Analog & digital signals. Analog & digital signals

Size: px
Start display at page:

Download "Analog & digital signals. Analog & digital signals"

Transcription

1 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 = integer: Vk = V(tk)..3.3 Voltage [V] time [ms] Voltage [V] Uniform (periodic) sampling. Sampling frequency f S = / t S t s t s sampling time, t k [ms]

2 Digital vs analog proc ing Digital vs analog proc ing Digital Signal Processing (DSPing) Advantages More flexible. Often easier system upgrade. Data easily stored. Better control over accuracy requirements. Reproducibility. Limitations A/D & signal processors speed: wide-band signals still difficult to treat (real-time systems). Finite word-length effect. Obsolescence (analog electronics has it, too!).

3 Digital system example Digital system example General scheme Sometimes steps missing - Filter + A/D (ex: economics); - D/A + filter (ex: digital output wanted). V V A A ms ms k Filter Antialiasing A/D Digital Processing ANALOG DOMAIN DIGIAL DOMAIN V k D/A V ms ms Filter Reconstruction ANALOG DOMAIN

4 Digital system implementation Digital system implementation ANALOG INPU KEY DECISION POINS: Analysis bandwidth, Dynamic range Antialiasing Filter A/D Pass / stop bands. Sampling rate. No. of bits. Parameters. 2 Digital Processing DIGIAL OUPU Digital format. What to use for processing? See slide DSPing aim & tools 3

5 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. rain starts wheels go clockwise. rain accelerates wheels go counter-clockwise. Why? Frequency misidentification due to low sampling frequency. * Sampling: independent variable (ex: time) continuous discrete. Quantisation: dependent variable (ex: voltage) continuous discrete. Here we ll talk about uniform sampling.

6 Sampling - 2 Sampling t s(t) = sin(2πf t) f S f = Hz, f S = 3 Hz s (t) = sin(8πf t) s2 (t) = sin(4πf t) f S represents exactly all sine-waves s k (t) defined by: s k (t) = sin( 2π (f + k f S ) t ), k

7 he sampling theorem he sampling theorem heo* 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) = 3 cos(5 π t) + sin(3 π t) cos(π t) Condition on f S? F F 2 F 3 F =25 Hz, F 2 = 5 Hz, F 3 = 5 Hz f S > 3 Hz f MAX

8 Frequency domain (hints) Frequency domain (hints) ime & frequency: two complementary signal descriptions. Signals seen as projected onto time or frequency domains. Example Ear + brain act as frequency analyser: audio spectrum split into many narrow bands low-power sounds detected out of loud background. Bandwidth: indicates rate of change of a signal. High bandwidth signal changes fast.

9 Sampling low-pass signals Sampling low-pass signals (a) Continuous spectrum (a) Band-limited signal: frequencies in [-B, B] (f MAX = B). (b) -B B f Discrete spectrum No aliasing -B B f S /2 f (b) ime sampling frequency repetition. f S > 2 B no aliasing. (c) Discrete spectrum Aliasing & corruption (c) f S 2 B aliasing! f S /2 f Aliasing: signal ambiguity in frequency domain

10 Antialiasing filter Antialiasing filter (a) Out of band noise Signal of interest Out of band noise (a),(b) Out-of-band noise can alias into band of interest. Filter it before! (b) (c) Passband frequency -B B f -B B f S /2 f Antialiasing filter -B B f (c) Antialiasing filter Passband: depends on bandwidth of interest. Attenuation A MIN : depends on ADC resolution ( number of bits N). A MIN, db ~ 6.2 N +.76 Out-of-band noise magnitude. Other parameters: ripple, stopband frequency...

11 2 ADC - Number of bits N ADC - Number of bits N Continuous input signal digitized into 2 N levels. 3 Uniform, bipolar transfer function (N=3) V Quantization step q = V FSR 2 N Ex: V FSR = V, N = 2 q = 244. µv V FSR LSB Voltage ( = q) Scale factor (= / 2 N ).5 q / 2 Percentage (= / 2 N ) q / 2 Quantisation error

12 2 ADC - Quantisation error ADC - Quantisation error.3 Voltage [V] time [ms] Quantisation Error e q in [-.5 q, +.5 q]. e q limits ability to resolve small signal. Higher resolution means lower e q.

