Basics on Digital Signal Processing


 Ursula French
 1 years ago
 Views:
Transcription
1 Basics on Digital Signal Processing Introduction Vassilis Anastassopoulos Electronics Laboratory, Physics Department, University of Patras
2 Outline of the Course 1. Introduction (sampling quantization) 2. Signals and Systems 3. ZTransform 4. The Discreet and the Fast Fourier Transform 5. Linear Filter Design 6. Noise 7. Median Filters 2/36
3 Voltage [V] Voltage [V] Analog & digital signals Analog Continuous function V of continuous variable t (time, space etc) : V(t). Sampled Signal Digital Discrete function V k of discrete sampling variable t k, with k = integer: V k = V(t k ) time [ms] Uniform (periodic) sampling. Sampling frequency f S = 1/ t S t s t s sampling time, t k [ms] 3/36
4 Analog & digital systems 4/36
5 Digital vs analog processing Digital Signal Processing (DSPing) Advantages More flexible. Often easier system upgrade. Data easily stored memory. Better control over accuracy requirements. Reproducibility. Linear phase No drift with time and temperature Limitations A/D & signal processors speed: wideband signals still difficult to treat (realtime systems). Finite wordlength effect. 5/36
6 DSPing: aim & tools Applications Predicting a system s output. Implementing a certain processing task. Studying a certain signal. Hardware General purpose processors (GPP), controllers. Digital Signal Processors (DSP). Programmable logic ( PLD, FPGA ). Fast Faster realtime DSPing Software Programming languages: Pascal, C / C++... High level languages: Matlab, Mathcad, Mathematica Dedicated tools (ex: filter design s/w packages). 6/36
7 Related areas 7/36
8 Applications 8/36
9 Important digital signals δ(nt s ) δ[(n3)τ s ] nτ s past Unit Impulse or Unit Sample. The most important signal for two reasons δ(n)=1 for n=0 u(nt s) nτ s past Unit Step u(n)=1 for n0 δ(n)=u(n)u(n1) r(nt s) nτ s past Unit Ramp r(n)=nu(n) 9/36
10 Digital system example General scheme Sometimes steps missing  Filter + A/D (ex: economics);  D/A + filter (ex: digital output wanted). V V A A V ms ms k k Filter Antialiasing Antialiasing A/D A/D Digital Processing Digital Processing D/A ANALOG DOMAIN DIGITAL DOMAIN Topics of this lecture. V ms ms Filter Reconstruction ANALOG DOMAIN 10/36
11 Digital system implementation ANALOG INPUT KEY DECISION POINTS: Analysis bandwidth, Dynamic range Antialiasing Filter A/D Pass / stop bands. Sampling rate. No. of bits. Parameters. 1 2 Digital Processing DIGITAL OUTPUT Digital format. What to use for processing? 3 11/36
12 AD/DA Conversion General Scheme 12/36
13 AD Conversion  Details 13/36
14 Sampling 14/36
15 1 Sampling How fast must we sample a continuous signal to preserve its info content? Ex: train wheels in a movie. 25 frames (=samples) per second. Train starts wheels go clockwise. Train accelerates wheels go counterclockwise. Why? Frequency misidentification due to low sampling frequency. 15/36
16 Rotating Disk How fast do we have to instantly stare at the disk if it rotates with frequency 0.5 Hz? 16/36
17 1 The sampling theorem Theo* A signal s(t) with maximum frequency f MAX can be recovered if sampled at frequency f S > 2 f MAX. * Multiple proposers: Whittaker(s), Nyquist, Shannon, Kotel nikov. Naming gets confusing! Nyquist frequency (rate) f N = 2 f MAX or f MAX or f S,MIN or f S,MIN /2 Example s(t) 3cos(50π t) 10sin(300π t) cos(100π t) Condition on f S? F 1 F 2 F 3 F 1 =25 Hz, F 2 = 150 Hz, F 3 = 50 Hz f S > 300 Hz f MAX 17/36
18 Sampling and Spectrum 18/36
19 1 Sampling lowpass signals (a) Continuous spectrum (a) Bandlimited signal: frequencies in [B, B] (f MAX = B). (b) B 0 B f Discrete spectrum No aliasing (b) Time sampling frequency repetition. f S > 2 B no aliasing. B 0 B f S /2 f (c) Discrete spectrum Aliasing & corruption (c) f S 2 B aliasing! 0 f S /2 f Aliasing: signal ambiguity in frequency domain 19/36
