PROGRAM TO VERIFY DECIMATION AND INTERPOLATION OF A GIVEN SEQUENCE
Introduction
% Software Used: Matlab Version 7.6.0.324
% Submitted by : GG
Initial Command (Closing and Clearing)
clc; %
clears the command window
close all; %
closes all the previously open window
clear all; %
clears previously stored values
Generating Input Sequence
fm = 10;
% input signal frequency
Fs = 140;
% sampling frequency
t = 0:1/Fs:0.5; %
time range for the input sequence
x = sin(2*pi*fm*t); % input sinusoidal signal
figure(1)
subplot(4,1,1)
stem(x); % Discrete plot of the input
sequence,...
... where x-axis corresponds to the number of samples
xlabel('No. of samples');
% labelling x-axis
ylabel('Amplitude');
% labelling y-axis
title('input discrete sinusoidal sequence'); % giving title to
the plot
% Inference: A sinsoidal input signal was generated with the
signal
% frequenccy of 10 Hz and was again sampled using the sampling
frequency of
% 140 Hz which is well above to satisfy the nyquist criterion.So,
we
% obtained 72 samples from 0 to 0.5 sec when sampled at 140 Hz.
The
% obtained sinusoidal sequence was subjected to discrete plot
using
% stem plot option which plots the sampled signal amplitude
with respect
% to the number of samples. The first plot of the figure
corresponds to
% the generated sinusoidal sequence
Decimation of the Input Sequence
M = 2; %
factor by which the input sequence is decimated
xd = decimate(x,M); % resamples the sample in x with a rate
(1/M) times the original rate
subplot(4,1,2)
stem(xd) %
Discrete plot of the input sequence,...
...
where x-axis corresponds to the number of samples
xlabel('No. of samples'); % labelling x-axis
ylabel('Amplitude');
% labelling y-axis
title('Decimated Sinusoidal Sequence'); % giving title to the
plot
% Inference: The obtained sinusoidal sequence was subjected for
the
% decimation by the factor M = 2. The process of decimation
involves
% resampling the sequence in low data rate after the process of
low pass
% filtering.Since the given sequence is decimated by the factor
2,
% the resultant sequence after the decimation should have
exactly
% half the number of samples than that of the original
sequence.
% It is clearly seen in the plot that the decimated sequence
has
% 36 samples in comarison to 72 of the original sample. Hence
% the decimation of a sequence is verified.
Interolation of the Input Sequence
L = 2; %
factor by which the input sequence is interpolated
xI = interp(x,L); %
resamples the sample in x with a rate L times the original rate
subplot(4,1,3);
stem(xI); %
Discrete plot of the input sequence,...
...
where x-axis corresponds to the number of samples
xlabel('No. of
samples'); % laeblling x-axis
ylabel('Amplitude');
% labelling y-axis
title('Interpolated Sinuoidal Sequence') % giving title to the plot
% Inference: The obtained sinusoidal sequence was also
subjected for the
% interpolation by the factor L = 2. The Process of
interpolation involves
% resampling the sequence at higher sampling rate using low
pass filter.
% Since the interpolation factor is 2, the samples in
interpolated signal
% must double than that of the original signal and it can be
verfied from
% the plots obtained. Hence the interpolation is also verfied.
Interpolation of the Decimated Signal
L = 2; %
coefficient by which the singal is interpolated
xI = interp(xd,L); %
resamples the sample in x with a rate L times the original rate
subplot(4,1,4)
stem(xI); %
Discrete plot of the input sequence,...
...
where x-axis corresponds to the number of samples
xlabel('No. of
samples'); % labelling x-axis
ylabel('Amplitude');
% labelling y-axis
title('Original Signal Obtained After Interpolating the
Decimated Signal'); % giving title to the graph
% Inference: When a sequence is decimated by a certain factor
and then
% again subjected to the interpolation by the same factor,
original
% sequence can be recovered. This has been verified by the 4th
plot
% on the figure, which is the interpolation of the decimated
signal in the
% 2nd plot. The 4th plot obtained is similar to the input
sequence. So,
% interpolating a decimated signal or decimating a interpolated
signal
% gives the original signal.