13 Frequency analysis: why? Frequency analysis: why? Fast & efficient insight on signal s building blocks. Simplifies original problem - ex.: solving Part. Diff. Eqns. (PDE). Powerful & complementary to time domain analysis techniques. he brain does it? time, t s(t) analysis F synthesis General ransform as problem-solving tool frequency, f S(f) = F[s(t)] s(t), S(f) : ransform Pair

14 Fourier analysis - tools Fourier analysis - tools 2.5 Input ime Signal Frequency spectrum time, t Continuous Periodic (period ) Aperiodic FS F Discrete Continuous c jk ω t k = s(t) e dt + j2 π f t S(f) = s(t) e dt time, t time, t k time, t k 8 2 Discrete Periodic (period ) Aperiodic DFS DF DF ** ** Discrete Continuous Discrete c ~ k = N N j s[n] e n= N j s[n] e n= 2πk n N + S(f) = s[n] e j2π f n n= 2πk n c ~ k = N N Note: j = -, ω = 2π/, s[n]=s(tn), N = No. of samples ** Calculated via FF

15 A little history A little history Astronomic predictions by Babylonians/Egyptians likely via trigonometric sums. 669: Newton stumbles upon light spectra (specter = ghost) but fails to recognise frequency concept (corpuscular theory of light, & no waves). 8 th century: two outstanding problems celestial bodies orbits: Lagrange, Euler & Clairaut approximate observation data with linear combination of periodic functions; Clairaut,754(!) first DF formula. vibrating strings: Euler describes vibrating string motion by sinusoids (wave equation). 87: Fourier presents his work on heat conduction Fourier analysis born. Diffusion equation series (infinite) of sines & cosines. Strong criticism by peers blocks publication. Work published, 822 ( heorie Analytique de la chaleur ).

16 A little history -2 A little history -2 9 th / 2 th century: two paths for Fourier analysis - Continuous & Discrete. CONINUOUS Fourier extends the analysis to arbitrary function (Fourier ransform). Dirichlet, Poisson, Riemann, Lebesgue address FS convergence. Other F variants born from varied needs (ex.: Short ime F - speech analysis). DISCREE: Fast calculation methods (FF) 85 - Gauss, first usage of FF (manuscript in Latin went unnoticed!!! Published 866) IBM s Cooley & ukey rediscover FF algorithm ( An algorithm for the machine calculation of complex Fourier series ). Other DF variants for different applications (ex.: Warped DF - filter design & signal compression). FF algorithm refined & modified for most computer platforms.

17 Fourier Series (FS) Fourier Series (FS) A periodic function s(t) satisfying Dirichlet s conditions * can be expressed as a Fourier series, with harmonically related sine/cosine terms. synthesis synthesis + s(t) = a + k= analysis analysis a a k -bk = = = 2 2 [ ak cos(k ω t) bk sin(k ω t) ] For all t but discontinuities s(t)dt s(t) cos(k ω t)dt s(t) sin(k ω t)dt a, a k, b k : Fourier coefficients. k: harmonic number, : period, ω = 2π/ (signal average over a period, i.e. DC term & zero-frequency component.) Note: {cos(kωt), sin(kωt) } k form orthogonal base of function space. * see next slide

18 FS convergence FS convergence Dirichlet conditions (a) s(t) piecewise-continuous; In any period: (b) (c) s(t) piecewise-monotonic; s(t) absolutely integrable, s(t) dt < Example: square wave Rate of convergence if s(t) discontinuous then a k <M/k for large k (M>) s(t) (a) (b) (c)

19 FS analysis - FS analysis - FS of odd* function: square wave. π 2π a = dt ( )dt = 2π + π π 2π a k = coskt dt coskt dt = π π = 2π ω = (zero average) (odd function) square signal, sw(t) π t -b k π 2π 2 sinkt dt sinkt dt =... = { cos }= π k π π = kπ * Even & Odd functions s(x) = 4 k π,, k odd k even Even : s(-x) = s(x) s(x) x sw(t) = sin t + sin 3 t + sin 5 t +... π 3 π 5 π Odd : s(-x) = -s(x) x

20 FS synthesis FS synthesis Square wave reconstruction from spectral terms sw7(t) sw3(t) sw9(t) 5(t) = [ [ -bk kk sin(kt) ] ] k = square signal, sw(t) Convergence may be slow (~/k) - ideally need infinite terms. Practically, series truncated when remainder below computer tolerance ( error). BU Gibbs Phenomenon. t

21 Gibbs phenomenon Gibbs phenomenon.5 Overshoot each discontinuity 79 [ -bk ] sw79(t) = sin(kt) k= square signal, sw(t) t First observed by Michelson, 898. Explained by Gibbs. Max overshoot pk-to-pk = 8.95% of discontinuity magnitude. Just a minor annoyance. FS converges to (-+)/2 discontinuities, in this case.

