTN-107 TEST SETUP FOR THE MEASUREMENT OF X-MOD, CTB, AND CSO USING A MEAN SQUARE CIRCUIT AS A DETECTOR

### Digital image processing

746A27 Remote Sensing and GIS Lecture 4 Digital image processing Chandan Roy Guest Lecturer Department of Computer and Information Science Linköping University Digital Image Processing Most of the common

### Analog Signal Conditioning

Analog Signal Conditioning Analog and Digital Electronics Electronics Digital Electronics Analog Electronics 2 Analog Electronics Analog Electronics Operational Amplifiers Transistors TRIAC 741 LF351 TL084

### Convolution. 1D Formula: 2D Formula: Example on the web: http://www.jhu.edu/~signals/convolve/

Basic Filters (7) Convolution/correlation/Linear filtering Gaussian filters Smoothing and noise reduction First derivatives of Gaussian Second derivative of Gaussian: Laplacian Oriented Gaussian filters

### Advanced Signal Processing and Digital Noise Reduction

Advanced Signal Processing and Digital Noise Reduction Saeed V. Vaseghi Queen's University of Belfast UK WILEY HTEUBNER A Partnership between John Wiley & Sons and B. G. Teubner Publishers Chichester New

### 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

### 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

### Selected Filter Circuits Dr. Lynn Fuller

ROCHESTER INSTITUTE OF TECHNOLOGY MICROELECTRONIC ENGINEERING Selected Filter Circuits Dr. Lynn Fuller Webpage: http://people.rit.edu/lffeee 82 Lomb Memorial Drive Rochester, NY 146235604 Tel (585) 4752035

### Matlab GUI for WFB spectral analysis

Matlab GUI for WFB spectral analysis Jan Nováček Department of Radio Engineering K13137, CTU FEE Prague Abstract In the case of the sound signals analysis we usually use logarithmic scale on the frequency

### isim ACTIVE FILTER DESIGNER NEW, VERY CAPABLE, MULTI-STAGE ACTIVE FILTER DESIGN TOOL

isim ACTIVE FILTER DESIGNER NEW, VERY CAPABLE, MULTI-STAGE ACTIVE FILTER DESIGN TOOL Michael Steffes Sr. Applications Manager 12/15/2010 SIMPLY SMARTER Introduction to the New Active Filter Designer Scope

### A Basic Introduction to Filters Active Passive and Switched-Capacitor

A Basic Introduction to Filters Active Passive and Switched-Capacitor 1 0 INTRODUCTION Filters of some sort are essential to the operation of most electronic circuits It is therefore in the interest of

### Analysis/resynthesis with the short time Fourier transform

Analysis/resynthesis with the short time Fourier transform summer 2006 lecture on analysis, modeling and transformation of audio signals Axel Röbel Institute of communication science TU-Berlin IRCAM Analysis/Synthesis

### Bildverarbeitung und Mustererkennung Image Processing and Pattern Recognition

Bildverarbeitung und Mustererkennung Image Processing and Pattern Recognition 1. Image Pre-Processing - Pixel Brightness Transformation - Geometric Transformation - Image Denoising 1 1. Image Pre-Processing

### 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

### Evaluating Oscilloscope Sample Rates vs. Sampling Fidelity

Evaluating Oscilloscope Sample Rates vs. Sampling Fidelity Application Note How to Make the Most Accurate Digital Measurements Introduction Digital storage oscilloscopes (DSO) are the primary tools used

### Simulation of Frequency Response Masking Approach for FIR Filter design

Simulation of Frequency Response Masking Approach for FIR Filter design USMAN ALI, SHAHID A. KHAN Department of Electrical Engineering COMSATS Institute of Information Technology, Abbottabad (Pakistan)

### ELECTRONIC FILTER DESIGN HANDBOOK

ELECTRONIC FILTER DESIGN HANDBOOK Arthur B.Williams Fred J.Taylor Fourth Edition McGFUW-HILL New York Chicago San Francisco Lisbon London Madrid Mexico City Milan New Delhi San Juan Seoul Singapore Sydney

### RF Network Analyzer Basics

RF Network Analyzer Basics A tutorial, information and overview about the basics of the RF Network Analyzer. What is a Network Analyzer and how to use them, to include the Scalar Network Analyzer (SNA),

### RADIO FREQUENCY INTERFERENCE AND CAPACITY REDUCTION IN DSL

RADIO FREQUENCY INTERFERENCE AND CAPACITY REDUCTION IN DSL Padmabala Venugopal, Michael J. Carter*, Scott A. Valcourt, InterOperability Laboratory, Technology Drive Suite, University of New Hampshire,

### Software for strong-motion data display and processing

Project S6 Data base of the Italian strong-motion data relative to the period 1972-2004 Coordinators: Lucia Luzi (INGV-MI) and Fabio Sabetta (DPC-USSN) TASK 2 - Deliverable 4 Software for strong-motion

### Automatic Evaluation Software for Contact Centre Agents voice Handling Performance

International Journal of Scientific and Research Publications, Volume 5, Issue 1, January 2015 1 Automatic Evaluation Software for Contact Centre Agents voice Handling Performance K.K.A. Nipuni N. Perera,

### Admin stuff. 4 Image Pyramids. Spatial Domain. Projects. Fourier domain 2/26/2008. Fourier as a change of basis

Admin stuff 4 Image Pyramids Change of office hours on Wed 4 th April Mon 3 st March 9.3.3pm (right after class) Change of time/date t of last class Currently Mon 5 th May What about Thursday 8 th May?

### DESIGN AND SIMULATION OF TWO CHANNEL QMF FILTER BANK FOR ALMOST PERFECT RECONSTRUCTION

DESIGN AND SIMULATION OF TWO CHANNEL QMF FILTER BANK FOR ALMOST PERFECT RECONSTRUCTION Meena Kohli 1, Rajesh Mehra 2 1 M.E student, ECE Deptt., NITTTR, Chandigarh, India 2 Associate Professor, ECE Deptt.,

### 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

### 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

### Agilent AN 1315 Optimizing RF and Microwave Spectrum Analyzer Dynamic Range. Application Note

Agilent AN 1315 Optimizing RF and Microwave Spectrum Analyzer Dynamic Range Application Note Table of Contents 3 3 3 4 4 4 5 6 7 7 7 7 9 10 10 11 11 12 12 13 13 14 15 1. Introduction What is dynamic range?

### INFERRING TRADING STRATEGIES FROM PROBABILITY DISTRIBUTION FUNCTIONS

INFERRING TRADING STRATEGIES FROM PROBABILITY DISTRIBUTION FUNCTIONS INFERRING TRADING STRATEGIES FROM PROBABILITY DISTRIBUTION FUNCTIONS BACKGROUND The primary purpose of technical analysis is to observe