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Welch Method for Spectral Estimation in MATLAB


MATLAB Code

% The code is developed by SalimWireless.com

clc;
clear;
close all;


% Input Signal and Parameters

Fs = 1000; % Sampling frequency
t = 0:1/Fs:0.3; % Time vector
x = cos(2*pi*200*t) + randn(size(t)); % Signal: 200 Hz cosine + noise


% Welch's Method Parameters

segmentLength = 256; % Length of each segment
overlapFraction = 0.5; % Fractional overlap (50%)
overlapSamples = floor(segmentLength * overlapFraction); % Overlap in samples
step = segmentLength - overlapSamples; % Step size
N = length(x); % Length of the input signal



% Define Hann Window

hannWindow = 0.5 * (1 - cos(2 * pi * (0:segmentLength-1)' / (segmentLength - 1)));
windowEnergy = sum(hannWindow.^2); % Normalization factor


% Segment the Signal into Overlapping Windows

numSegments = floor((N - overlapSamples) / step); % Number of segments
segments = zeros(segmentLength, numSegments);

for i = 1:numSegments
startIdx = (i - 1) * step + 1;
endIdx = startIdx + segmentLength - 1;
segments(:, i) = x(startIdx:endIdx);
end


% Initialize PSD Array

psdSum = zeros(floor(segmentLength/2) + 1, 1);


% Process Each Segment

for i = 1:numSegments

% Apply Hann Window to the Segment

windowedSegment = segments(:, i) .* hannWindow;


% Compute FFT of Windowed Segment

fftSegment = fft(windowedSegment);


% Compute One-Sided PSD

segmentPSD = (1 / (Fs * segmentLength * windowEnergy)) * abs(fftSegment(1:floor(segmentLength/2) + 1)).^2;


% Accumulate PSD

psdSum = psdSum + segmentPSD;
end


% Average PSD Over All Segments

psd = psdSum / numSegments;


% Adjust for One-Sided Spectrum (Excluding DC and Nyquist)

psd(2:end-1) = 2 * psd(2:end-1);


% Generate Frequency Axis

frequencies = (0:floor(segmentLength/2)) * (Fs / segmentLength);


% Plot the PSD

figure;
plot(frequencies, 10*log10(psd)); % Plot PSD in dB/Hz
xlabel('Frequency (Hz)');
ylabel('Power Spectral Density (dB/Hz)');
title('Power Spectral Density (Welch’s Method)');
grid on;

Output






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  Interests: Signal Processing, Telecommunication, 5G Technology, Present & Future Wireless Technologies, Digital Signal Processing, Computer Networks, Millimeter Wave Band Channel, Web Development
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