22 FS time shifting FS time shifting FS of even function: π/2-advanced squares quare-wave a = -b k 4 k π ak = 4 k π =, (zero average), k odd, k odd,, k =, 5, 9... k = 3, 7,... k even. (even function) square signal, sw(t) amplitude amplitude r k 4/π 4/3π θ k 2 π t f 3f 5f 7f f Note: amplitudes unchanged BU phases advance by k π/2. phase phase π f 3f 5f 7f f

23 Complex FS Complex FS Euler s notation: e -jt = (e jt )* = cos(t) - j sin(t) ck analysis analysis s(t) = jk ω t ck e k= synthesis synthesis = s(t) e -jk ω t dt phasor cos(t) = e jt jt + e 2 sin(t) = e 2 j Complex form of FS (Laplace 782). Harmonics c k separated by f = / on frequency plot. e jt jt Note: c -k = (c k )* z = r e jθ c = ck = a 2 2 ( + j ) = ( a j b ) ak Link to FS real coeffs. bk k k b r θ a r = a 2 + b 2 θ = arctan(b/a)

24 FS properties FS properties ime Frequency Homogeneity a s(t) a S(k) Additivity s(t) + u(t) S(k)+U(k) Linearity a s(t) + b u(t) a S(k)+b U(k) ime reversal s(-t) S(-k) Multiplication * Convolution * ime shifting s(t) u(t) s(t t) u( t)dt s(t t) 2π m t + j m= S(k m)u(m) S(k) U(k) Frequency shifting e s(t) S(k - m) * e 2π k t j S(k)

25 FS - oddities FS - oddities Orthonormal base Fourier components {uk}{ } form orthonormal base of signal space: u k = (/ ) exp(jkωt) ( k =, 2, + ) Def.: Internal product : u k u m = δ k,m ( if k = m, otherwise). (Remember (e jt )* = e -jt ) u k u m = u u o k * m dt hen c k = (/ ) s(t) u k i.e. (/ ) times projection of signal s(t) on component u k Negative frequencies & time reversal k = -, -2,-,,,2, +, ω k = kω, φ k = ω k t, phasor turns anti-clockwise. Negative k phasor turns clockwise (negative phase φ k ), equivalent to negative time t, time reversal. Careful: phases important when combining several signals!

26 FS - power FS - power Average power W : Parseval s s heorem 2 W = = 2 ck a + k= 2 W = o s(t) ak bk k= dt s(t) s(t) FS convergence ~/k lower frequency terms W k = c k 2 carry most power. W k vs. ω k : Power density spectrum. Example Pulse train, duty cycle δ = 2 τ / s(t) 2 τ 2 - W k /W W k = 2 W sync 2 (k δ) -2 b k = a = δ s MAX a k = 2δs MAX sync(k δ) t -3 W = (δ s MAX ) sync(u) = sin(π u)/(π u) W W = + k W W k= k f

27 FS of main waveforms FS of main waveforms

28 Discrete Fourier Series (DFS) Discrete Fourier Series (DFS) Band-limited signal s[n], period = N. DFS defined as: N 2πk n j c ~ k = s[n] e N N n= ~ ~ Note: c k+n = c k same period N analysis analysis i.e. time periodicity propagates to frequencies! synthesis synthesis N 2πk n j s[n] = c ~ k e N k= Synthesis: finite sum band-limited s[n] DFS generate periodic c k with same signal period Orthogonality in DFS: N N 2π n(k-m) j e N n= = δ k,m Kronecker s delta N consecutive samples of s[n] completely describe s in time or frequency domains.

29 DFS analysis DFS analysis DFS of periodic discrete -Volt square-wave s[n] c ~ k s[n]: period N, duty factor L/N L, k =, + N, ± 2N,... N = πk(l ) j π kl sin e N N, otherwise N π k sin N Discrete signals periodic frequency spectra. Compare to continuous rectangular function (slide #, FS analysis - ) amplitude amplitude.24 phase phase.2π n L N.6.6 c k.4π k θ k n -.4π π ~.2π.6.6.4π -.4π π

30 DFS properties DFS properties ime Frequency Homogeneity a s[n] a S(k) Additivity s[n] + u[n] S(k)+U(k) Linearity a s[n] + b u[n] a S(k)+b U(k) Multiplication * Convolution * N m= s[n] u[n] s[m] u[n m] N h= S(k) U(k) ime shifting s[n - m] e S(k) Frequency shifting 2π h t + j e s[n] S(k - h) N S(h)U(k -h) 2π k m j

31 DF Window characteristics DF Window characteristics Finite discrete sequence spectrum convoluted with rectangular window spectrum. Leakage amount depends on chosen window & on how signal fits into the window. () Resolution: capability to distinguish different tones. Inversely proportional to mainlobe width. Wish: as high as possible. (2) (3) Peak-sidelobe level: maximum response outside the main lobe. Determines if small signals are hidden by nearby stronger ones. Wish: () as low as possible. (2) Sidelobe roll-off: sidelobe decay per decade. rade-off with (2). (3) Several windows used (application( application- dependent): Hamming, Hanning, Blackman, Kaiser... Rectangular window

