Down-sampling in MATLAB

The two basic operations in a multi-rate system are decreasing/down-sampling (decimation) and increasing (interpolation) the sampling rate of a signal.

In down-sampling we start with a constant time signal x(t) and convert it into a succession of tests x[n], in decimation we start with a discrete-time signal x[n] and convert it into another discrete-time signal y[n], which comprises of sub-tests of x[n].


We will be using the decimate() and stem() function.
The decimate() function is used to decrease a sample rate by an integer factor.

Syntax: a = decimate(x, r)
Parameters:

  • x: input signal,
  • r: decimation factor

Return Value: Decimated Signal



The stem() function is used to plot a discrete sequence data.

Syntax: stem(y)
Parameter:

  • y: data sequence

Return Value: Plot of data sequence in discrete time

MATLAB code for down-sampling:

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% Time vector
t = 0 : .00025 : 1;
  
% Original signal
x = sin(2 * pi * 50 * t) + sin(2 * pi * 100 * t);
  
% Reduces the sample rate of original signal by factor of 4
y = decimate(x, 4); 
  
figure()
subplot(2, 2, 1);
  
% Plot few samples of the Original signal
stem(x(1:75)) 
title('Original Signal');
  
subplot(2, 2, 2);
  
% Plots few samples of the Decimated signal
stem(y(1:75)); 
title('Decimated Signal');

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