20 1 Antialiasing filter (a) Out of band noise Signal of interest Out of band noise (a),(b) Outofband noise can aliase into band of interest. Filter it before! (b) (c) B 0 B f B 0 B f S /2 f (c) Antialiasing filter Passband: depends on bandwidth of interest. Attenuation A MIN : depends on ADC resolution ( number of bits N). A MIN, db ~ 6.02 N Outofband noise magnitude. Other parameters: ripple, stopband frequency... 20/36
21 1 Undersampling Using spectral replications to reduce sampling frequency f S req ments. Bandpass signal centered on f C B m 2fC B 2fC B fs m 1 m, selected so that f S > 2B 0 f C f Example f C = 20 MHz, B = 5MHz Without undersampling f S > 40 MHz. With undersampling f S = 22.5 MHz (m=1); = 17.5 MHz (m=2); = MHz (m=3). f S 0 f S 2f S f Advantages Slower ADCs / electronics needed. Simpler antialiasing filters. f C 21/36
22 Quantization and Coding N Quantization Levels q Quantization Noise 22/36
23 2 SNR of ideal ADC RMS input SNR ideal 20 log10 (1) RMS(eq) Also called SQNR (signaltoquantisationnoise ratio) Assumptions Ideal ADC: only quantisation error e q (p(e) constant, no stuck bits ) e q uncorrelated with signal. ADC performance constant in time. RMS 1 T T V FSR 2 0 input sin ωt 2 dt V FSR 2 2 Input(t) = ½ V FSR sin( t). p(e) quantisation error probability density RMS(eq) q/2 2 eq peq deq q/2 q 12 VFSR 2 N 12 1 q (sampling frequency f S = 2 f MAX ) q 2 q 2 e q Error value 23/36
24 2 SNR of ideal ADC  2 Substituting in (1) : SNR ideal 6.02N1.76 [db] (2) One additional bit SNR increased by 6 db Real SNR lower because:  Real signals have noise.  Forcing input to full scale unwise.  Real ADCs have additional noise (aperture jitter, nonlinearities etc). Actually (2) needs correction factor depending on ratio between sampling freq & Nyquist freq. Processing gain due to oversampling. 24/36
25 Coding  Conventional 25/36
26 Coding Flash AD 26/36
27 DAC process 27/36
28 Oversampling Noise shaping PSD Nyquist Sampler f b f N (a) Oversampling OSR=4 f The oversampling process takes apart the images of the signal band. (b) f s =4f N f 0 PSD Signal f N /2 Quantization noise in Nyquist converters Quantization noise in Oversampling converters f s /2 When the sampling rate increases (4 times) the quantization noise spreads over a larger region. The quantization noise power in the signal band is 4 times smaller. PSD Signal Quantization noise Nyquist converters Quantization noise Oversampling converters Quantization noise Oversampling and noise shaping converters Spectrum at the output of a noise shaping quantizer loop compared to those obtained from Nyquist and Oversampling converters. 0 F N /2 frequency F s /2 28/36
29 Digital Systems A discreettime system is a device or algorithm that operates on an input sequence according to some computational procedure It may be A general purpose computer A microprocessor dedicated hardware A combination of all these 29/36
30 Linear, Time Invariant Systems System Properties linear Time Invariant Stable Causal y( n) N k0 a k x( n k) Convolution 30/36
31 Linear Systems  Convolution 5+71=11 terms 31/36
32 Linear Systems  Convolution 5+71=11 terms 32/36
33 General Linear Structure y( n) M k0 a k x( n k) L k1 b k y( n k) 33/36
34 Simple Examples 34/36
35 Linearity Superposition Frequency Preservation Principle of Superposition x 1 (n) H y 1 (n) ax 1 (n)+bx 2 (n) H ay 1 (n)+by 2 (n) x 2 (n) H y 2 n) Principle of Superposition Frequency Preservation x 1 (n) x 2 1 (n) x 2 x 1 (n)+x 2 (n) x 2 x 1 2 (n)+x 2 2 (n)+2 x 1 (n) x 2 (n) Nonlinear x 2 (n) x 2 x 2 2 (n) If y(n)=x 2 (n) then for x(n)=sin(nω) y(n)=sin 2 (nω)= cos(2nω) 35/36
36 The END Have a nice Weekend Back on Tuesday 36/36
Signaling is the way data is communicated. This type of signal used can be either analog or digital
3.1 Analog vs. Digital Signaling is the way data is communicated. This type of signal used can be either analog or digital 1 3.1 Analog vs. Digital 2 WCB/McGrawHill The McGrawHill Companies, Inc., 1998
More informationCONVERTERS. Filters Introduction to Digitization DigitaltoAnalog Converters AnalogtoDigital Converters
CONVERTERS Filters Introduction to Digitization DigitaltoAnalog Converters AnalogtoDigital Converters Filters Filters are used to remove unwanted bandwidths from a signal Filter classification according