32 DF of main windows DF of main windows Windowing reduces leakage by minimising sidelobes magnitude. In time it reduces endpoints discontinuities. Sampled sequence Non windowed Windowed Some window functions

33 DF - Window choice DF - Window choice Common windows characteristics Window type -3 db Mainlobe width -6 db Mainlobe width Max sidelobe level Sidelobe roll-off [db/decade] [bins] [bins] [db] Rectangular Hamming Hanning Blackman Observed signal Far & strong interfering components Near & strong interfering components Accuracy measure of single tone Window wish list high roll-off rate. small max sidelobe level. wide main-lobe NB: Strong DC component can shadow nearby small signals. Remove it!

34 DF - Window loss remedial DF - Window loss remedial Smooth data-tapering tapering windows cause information loss near edges. Solution: sliding (overlapping) DFs. 2 x N samples (input signal) DF # Attenuated inputs get next window s full gain & leakage reduced. Usually 5% or 75% overlap (depends on main lobe width). DF #2 DF #3 Drawback: increased total processing time. DF AVERAGING

35 DF - parabolic interpolation DF - parabolic interpolation Rectangular window Hanning window Parabolic interpolation often enough to find position of peak (i.e. frequency). Other algorithms available depending on data.

36 Systems spectral analysis (hints) Systems spectral analysis (hints) System analysis: measure input-output relationship. Linear ime Invariant x[n] DIGIAL LI SYSEM h[n] y[n] δ[n] n DIGIAL LI SYSEM h[n] h[t] = impulse response n x[n] h[n] y[n] = x[n] h[n] = m= x[n m] h[m] y[n] predicted from { x[n], h[t] } X(f) H(f) Y(f) = X(f) H(f) H(f) ) : LI transfer function ransfer function can be estimated by Y(f) / X(f)

37 Estimating H(f) (hints) Estimating H(f) (hints) G G xx yx * (f) = X(f) X (f) Power Spectral Density of x[t] (F of autocorrelation). * (f) = Y(f) X (f) Cross Power Spectrum of x[t] & y[t] (F of cross-correlation). * Y(f) Y(f) X (f) Gyx = = ransfer Function X(f) * X(f) X (f) Gxx (ex: beam!) H(f) = It is a check on H(f) validity!

Analysis/resynthesis with the short time Fourier transform

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

More information

Design of FIR Filters

Design of FIR Filters Design of FIR Filters Elena Punskaya www-sigproc.eng.cam.ac.uk/~op205 Some material adapted from courses by Prof. Simon Godsill, Dr. Arnaud Doucet, Dr. Malcolm Macleod and Prof. Peter Rayner 68 FIR as

More information

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

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

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

Chapter 8 - Power Density Spectrum

Chapter 8 - Power Density Spectrum EE385 Class Notes 8/8/03 John Stensby Chapter 8 - Power Density Spectrum Let X(t) be a WSS random process. X(t) has an average power, given in watts, of E[X(t) ], a constant. his total average power is

More information

The continuous and discrete Fourier transforms

The continuous and discrete Fourier transforms FYSA21 Mathematical Tools in Science The continuous and discrete Fourier transforms Lennart Lindegren Lund Observatory (Department of Astronomy, Lund University) 1 The continuous Fourier transform 1.1

More information

1995 Mixed-Signal Products SLAA013

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

More information

Analog and Digital Signals, Time and Frequency Representation of Signals

Analog and Digital Signals, Time and Frequency Representation of Signals 1 Analog and Digital Signals, Time and Frequency Representation of Signals Required reading: Garcia 3.1, 3.2 CSE 3213, Fall 2010 Instructor: N. Vlajic 2 Data vs. Signal Analog vs. Digital Analog Signals

More information

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

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

More information

Computer Networks and Internets, 5e Chapter 6 Information Sources and Signals. Introduction

Computer 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 information

Appendix D Digital Modulation and GMSK

Appendix D Digital Modulation and GMSK D1 Appendix D Digital Modulation and GMSK A brief introduction to digital modulation schemes is given, showing the logical development of GMSK from simpler schemes. GMSK is of interest since it is used

More information

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

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

More information

The Calculation of G rms

The 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 information

Frequency Response of FIR Filters

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

More information

SGN-1158 Introduction to Signal Processing Test. Solutions

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:

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

B3. Short Time Fourier Transform (STFT)

B3. Short Time Fourier Transform (STFT) B3. Short Time Fourier Transform (STFT) Objectives: Understand the concept of a time varying frequency spectrum and the spectrogram Understand the effect of different windows on the spectrogram; Understand

