Correlogram in MATLAB

 

Steps to compute correlogram of an input signal

1. Compute the autocorrelation function of narrowband_signal

2. Computes the Fast Fourier Transform (FFT) of the autocorrelation function (acf), resulting in corr_spectrum.

3. freq = (0:N-1)*(fs/N); Constructs a frequency vector (freq) corresponding to the FFT results, spanning from 0 Hz to just under the Nyquist frequency (fs/2). Where, N = Number of Samples in the Input Signal

4. Plots the magnitude of the FFT (abs(corr_spectrum)) against the frequency vector (freq), showing the correlogram of the narrowband signal.

 

Output 

Copy the MATLAB Code from here

% The code is written by SalimWireless.Com % The code is written by SalimWireless.Com clc; clear; close all; % Parameters fs = 1000; t = 0:1/fs:1-1/fs; N = length(t); % Generate narrowband signal f0 = 50; x = sin(2*pi*f0*t) + 0.5*randn(size(t)); % Autocorrelation (biased, unnormalized) acf = xcorr(x, 'biased'); % Keep non-negative lags acf = acf(N:end); % Correlogram (FFT of ACF) Sxx = real(fft(acf)); % One-sided UNNORMALIZED spectrum powerSpec = Sxx(1:floor(N/2)+1); % One-sided scaling (except DC & Nyquist) powerSpec(2:end-1) = 2 * powerSpec(2:end-1); % Frequency axis f = (0:floor(N/2)) * (fs/N); % Plot unnormalized spectrum in dB figure; plot(f, 10*log10(powerSpec)); xlabel('Frequency (Hz)'); ylabel('Power (dB)'); title('Unnormalized Correlogram – Narrowband Signal'); grid on;