More informationDepartment of Electrical and Computer Engineering BenGurion University of the Negev. LAB 1  Introduction to USRP
Department of Electrical and Computer Engineering BenGurion University of the Negev LAB 1  Introduction to USRP  11 Introduction In this lab you will use software reconfigurable RF hardware from National
More informationAnalog to Digital, A/D, Digital to Analog, D/A Converters. An electronic circuit to convert the analog voltage to a digital computer value
Analog to Digital, A/D, Digital to Analog, D/A Converters An electronic circuit to convert the analog voltage to a digital computer value Best understood by understanding Digital to Analog first. A fundamental
More information1995 MixedSignal Products SLAA013
Application Report 995 MixedSignal 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
More informationSGN1158 Introduction to Signal Processing Test. Solutions
SGN1158 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:
More informationWhat the Nyquist Criterion Means to Your Sampled Data System Design. by Walt Kester
TUTORAL What the Nyquist Criterion Means to Your Sampled Data System Design NTRODUCTON by Walt Kester A quick reading of Harry Nyquist's classic Bell System Technical Journal article of 194 (Reference
More informationNyquist Sampling Theorem. By: Arnold Evia
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
More informationNonData Aided Carrier Offset Compensation for SDR Implementation
NonData Aided Carrier Offset Compensation for SDR Implementation Anders Riis Jensen 1, Niels Terp Kjeldgaard Jørgensen 1 Kim Laugesen 1, Yannick Le Moullec 1,2 1 Department of Electronic Systems, 2 Center
More informationA Brief Introduction to Sigma Delta Conversion
A Brief Introduction to Sigma Delta Conversion Application Note May 995 AN954 Author: David Jarman Introduction The sigma delta conversion techniue has been in existence for many years, but recent technological
More informationSampling 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 informationchapter 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
More informationVoiceis analog in character and moves in the form of waves. 3important wavecharacteristics:
Voice Transmission Basic Concepts Voiceis analog in character and moves in the form of waves. 3important wavecharacteristics: Amplitude Frequency Phase Voice Digitization in the POTS Traditional
More informationAnalog and Digital Interfacing
Analog and Digital Interfacing BJ Furman Spring, 1999 DAC & ADC DigitaltoAnalog Conversion (DAC) Converts a binary word from computer to a scaled analog voltage Used for controlling systems that require
More informationSampling 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 informationFAST 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
More informationSpikeBased Sensing and Processing: What are spikes good for? John G. Harris Electrical and Computer Engineering Dept
SpikeBased Sensing and Processing: What are spikes good for? John G. Harris Electrical and Computer Engineering Dept ONR NEUROSILICON WORKSHOP, AUG 12, 2006 Take Home Messages Introduce integrateandfire
More informationANALYZER BASICS WHAT IS AN FFT SPECTRUM ANALYZER? 21
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
More informationMotorola Digital Signal Processors
Motorola Digital Signal Processors Principles of SigmaDelta Modulation for Analogto Digital Converters by Sangil Park, Ph. D. Strategic Applications Digital Signal Processor Operation MOTOROLA APR8
More informationApplication Note 9. Digital FIR Decimator & Analog Lowpass
Application Note 9 App Note Application Note 9 Highlights Multirate FIR Design Cascade Analog Lowpass Circuit Optimization Comb Filter Correction Sin(x)/x Correction n Design Objective 16:1 FIR Decimation
More informationIntroduction to Digital Audio
Introduction to Digital Audio Before the development of highspeed, lowcost digital computers and analogtodigital conversion circuits, all recording and manipulation of sound was done using analog techniques.