More information

TCOM 370 NOTES 99-4 BANDWIDTH, FREQUENCY RESPONSE, AND CAPACITY OF COMMUNICATION LINKS

TCOM 370 NOTES 99-4 BANDWIDTH, FREQUENCY RESPONSE, AND CAPACITY OF COMMUNICATION LINKS TCOM 370 NOTES 99-4 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 information

FFT Algorithms. Chapter 6. Contents 6.1

FFT Algorithms. Chapter 6. Contents 6.1 Chapter 6 FFT Algorithms Contents Efficient computation of the DFT............................................ 6.2 Applications of FFT................................................... 6.6 Computing DFT

More information

SIGNAL PROCESSING FOR EFFECTIVE VIBRATION ANALYSIS

SIGNAL PROCESSING FOR EFFECTIVE VIBRATION ANALYSIS SIGNAL PROCESSING FOR EFFECTIVE VIBRATION ANALYSIS Dennis H. Shreve IRD Mechanalysis, Inc Columbus, Ohio November 1995 ABSTRACT Effective vibration analysis first begins with acquiring an accurate time-varying

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

Applications of the DFT

Applications of the DFT CHAPTER 9 Applications of the DFT The Discrete Fourier Transform (DFT) is one of the most important tools in Digital Signal Processing. This chapter discusses three common ways it is used. First, the DFT

More information

Improving A D Converter Performance Using Dither

Improving A D Converter Performance Using Dither Improving A D Converter Performance Using Dither 1 0 INTRODUCTION Many analog-to-digital converter applications require low distortion for a very wide dynamic range of signals Unfortunately the distortion

More information

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

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

More information

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 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

More information

Lab 1. The Fourier Transform

Lab 1. The Fourier Transform Lab 1. The Fourier Transform Introduction In the Communication Labs you will be given the opportunity to apply the theory learned in Communication Systems. Since this is your first time to work in the

More information

Power Spectral Density

Power Spectral Density C H A P E R 0 Power Spectral Density INRODUCION Understanding how the strength of a signal is distributed in the frequency domain, relative to the strengths of other ambient signals, is central to the

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

The 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 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 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

Aliasing, Image Sampling and Reconstruction

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

More information

S. Boyd EE102. Lecture 1 Signals. notation and meaning. common signals. size of a signal. qualitative properties of signals.

S. Boyd EE102. Lecture 1 Signals. notation and meaning. common signals. size of a signal. qualitative properties of signals. S. Boyd EE102 Lecture 1 Signals notation and meaning common signals size of a signal qualitative properties of signals impulsive signals 1 1 Signals a signal is a function of time, e.g., f is the force

More information

SIGNAL PROCESSING & SIMULATION NEWSLETTER

SIGNAL PROCESSING & SIMULATION NEWSLETTER 1 of 10 1/25/2008 3:38 AM SIGNAL PROCESSING & SIMULATION NEWSLETTER Note: This is not a particularly interesting topic for anyone other than those who ar e involved in simulation. So if you have difficulty

More information

SECTION 6 DIGITAL FILTERS

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

More information

5 Signal Design for Bandlimited Channels

5 Signal Design for Bandlimited Channels 225 5 Signal Design for Bandlimited Channels So far, we have not imposed any bandwidth constraints on the transmitted passband signal, or equivalently, on the transmitted baseband signal s b (t) I[k]g

More information

Introduction to Frequency Domain Processing 1

Introduction to Frequency Domain Processing 1 MASSACHUSETTS INSTITUTE OF TECHNOLOGY DEPARTMENT OF MECHANICAL ENGINEERING 2.151 Advanced System Dynamics and Control Introduction to Frequency Domain Processing 1 1 Introduction - Superposition In this

More information

Motorola Digital Signal Processors

Motorola Digital Signal Processors Motorola Digital Signal Processors Principles of Sigma-Delta Modulation for Analog-to- Digital Converters by Sangil Park, Ph. D. Strategic Applications Digital Signal Processor Operation MOTOROLA APR8

More information

f x a 0 n 1 a 0 a 1 cos x a 2 cos 2x a 3 cos 3x b 1 sin x b 2 sin 2x b 3 sin 3x a n cos nx b n sin nx n 1 f x dx y

f x a 0 n 1 a 0 a 1 cos x a 2 cos 2x a 3 cos 3x b 1 sin x b 2 sin 2x b 3 sin 3x a n cos nx b n sin nx n 1 f x dx y Fourier Series When the French mathematician Joseph Fourier (768 83) was tring to solve a problem in heat conduction, he needed to epress a function f as an infinite series of sine and cosine functions:

