MULTIRATE DIGITAL SIGNAL PROCESSING

MULTIRATE DIGITAL SIGNAL PROCESSING

Program to study the operation of a up-sampler.

% Program

% Illustration of Up-Sampling by an Integer Factor

%

clf;

n = 0:50;

x = sin(2*pi*0.12*n);

y = zeros(1, 3*length(x));

y([1: 3: length(y)]) = x;

subplot(2,1,1)

stem(n,x);

title(’Input Sequence’);

xlabel(’Time index n’);ylabel(’Amplitude’);

subplot(2,1,2)

stem(n,y(1:length(x)));

title(’Output Sequence’);

xlabel(’Time index n’);ylabel(’Amplitude’);

Program can be used to study the operation of a down-sampler.

% Program

% Illustration of Down-Sampling by an Integer Factor

%

clf;

n = 0: 49;

m = 0: 50*3 - 1;

x = sin(2*pi*0.042*m);

y = x([1: 3: length(x)]);

subplot(2,1,1)

stem(n, x(1:50)); axis([0 50 -1.2 1.2]);

title(’Input Sequence’);

xlabel(’Time index n’);

ylabel(’Amplitude’);

subplot(2,1,2)

stem(n, y); axis([0 50 -1.2 1.2]);

title(’Output Sequence’);

xlabel(’Time index n’);

ylabel(’Amplitude’);

Program illustrates the use of the M-function interp in the design and implementation

of an interpolator with an integer-valued interpolation factor L. interp designs and

uses a lowpass interpolation filter with a stopband edge satisfying Eq. (10.6).

% Program

% Illustration of Interpolation Process

%

clf;

L = input(’Up-sampling factor = ’);

% Generate the input sequence

n = 0:49;

x = sin(2*pi*0.043*n) + sin(2*pi*0.031*n);

% Generate the interpolated output sequence

y = interp(x,L);

% Plot the input and the output sequences

subplot(2,1,1);

stem(n,x(1:50));

title(’Input Sequence’);

xlabel(’Time index n’); ylabel(’Amplitude’);

subplot(2,1,2);

m = 0:(50*L)-1;

stem(m,y(1:50*L));

title(’Output Sequence’);

xlabel(’Time index n’); ylabel(’Amplitude’);

Program to illustrates the use of the M-function resample in the design and implementation of an interpolator with a fractional-rate interpolation factor L/M. resample designs and uses a lowpass interpolation filter with a stopband edge satisfying

% Program

% Illustration of Sampling Rate Alteration by

% a Ratio of Two Integers

%

clf;

L = input(’Up-sampling factor = ’);

M = input(’Down-sampling factor = ’);

n = 0:29;

x = sin(2*pi*0.43*n) + sin(2*pi*0.31*n);

y = resample(x,L,M);

subplot(2,1,1);

stem(n,x(1:30));axis([0 29 -2.2 2.2]);

title(’Input Sequence’);

xlabel(’Time index n’); ylabel(’Amplitude’);

subplot(2,1,2);

m = 0:(30*L/M)-1;

stem(m,y(1:30*L/M));axis([0 (30*L/M)-1 -2.2 2.2]);

title(’Output Sequence’);

xlabel(’Time index n’); ylabel(’Amplitude’);