More informationCHAPTER 3: DIGITAL IMAGING IN DIAGNOSTIC RADIOLOGY. 3.1 Basic Concepts of Digital Imaging
Physics of Medical XRay 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
More informationThe Effective Number of Bits (ENOB) of my R&S Digital Oscilloscope Technical Paper
The Effective Number of Bits (ENOB) of my R&S Digital Oscilloscope Technical Paper Products: R&S RTO1012 R&S RTO1014 R&S RTO1022 R&S RTO1024 This technical paper provides an introduction to the signal
More informationb 1 is the most significant bit (MSB) The MSB is the bit that has the most (largest) influence on the analog output
CMOS Analog IC Design  Chapter 10 Page 10.05 BLOCK DIAGRAM OF A DIGITALANALOG CONVERTER b 1 is the most significant bit (MSB) The MSB is the bit that has the most (largest) influence on the analog output
More informationFilter 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 headtohead competition between filters; we'll select
More informationTime series analysis Matlab tutorial. Joachim Gross
Time series analysis Matlab tutorial Joachim Gross Outline Terminology Sampling theorem Plotting Baseline correction Detrending Smoothing Filtering Decimation Remarks Focus on practical aspects, exercises,
More informationAnalog 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 informationFourier Transform and Image Filtering. CS/BIOEN 6640 Lecture Marcel Prastawa Fall 2010
Fourier Transform and Image Filtering CS/BIOEN 6640 Lecture Marcel Prastawa Fall 2010 The Fourier Transform Fourier Transform Forward, mapping to frequency domain: Backward, inverse mapping to time domain:
More informationENEE 425 Spring 2010 Assigned Homework Oppenheim and Shafer (3rd ed.) Instructor: S.A. Tretter
ENEE 425 Spring 2010 Assigned Homework Oppenheim and Shafer (3rd ed.) Instructor: S.A. Tretter Note: The dates shown are when the problems were assigned. Homework will be discussed in class at the beginning
More informationSECTION 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
More informationDigitaltoAnalog Conversion
ANALOG.PPT(01/10/2009) 4.1 Lecture 10 DigitaltoAnalog Conversion Objectives Understand how a weightedresister DAC can be used to convert numbers with binary or nonbinary bit weightings Understand the
More informationThe counterpart to a DAC is the ADC, which is generally a more complicated circuit. One of the most popular ADC circuit is the successive
The counterpart to a DAC is the ADC, which is generally a more complicated circuit. One of the most popular ADC circuit is the successive approximation converter. 1 2 The idea of sampling is fully covered
More informationT = 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
More information6.025J Medical Device Design Lecture 3: AnalogtoDigital 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 informationTaking the Mystery out of the Infamous Formula, "SNR = 6.02N + 1.76dB," and Why You Should Care. by Walt Kester
ITRODUCTIO Taking the Mystery out of the Infamous Formula, "SR = 6.0 + 1.76dB," and Why You Should Care by Walt Kester MT001 TUTORIAL You don't have to deal with ADCs or DACs for long before running across
More informationAnalog 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
More informationThe Calculation of G rms
The Calculation of G rms QualMark Corp. Neill Doertenbach The metric of G rms is typically used to specify and compare the energy in repetitive shock vibration systems. However, the method of arriving
More information4.3 AnalogtoDigital Conversion
4.3 AnalogtoDigital Conversion overview including timing considerations block diagram of a device using a DAC and comparator example of a digitized spectrum number of data points required to describe
More informationPropagation Channel Emulator ECP_V3
Navigation simulators Propagation Channel Emulator ECP_V3 1 Product Description The ECP (Propagation Channel Emulator V3) synthesizes the principal phenomena of propagation occurring on RF signal links
More informationIMPLEMENTATION OF FIR FILTER USING EFFICIENT WINDOW FUNCTION AND ITS APPLICATION IN FILTERING A SPEECH SIGNAL
IMPLEMENTATION OF FIR FILTER USING EFFICIENT WINDOW FUNCTION AND ITS APPLICATION IN FILTERING A SPEECH SIGNAL Saurabh Singh Rajput, Dr.S.S. Bhadauria Department of Electronics, Madhav Institute of Technology
More informationMoving Average Filters
CHAPTER 15 Moving Average Filters The moving average is the most common filter in DSP, mainly because it is the easiest digital filter to understand and use. In spite of its simplicity, the moving average
More informationAnalysis/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 TUBerlin IRCAM Analysis/Synthesis
More informationFUNDAMENTALS OF MODERN SPECTRAL ANALYSIS. Matthew T. Hunter, Ph.D.