More information

Doppler. Doppler. Doppler shift. Doppler Frequency. Doppler shift. Doppler shift. Chapter 19

Doppler. Doppler. Doppler shift. Doppler Frequency. Doppler shift. Doppler shift. Chapter 19 Doppler Doppler Chapter 19 A moving train with a trumpet player holding the same tone for a very long time travels from your left to your right. The tone changes relative the motion of you (receiver) and

More information

Correlation and Convolution Class Notes for CMSC 426, Fall 2005 David Jacobs

Correlation and Convolution Class Notes for CMSC 426, Fall 2005 David Jacobs Correlation and Convolution Class otes for CMSC 46, Fall 5 David Jacobs Introduction Correlation and Convolution are basic operations that we will perform to extract information from images. They are in

More information

The Fourier Analysis Tool in Microsoft Excel

The Fourier Analysis Tool in Microsoft Excel The Fourier Analysis Tool in Microsoft Excel Douglas A. Kerr Issue March 4, 2009 ABSTRACT AD ITRODUCTIO The spreadsheet application Microsoft Excel includes a tool that will calculate the discrete Fourier

More information

USB 3.0 CDR Model White Paper Revision 0.5

USB 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 information

Review of Fourier series formulas. Representation of nonperiodic functions. ECE 3640 Lecture 5 Fourier Transforms and their properties

Review of Fourier series formulas. Representation of nonperiodic functions. ECE 3640 Lecture 5 Fourier Transforms and their properties ECE 3640 Lecture 5 Fourier Transforms and their properties Objective: To learn about Fourier transforms, which are a representation of nonperiodic functions in terms of trigonometric functions. Also, to

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

Lecture 1-6: Noise and Filters

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

More information

Auto-Tuning Using Fourier Coefficients

Auto-Tuning Using Fourier Coefficients Auto-Tuning Using Fourier Coefficients Math 56 Tom Whalen May 20, 2013 The Fourier transform is an integral part of signal processing of any kind. To be able to analyze an input signal as a superposition

More information

Introduction to IQ-demodulation of RF-data

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

More information

Experiment 3: Double Sideband Modulation (DSB)

Experiment 3: Double Sideband Modulation (DSB) Experiment 3: Double Sideband Modulation (DSB) This experiment examines the characteristics of the double-sideband (DSB) linear modulation process. The demodulation is performed coherently and its strict

More information

Digital Transmission (Line Coding)

Digital Transmission (Line Coding) Digital Transmission (Line Coding) Pulse Transmission Source Multiplexer Line Coder Line Coding: Output of the multiplexer (TDM) is coded into electrical pulses or waveforms for the purpose of transmission

More information

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

(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,

More information

TTT4120 Digital Signal Processing Suggested Solution to Exam Fall 2008

TTT4120 Digital Signal Processing Suggested Solution to Exam Fall 2008 Norwegian University of Science and Technology Department of Electronics and Telecommunications TTT40 Digital Signal Processing Suggested Solution to Exam Fall 008 Problem (a) The input and the input-output

More information

EE 179 April 21, 2014 Digital and Analog Communication Systems Handout #16 Homework #2 Solutions

EE 179 April 21, 2014 Digital and Analog Communication Systems Handout #16 Homework #2 Solutions EE 79 April, 04 Digital and Analog Communication Systems Handout #6 Homework # Solutions. Operations on signals (Lathi& Ding.3-3). For the signal g(t) shown below, sketch: a. g(t 4); b. g(t/.5); c. g(t

More information

Contents. A Error probability for PAM Signals in AWGN 17. B Error probability for PSK Signals in AWGN 18

Contents. A Error probability for PAM Signals in AWGN 17. B Error probability for PSK Signals in AWGN 18 Contents 5 Signal Constellations 3 5.1 Pulse-amplitude Modulation (PAM).................. 3 5.1.1 Performance of PAM in Additive White Gaussian Noise... 4 5.2 Phase-shift Keying............................

More information

L9: Cepstral analysis

L9: Cepstral analysis L9: Cepstral analysis The cepstrum Homomorphic filtering The cepstrum and voicing/pitch detection Linear prediction cepstral coefficients Mel frequency cepstral coefficients This lecture is based on [Taylor,

More information

Introduction to Digital Filters

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

More information

Sampling Theory For Digital Audio By Dan Lavry, Lavry Engineering, Inc.

