Proposal
School of Communications Technology and Mathematical Sciences
Digital Signal Processing
Part 3
Discrete-Time Signals & Systems
Case Studies
S R Taghizadeh <srt@unl.ac.uk>
January 2000
Introduction
Matlab and its applications in analysis of continuous-time signals and systems has been discussed in part 1 and 2 of this series of practical manuals. The purpose of part
3 is to discuss the way Matlab is used in analysis of discrete-time signals and systems.
Each section provides a series of worked examples followed by a number of investigative problems. You are required to perform each of the worked examples in order to get familiar to the concept of Matlab environment and its important functions.
In order to test your understanding of the concept of discrete-time signals & systems analysis, you are required to complete as many of the investigation / case study problems as possible. The areas covered are designed to enforce some of the topics covered in the formal lecture classes. These are:
q
Signal Generation and Presentation
q
Discrete Fourier Transform
q
Spectral analysis
q
Autocorrelation and Cross correlation
q
Time delay estimation
Digital Signal Processing Case Study
Copyright-ãS.R.Taghizadeh
2
Signal Generation and Manipulation
Sinusoidal Signal Generation
Consider generating 64 samples of a sinusoidal signal of frequency 1KHz, with a sampling frequency of 8KHz.
A sampled sinusoid may be written as: x(n) = A sin( 2p
f n + J) fs where f is the signal frequency, fs is the sampling frequency, q is the phase and A is the amplitude of the signal. The program and its output is shown below:
% Program: W2E1b.m
% Generating 64 samples of x(t)=sin(2*pi*f*t) with a
% Frequency of 1KHz, and sampling frequency of 8KHz.
N=64;
% Define Number of samples n=0:N-1; % Define vector n=0,1,2,3,...62,63 f=1000; % Define the frequency fs=8000; % Define the sampling frequency x=sin(2*pi*(f/fs)*n); % Generate x(t) plot(n,x); % Plot x(t) vs. t grid; title('Sinewave
Digital Signal Processing
Part 3
Discrete-Time Signals & Systems
Case Studies
S R Taghizadeh <srt@unl.ac.uk>
January 2000
Introduction
Matlab and its applications in analysis of continuous-time signals and systems has been discussed in part 1 and 2 of this series of practical manuals. The purpose of part
3 is to discuss the way Matlab is used in analysis of discrete-time signals and systems.
Each section provides a series of worked examples followed by a number of investigative problems. You are required to perform each of the worked examples in order to get familiar to the concept of Matlab environment and its important functions.
In order to test your understanding of the concept of discrete-time signals & systems analysis, you are required to complete as many of the investigation / case study problems as possible. The areas covered are designed to enforce some of the topics covered in the formal lecture classes. These are:
q
Signal Generation and Presentation
q
Discrete Fourier Transform
q
Spectral analysis
q
Autocorrelation and Cross correlation
q
Time delay estimation
Digital Signal Processing Case Study
Copyright-ãS.R.Taghizadeh
2
Signal Generation and Manipulation
Sinusoidal Signal Generation
Consider generating 64 samples of a sinusoidal signal of frequency 1KHz, with a sampling frequency of 8KHz.
A sampled sinusoid may be written as: x(n) = A sin( 2p
f n + J) fs where f is the signal frequency, fs is the sampling frequency, q is the phase and A is the amplitude of the signal. The program and its output is shown below:
% Program: W2E1b.m
% Generating 64 samples of x(t)=sin(2*pi*f*t) with a
% Frequency of 1KHz, and sampling frequency of 8KHz.
N=64;
% Define Number of samples n=0:N-1; % Define vector n=0,1,2,3,...62,63 f=1000; % Define the frequency fs=8000; % Define the sampling frequency x=sin(2*pi*(f/fs)*n); % Generate x(t) plot(n,x); % Plot x(t) vs. t grid; title('Sinewave