FUNDAMENTALS OF MODERN SPECTRAL ANALYSIS Matthew T. Hunter, Ph.D. AGENDA Introduction Spectrum Analyzer Architecture Dynamic Range Instantaneous Bandwidth The Importance of Image Rejection and AntiAliasing
More informationUSB 3.0 CDR Model White Paper Revision 0.5
USB 3.0 CDR Model White Paper Revision 0.5 January 15, 2009 INTELLECTUAL PROPERTY DISCLAIMER THIS WHITE PAPER IS PROVIDED TO YOU AS IS WITH NO WARRANTIES WHATSOEVER, INCLUDING ANY WARRANTY OF MERCHANTABILITY,
More informationAgilent Creating Multitone Signals With the N7509A Waveform Generation Toolbox. Application Note
Agilent Creating Multitone Signals With the N7509A Waveform Generation Toolbox Application Note Introduction Of all the signal engines in the N7509A, the most complex is the multitone engine. This application
More informationDIGITALTOANALOGUE AND ANALOGUETODIGITAL CONVERSION
DIGITALTOANALOGUE AND ANALOGUETODIGITAL CONVERSION Introduction The outputs from sensors and communications receivers are analogue signals that have continuously varying amplitudes. In many systems
More informationFrequency Shift Dither for Analogue to Digital Converters
Frequency Shift Dither for Analogue to Digital Converters Authors: Cornelis Jan Kikkert Associate Professor Head of Electrical and Computer Engineering Townsville, Queensland, 4811 Phone 0747814259 Fax
More informationImproving A D Converter Performance Using Dither
Improving A D Converter Performance Using Dither 1 0 INTRODUCTION Many analogtodigital converter applications require low distortion for a very wide dynamic range of signals Unfortunately the distortion
More informationby Anurag Pulincherry A THESIS submitted to Oregon State University in partial fulfillment of the requirements for the degree of Master of Science
A Continuous Time Frequency Translating Delta Sigma Modulator by Anurag Pulincherry A THESIS submitted to Oregon State University in partial fulfillment of the requirements for the degree of Master of
More informationFILTER CIRCUITS. A filter is a circuit whose transfer function, that is the ratio of its output to its input, depends upon frequency.
