The operation of signal dilation (or decimation or down-sampling) is defined by

 

y(n) = x(nM)

in which the sequence x(n) is down-sampled by an integer factor M. For example, if

then the down-sampled sequences by a factor 2 are given by

1. Develop a MATLAB function dnsample that has the form

function [y,m] = dnsample(x,n,M) % Downsample sequence x(n) by a factor M to obtain y(m).

to implement the above operation. Use the indexing mechanism of MATLAB with careful attention to the origin of the time axis n = 0. 2. Generate x(n) = sin(0.125πn), − 50 ≤ n ≤ 50. Decimate x(n) by a factor of 4 to generate y(n). Plot both x(n) and y(n) using subplot and comment on the results. 3. Repeat the above using x(n) = sin(0.5πn), − 50 ≤ n ≤ 50. Qualitatively discuss the effect of down-sampling on signals.