Arrays have incompatible sizes for this operation. Error in CDproydosverdos (line 28) Rx_sample = bsxfun(@times, x(t + lags), x(t)); Related documentation

% Define parameters
fc = 0.002;  % Sinusoidal signal frequency (Hz)
T = 1000;     % Duration of the signal (seconds)
N0 = 2;      % Noise power spectral density (W/Hz)
A = sqrt(2);  % Amplitude of the sinusoidal signal
M = 500;     % Number of realizations for ensemble average

% Generate time vector
t = linspace(0, T, 10001);

% Calculate autocorrelation function components
Rx_sin = A^2 * cos(2*pi*fc*t);
Rx_noise = N0/2 * dirac(t);

% Initialize autocorrelation function and time lags
Rx = zeros(1, length(t));
lags = -T/2:T/2;

% Loop through realizations and time lags
for m = 1:M
  % Generate random phase for each realization
  theta = pi*(2*rand() - 1);

  % Generate noisy sinusoidal signal
  x = A*cos(2*pi*fc*t + theta) + sqrt(N0)*randn(size(t));

  % Calculate autocorrelation for current realization
  Rx_sample = bsxfun(@times, x(t + lags), x(t));%%%%%%%%%%%%%%%ERROR

  % Accumulate average autocorrelation
  Rx = Rx + Rx_sample/M;
end

% Plot autocorrelation function
figure;
plot(lags, Rx);
xlabel('Time lag (seconds)');
ylabel('Autocorrelation');
title('Autocorrelation of Sinusoidal Signal + White Gaussian Noise');

% Add theoretical curve for comparison
hold on;
plot(lags, Rx_sin + Rx_noise, 'r--');
legend('Calculated Autocorrelation', 'Theoretical Autocorrelation');

Answer 1

[Walter Roberson]

t = linspace(0, T, 10001);
%...
  x = A*cos(2*pi*fc*t + theta) + sqrt(N0)*randn(size(t));

x becames a 1 x 10001

  T = 1000;     % Duration of the signal (seconds)
  lags = -T/2:T/2;

lags becomes -500:500 which is 1 x 1001

  Rx_sample = bsxfun(@times, x(t + lags), x(t));%%%%%%%%%%%%%%%ERROR

t is 1 x 10001, logs is 1 x 1001 . You cannot add those two together.

If you could add them together (perhaps generating a 10001 x 1001 array) then the values would range from -500 to 1500, which would not be valid indices for x: indices for x must be positive integers.