Sampling Theory For Digital Audio By Dan Lavry, Lavry Engineering, Inc. Sampling Theory Page Copyright Dan Lavry, Lavry Engineering, Inc, 24 Sampling Theory For Digital Audio By Dan Lavry, Lavry Engineering, Inc. Credit: Dr. Nyquist discovered the sampling theorem, one of

More information

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

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

More information

CHAPTER 8 ANALOG FILTERS

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

More information

ANALYTICAL METHODS FOR ENGINEERS

ANALYTICAL METHODS FOR ENGINEERS UNIT 1: Unit code: QCF Level: 4 Credit value: 15 ANALYTICAL METHODS FOR ENGINEERS A/601/1401 OUTCOME - TRIGONOMETRIC METHODS TUTORIAL 1 SINUSOIDAL FUNCTION Be able to analyse and model engineering situations

More information

LABORATORY 10 TIME AVERAGES, RMS VALUES AND THE BRIDGE RECTIFIER. Bridge Rectifier

LABORATORY 10 TIME AVERAGES, RMS VALUES AND THE BRIDGE RECTIFIER. Bridge Rectifier LABORATORY 10 TIME AVERAGES, RMS VALUES AND THE BRIDGE RECTIFIER Full-wave Rectification: Bridge Rectifier For many electronic circuits, DC supply voltages are required but only AC voltages are available.

More information

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 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

More information

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

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

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

A Sound Analysis and Synthesis System for Generating an Instrumental Piri Song

A Sound Analysis and Synthesis System for Generating an Instrumental Piri Song , pp.347-354 http://dx.doi.org/10.14257/ijmue.2014.9.8.32 A Sound Analysis and Synthesis System for Generating an Instrumental Piri Song Myeongsu Kang and Jong-Myon Kim School of Electrical Engineering,

More information

Performance of Quasi-Constant Envelope Phase Modulation through Nonlinear Radio Channels

Performance of Quasi-Constant Envelope Phase Modulation through Nonlinear Radio Channels Performance of Quasi-Constant Envelope Phase Modulation through Nonlinear Radio Channels Qi Lu, Qingchong Liu Electrical and Systems Engineering Department Oakland University Rochester, MI 48309 USA E-mail:

More information

CHAPTER 6 Frequency Response, Bode Plots, and Resonance

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

More information

Non-Data Aided Carrier Offset Compensation for SDR Implementation

Non-Data Aided Carrier Offset Compensation for SDR Implementation Non-Data 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 information

Spectral Analysis Using a Deep-Memory Oscilloscope Fast Fourier Transform (FFT)

Spectral Analysis Using a Deep-Memory Oscilloscope Fast Fourier Transform (FFT) Spectral Analysis Using a Deep-Memory Oscilloscope Fast Fourier Transform (FFT) For Use with Infiniium 54830B Series Deep-Memory Oscilloscopes Application Note 1383-1 Table of Contents Introduction........................

More information

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

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

More information

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 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

More information

The Fourier Series of a Periodic Function

The Fourier Series of a Periodic Function 1 Chapter 1 he Fourier Series of a Periodic Function 1.1 Introduction Notation 1.1. We use the letter with a double meaning: a) [, 1) b) In the notations L p (), C(), C n () and C () we use the letter

More information

The Heat Equation. Lectures INF2320 p. 1/88

The Heat Equation. Lectures INF2320 p. 1/88 The Heat Equation Lectures INF232 p. 1/88 Lectures INF232 p. 2/88 The Heat Equation We study the heat equation: u t = u xx for x (,1), t >, (1) u(,t) = u(1,t) = for t >, (2) u(x,) = f(x) for x (,1), (3)

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

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

Lecture 8 ELE 301: Signals and Systems

Lecture 8 ELE 301: Signals and Systems Lecture 8 ELE 3: Signals and Systems Prof. Paul Cuff Princeton University Fall 2-2 Cuff (Lecture 7) ELE 3: Signals and Systems Fall 2-2 / 37 Properties of the Fourier Transform Properties of the Fourier

More information

Wavelet analysis. Wavelet requirements. Example signals. Stationary signal 2 Hz + 10 Hz + 20Hz. Zero mean, oscillatory (wave) Fast decay (let)

Wavelet analysis. Wavelet requirements. Example signals. Stationary signal 2 Hz + 10 Hz + 20Hz. Zero mean, oscillatory (wave) Fast decay (let) Wavelet analysis In the case of Fourier series, the orthonormal basis is generated by integral dilation of a single function e jx Every 2π-periodic square-integrable function is generated by a superposition

More information

CBS RECORDS PROFESSIONAL SERIES CBS RECORDS CD-1 STANDARD TEST DISC

CBS RECORDS PROFESSIONAL SERIES CBS RECORDS CD-1 STANDARD TEST DISC CBS RECORDS PROFESSIONAL SERIES CBS RECORDS CD-1 STANDARD TEST DISC 1. INTRODUCTION The CBS Records CD-1 Test Disc is a highly accurate signal source specifically designed for those interested in making

