DSP Practical - Experiment 9

Aim

To study and perform various window functions, including Rectangular, Hamming, Hanning, and Kaiser windows, using MATLAB.

Problem Statement

In this experiment, you will design and analyze different types of window functions and observe their impact on signal processing tasks like filtering.

Theory

A window function is used in signal processing to shape the frequency response of filters and to reduce spectral leakage. The following window types are covered in this experiment:

Rectangular Window: A simple window that gives sharp cutoff but results in spectral leakage.
Hamming Window: A window that reduces spectral leakage compared to the rectangular window, using a weighted cosine function.
Hanning Window: Similar to the Hamming window, but with a different cosine weighting that provides smoother transitions.
Kaiser Window: A more flexible window function with a parameter that allows for control over the trade-off between mainlobe width and sidelobe attenuation.

MATLAB Code

% MATLAB Code for Various Window Functions

clc;
close all;
clear all;

% Window length
N = 19;
n = 0:1:N-1;

% Rectangular Window
Wr = rectwin(N);

% Hamming Window
Whm = 0.54 - 0.46 * cos(2 * pi * n / (N - 1));

% Hanning Window
Whn = 0.5 - 0.5 * cos(2 * pi * n / (N - 1));

% Kaiser Window
Wk = kaiser(N, 4); % Kaiser window with beta=4

% Plotting all windows
subplot(2, 2, 1);
stem(Wr);
title('Rectangular Window');

subplot(2, 2, 2);
stem(Whm);
title('Hamming Window');

subplot(2, 2, 3);
stem(Whn);
title('Hanning Window');

subplot(2, 2, 4);
stem(Wk);
title('Kaiser Window');

Expected Output

The MATLAB code generates four subplots displaying the following window functions:

Rectangular Window: A simple box-shaped function with constant amplitude.
Hamming Window: A cosine-shaped window that tapers at both ends to reduce side lobes.
Hanning Window: Similar to the Hamming window, but with a different weighting function.
Kaiser Window: A more flexible window that can be tuned to balance mainlobe width and sidelobe suppression.

These plots visually demonstrate the effects of different windowing functions, showcasing their influence on the frequency response and trade-offs in filter design.