FILTER CIRCUITS Introduction Circuits with a response that depends upon the frequency of the input voltage are known as filters. Filter circuits can be used to perform a number of important functions in
More informationIntroduction to IQdemodulation of RFdata
Introduction to IQdemodulation of RFdata 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
More informationLecture 3 Power System Measurement. Course map
Lecture 3 Power System Measurement 1 Course map 2 1 Outline of the Lecture Instrument Transformers (NPAG Ch. 6) Voltage Transformer Current Transformers Measurement Setups Transducers (NPAG Ch. 22) 3 The
More informationTDS5000B, TDS6000B, TDS/CSA7000B Series Acquisition Modes
TDS5000B, TDS6000B, TDS/CSA7000B Series Acquisition Modes Tektronix oscilloscopes provide several different acquisition modes. While this gives the user great flexibility and choice, each mode is optimized
More informationDigital vs. Analog Transmission Nyquist and Shannon Laws
1 Digital vs. Analog Transmission Nyquist and Shannon Laws Required reading: Garcia 3.1 to 3.5 CSE 3213, Fall 2010 Instructor: N. Vlajic Transmission Impairments 2 Transmission / Signal Impairments caused
More informationZbigniew KULKA, Piotr WOSZCZEK
ARCHIVES OF ACOUSTICS 33, 1, 93 101 (2008) IMPLEMENTATION OF DIGITAL SIGMADELTA MODULATORS FOR HIGHRESOLUTION AUDIO DIGITALTOANALOG CONVERTERS BASED ON FIELD PROGRAMMABLE GATE ARRAY Zbigniew KULKA,
More informationThe 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 informationUnderstand the effects of clock jitter and phase noise on sampled systems A s higher resolution data converters that can
designfeature By Brad Brannon, Analog Devices Inc MUCH OF YOUR SYSTEM S PERFORMANCE DEPENDS ON JITTER SPECIFICATIONS, SO CAREFUL ASSESSMENT IS CRITICAL. Understand the effects of clock jitter and phase
More informationELG3336: Converters Analog to Digital Converters (ADCs) Digital to Analog Converters (DACs) 111 110 101 100 011 010
ELG3336: Converters Analog to Digital Converters (ADCs) Digital to Analog Converters (DACs) Digital Output Dout 111 110 101 100 011 010 001 000 ΔV, V LSB V ref 8 V FS 4 V 8 ref 7 V 8 ref Analog Input V
More informationImpedance 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 informationComputer Networks and Internets, 5e Chapter 6 Information Sources and Signals. Introduction
Computer Networks and Internets, 5e Chapter 6 Information Sources and Signals Modified from the lecture slides of Lami Kaya (LKaya@ieee.org) for use CECS 474, Fall 2008. 2009 Pearson Education Inc., Upper
More informationAnalog & digital signals. Analog & digital signals
Analog & digital signals Analog & digital signals Analog Continuous function V of continuous variable t (time, space etc) : V(t). Digital Discrete function Vk of discrete sampling variable tk, with k =
More informationImprovement of The ADC Resolution Based on FPGA Implementation of Interpolating Algorithm
International Journal of New Technology and Research (IJNTR) ISSN:24544116, Volume2, Issue1, January 2016 Pages 100103 Improvement of The ADC Resolution Based on FPGA Implementation of Interpolating
More informationAN837 APPLICATION NOTE
APPLICATION NOTE One Technology Way P.O. Box 916 Norwood, MA 262916, U.S.A. Tel: 781.329.47 Fax: 781.461.3113 www.analog.com DDSBased Clock Jitter Performance vs. DAC Reconstruction Filter Performance
More informationLecture 3: Signaling and Clock Recovery. CSE 123: Computer Networks Stefan Savage
Lecture 3: Signaling and Clock Recovery CSE 123: Computer Networks Stefan Savage Last time Protocols and layering Application Presentation Session Transport Network Datalink Physical Application Transport
More informationDithering in Analogtodigital Conversion
Application Note 1. Introduction 2. What is Dither Highspeed ADCs today offer higher dynamic performances and every effort is made to push these stateofthe art performances through design improvements
More informationIn modern electronics, it is important to be able to separate a signal into different
Introduction In modern electronics, it is important to be able to separate a signal into different frequency regions. In analog electronics, four classes of filters exist to process an input signal: lowpass,
More informationDigital 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 informationAnalog/Digital Conversion. Analog Signals. Digital Signals. Analog vs. Digital. Interfacing a microprocessorbased system to the real world.