More information

PHYS 331: Junior Physics Laboratory I Notes on Noise Reduction

PHYS 331: Junior Physics Laboratory I Notes on Noise Reduction PHYS 331: Junior Physics Laboratory I Notes on Noise Reduction When setting out to make a measurement one often finds that the signal, the quantity we want to see, is masked by noise, which is anything

More information

AN-837 APPLICATION NOTE

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

More information

4.5 Chebyshev Polynomials

4.5 Chebyshev Polynomials 230 CHAP. 4 INTERPOLATION AND POLYNOMIAL APPROXIMATION 4.5 Chebyshev Polynomials We now turn our attention to polynomial interpolation for f (x) over [ 1, 1] based on the nodes 1 x 0 < x 1 < < x N 1. Both

More information

AN1200.04. Application Note: FCC Regulations for ISM Band Devices: 902-928 MHz. FCC Regulations for ISM Band Devices: 902-928 MHz

AN1200.04. Application Note: FCC Regulations for ISM Band Devices: 902-928 MHz. FCC Regulations for ISM Band Devices: 902-928 MHz AN1200.04 Application Note: FCC Regulations for ISM Band Devices: Copyright Semtech 2006 1 of 15 www.semtech.com 1 Table of Contents 1 Table of Contents...2 1.1 Index of Figures...2 1.2 Index of Tables...2

More information

MODULATION Systems (part 1)

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.,

More information

CIRCUITS LABORATORY EXPERIMENT 3. AC Circuit Analysis

CIRCUITS LABORATORY EXPERIMENT 3. AC Circuit Analysis CIRCUITS LABORATORY EXPERIMENT 3 AC Circuit Analysis 3.1 Introduction The steady-state behavior of circuits energized by sinusoidal sources is an important area of study for several reasons. First, the

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

Spectrum Level and Band Level

Spectrum 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 information

Agilent Time Domain Analysis Using a Network Analyzer

Agilent Time Domain Analysis Using a Network Analyzer Agilent Time Domain Analysis Using a Network Analyzer Application Note 1287-12 0.0 0.045 0.6 0.035 Cable S(1,1) 0.4 0.2 Cable S(1,1) 0.025 0.015 0.005 0.0 1.0 1.5 2.0 2.5 3.0 3.5 4.0 Frequency (GHz) 0.005

More information

Ralph L. Brooker, Member, IEEE. Andrew Corporation, Alexandria, VA 22314, USA

Ralph L. Brooker, Member, IEEE. Andrew Corporation, Alexandria, VA 22314, USA Spectral-Null Pulse Waveform For Characterizing Gain and Phase Distortion in Devices with Uncorrelated Frequency Translation or Limited CW Power Capability Ralph L. Brooker, Member, IEEE Andrew Corporation,

More information

Em bedded DSP : I ntroduction to Digital Filters

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

More information

Lecture 7 ELE 301: Signals and Systems

Lecture 7 ELE 301: Signals and Systems Lecture 7 ELE 3: Signals and Systems Prof. Paul Cuff Princeton University Fall 2-2 Cuff (Lecture 7) ELE 3: Signals and Systems Fall 2-2 / 22 Introduction to Fourier Transforms Fourier transform as a limit

More information

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

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

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

L and C connected together. To be able: To analyse some basic circuits.

L and C connected together. To be able: To analyse some basic circuits. circuits: Sinusoidal Voltages and urrents Aims: To appreciate: Similarities between oscillation in circuit and mechanical pendulum. Role of energy loss mechanisms in damping. Why we study sinusoidal signals

More information

Acceleration levels of dropped objects

Acceleration levels of dropped objects Acceleration levels of dropped objects cmyk Acceleration levels of dropped objects Introduction his paper is intended to provide an overview of drop shock testing, which is defined as the acceleration

More information

FAST Fourier Transform (FFT) and Digital Filtering Using LabVIEW

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

More information

Advanced Signal Processing and Digital Noise Reduction

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

More information

14: FM Radio Receiver

14: FM Radio Receiver (1) (2) (3) DSP and Digital Filters (2015-7310) FM Radio: 14 1 / 12 (1) (2) (3) FM spectrum: 87.5 to 108 MHz Each channel: ±100 khz Baseband signal: Mono (L + R): ±15kHz Pilot tone: 19 khz Stereo (L R):

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

Laboratory Manual and Supplementary Notes. CoE 494: Communication Laboratory. Version 1.2

Laboratory Manual and Supplementary Notes. CoE 494: Communication Laboratory. Version 1.2 Laboratory Manual and Supplementary Notes CoE 494: Communication Laboratory Version 1.2 Dr. Joseph Frank Dr. Sol Rosenstark Department of Electrical and Computer Engineering New Jersey Institute of Technology

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