Analog/Digital Conversion Analog Signals Interacing a microprocessorbased system to the real world. continuous range x(t) Analog and digital signals he bridge: Sampling heorem Conversion concepts Conversion
More informationCombining the ADS1202 with an FPGA Digital Filter for Current Measurement in Motor Control Applications
Application Report SBAA094 June 2003 Combining the ADS1202 with an FPGA Digital Filter for Current Measurement in Motor Control Applications Miroslav Oljaca, Tom Hendrick Data Acquisition Products ABSTRACT
More informationRSP Firmware Functional Specification
Embedded Processing Applications RSP Firmware Functional Specification Verified: Name Signature Date Rev.nr. Accepted: Work Package Manager System Engineering Manager Program Manager W.H. Lubberhuizen
More informationApplication Report. 1 Introduction. 2 Resolution of an AD Converter. 2.1 SignaltoNoise Ratio (SNR) Harman Grewal... ABSTRACT
Application Report SLAA323 JULY 2006 Oversampling the ADC12 for Higher Resolution Harman Grewal... ABSTRACT This application report describes the theory of oversampling to achieve resolutions greater than
More informationPublic Switched Telephone System
Public Switched Telephone System Structure of the Telephone System The Local Loop: Modems, ADSL Structure of the Telephone System (a) Fullyinterconnected network. (b) Centralized switch. (c) Twolevel
More informationCS263: Wireless Communications and Sensor Networks
CS263: Wireless Communications and Sensor Networks Matt Welsh Lecture 2: RF Basics and Signal Encoding September 22, 2005 2005 Matt Welsh Harvard University 1 Today's Lecture Basics of wireless communications
More informationTCOM 370 NOTES 994 BANDWIDTH, FREQUENCY RESPONSE, AND CAPACITY OF COMMUNICATION LINKS
TCOM 370 NOTES 994 BANDWIDTH, FREQUENCY RESPONSE, AND CAPACITY OF COMMUNICATION LINKS 1. Bandwidth: The bandwidth of a communication link, or in general any system, was loosely defined as the width of
More informationUnderstanding CIC Compensation Filters
Understanding CIC Compensation Filters April 2007, ver. 1.0 Application Note 455 Introduction f The cascaded integratorcomb (CIC) filter is a class of hardwareefficient linear phase finite impulse response
More informationAliasing, 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
More informationPrecision Fully Differential Op Amp Drives High Resolution ADCs at Low Power
Precision Fully Differential Op Amp Drives High Resolution ADCs at Low Power Kris Lokere The op amp produces differential outputs, making it ideal for processing fully differential analog signals or taking
More informationHigh Sensitivity Receiver Applications Benefit from Unique Features in 16bit 130Msps ADC
High Sensitivity Receiver Applications Benefit from Unique Features in 16bit 130Msps ADC RF IN RF BPF IF BPF LTC2208 ADC DDC/DSP LO1 ADC Driver Wireless receiver design requires extreme care in dealing
More informationLab 4 Sampling, Aliasing, FIR Filtering
47 Lab 4 Sampling, Aliasing, FIR Filtering This is a software lab. In your report, please include all Matlab code, numerical results, plots, and your explanations of the theoretical questions. The due
More informationSection 3. Sensor to ADC Design Example
Section 3 Sensor to ADC Design Example 31 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 informationMATRIX TECHNICAL NOTES
200 WOOD AVENUE, MIDDLESEX, NJ 08846 PHONE (732) 4699510 FAX (732) 4690418 MATRIX TECHNICAL NOTES MTN107 TEST SETUP FOR THE MEASUREMENT OF XMOD, CTB, AND CSO USING A MEAN SQUARE CIRCUIT AS A DETECTOR
More informationLecture 16: Noise and Filters
Lecture 16: 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
More informationRF Measurements Using a Modular Digitizer
RF Measurements Using a Modular Digitizer Modern modular digitizers, like the Spectrum M4i series PCIe digitizers, offer greater bandwidth and higher resolution at any given bandwidth than ever before.
More informationLEVERAGING FPGA AND CPLD DIGITAL LOGIC TO IMPLEMENT ANALOG TO DIGITAL CONVERTERS
LEVERAGING FPGA AND CPLD DIGITAL LOGIC TO IMPLEMENT ANALOG TO DIGITAL CONVERTERS March 2010 Lattice Semiconductor 5555 Northeast Moore Ct. Hillsboro, Oregon 97124 USA Telephone: (503) 2688000 www.latticesemi.com
More informationImplementation 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
More informationChapter 20 DAC, DAC AND ANALOG DIGITAL MIX INTERFACES
Chapter 20 DAC, DAC AND ANALOG DIGITAL MIX INTERFACES Lesson 2 DIGITAL TO ANALOG CONVERTER (DAC or D/A) Ch20L2"Digital Principles and Design", Raj Kamal, Pearson Education, 2006 2 Outline DAC DAC Circuit
More informationSpectrum Level and Band Level
Spectrum Level and Band Level ntensity, ntensity Level, and ntensity Spectrum Level As a review, earlier we talked about the intensity of a sound wave. We related the intensity of a sound wave to the acoustic
More informationMODULE 13  INTERFACING THE ANALOG WORLD TO DIGITAL CIRCUITS
Introduction to Digital Electronic Design Module 13, Interfacing Analog to Digital Circuits 1 MODULE 13  INTERFACING THE ANALOG WORLD TO DIGITAL CIRCUITS OVERVIEW: Digital circuits require the input signal
More informationQuantization. Yao Wang Polytechnic University, Brooklyn, NY11201
Quantization Yao Wang Polytechnic University, Brooklyn, NY11201 http://eeweb.poly.edu/~yao Outline Review the three process of A to D conversion Quantization Uniform Nonuniform Mulaw Demo on quantization
More informationRF SYSTEM DESIGN OF TRANSCEIVERS FOR WIRELESS COMMUNICATIONS
RF SYSTEM DESIGN OF TRANSCEIVERS FOR WIRELESS COMMUNICATIONS Qizheng Gu Nokia Mobile Phones, Inc. 4y Springer Contents Preface xiii Chapter 1. Introduction 1 1.1. Wireless Systems 1 1.1.1. Mobile Communications
More informationFrequency Domain Characterization of Signals. Yao Wang Polytechnic University, Brooklyn, NY11201 http: //eeweb.poly.edu/~yao
Frequency Domain Characterization of Signals Yao Wang Polytechnic University, Brooklyn, NY1121 http: //eeweb.poly.edu/~yao Signal Representation What is a signal Timedomain description Waveform representation
More informationMODULATION Systems (part 1)
Technologies and Services on Digital Broadcasting (8) MODULATION Systems (part ) "Technologies and Services of Digital Broadcasting" (in Japanese, ISBN4339622) is published by CORONA publishing co.,
More informationProbability 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
More informationSAMPLE: EXPERIMENT 10 Bandpass Filter / Fourier Analysis
SAMPLE: EXPERIMENT 10 Bandpass Filter / Fourier Analysis  This experiment is an excerpt from: Electric
More informationDigital Signal Processing Fundamentals
Application Note 023 Digital Signal Processing Fundamentals D. Koenig Introduction 1 Recent advances in digital signal processing (DSP) technology make it easier for scientists to develop powerful personal
More informationAN756 APPLICATION NOTE One Technology Way P.O. Box 9106 Norwood, MA 020629106 Tel: 781/3294700 Fax: 781/3268703 www.analog.com
APPLICATION NOTE One Technology Way P.O. Box 9106 Norwood, MA 020629106 Tel: 781/3294700 Fax: 781/3268703 www.analog.com Sampled Systems and the Effects of Clock Phase Noise and Jitter by Brad Brannon
More informationWireless Communication and RF System Design Using MATLAB and Simulink Giorgia Zucchelli Technical Marketing RF & MixedSignal
Wireless Communication and RF System Design Using MATLAB and Simulink Giorgia Zucchelli Technical Marketing RF & MixedSignal 2013 The MathWorks, Inc. 1 Outline of Today s Presentation Introduction to
More informationRF 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),
More informationDigital Signal Processing in RF Applications
Digital Signal Processing in RF Applications Part I Thomas Schilcher What are RF applications? any application which measures properties of an RF field (amplitude, phase, frequency, ); typical frequencies
More informationDADiSP / Octave. 1/N Octave Analysis Module. DSP Development Corporation KEY FEATURES. Toll Free: 18004243131
DADiSP / Octave 1/N Octave Analysis Module DADiSP/Octave is a menu driven module designed to simplify the task of octave, 1/3 octave and 1/N octave analysis used to characterize acoustic energy in a wide
More information