Expected a string scalar or character vector for the parameter name

% Set parameters

f_c = 0.002; % Hz, sinusoidal signal frequency

theta_range = [-pi, pi]; % radians, phase range

T = 1000; % seconds, signal duration

A = sqrt(2); % amplitude for unit average energy

No = 1; % power spectral density of noise

M = 500; % number of realizations for averaging

% Generate time vector

t = linspace(0, T, 10001);

% Autocorrelation function initialization

R_x_tau = zeros(1, length(t));

% Loop for M realizations

for i = 1:M

  % Generate random phase

  theta = theta_range(randi(2))*pi;

  % Generate sinusoidal signal

  x_t = A*cos(2*pi*f_c*t + theta);

  % Generate white Gaussian noise

  noise = randn(size(t)) * sqrt(No/2);

  % Generate signal with noise

  x_t_noise = x_t + noise;

end
% Loop for different tau values

for tau = 1:length(t)

  % Calculate product for current tau

  product_tau = x_t_noise(tau + 1:end) .* x_t_noise(1:end-tau);

  % Calculate and accumulate average product

  R_x_tau(tau) = R_x_tau(tau) + 1/M * mean(product_tau);

end
% Calculate theoretical autocorrelation function

R_x_theo = 2*A^2*cos(2*pi*f_c*t) + 2*No*delta(t);%%%%%%%%%%%%%%%%%%%%ERROR

delta requires RF PCB Toolbox.

% Plot results

figure;

subplot(211);

plot(t, x_t_noise);

xlabel('Time (s)');

ylabel('Signal with Noise');

title('Sinusoidal Signal with White Gaussian Noise');

subplot(212);

plot(t, R_x_tau);

hold on;

plot(t, R_x_theo);

legend('Estimated Autocorrelation', 'Theoretical Autocorrelation');

xlabel('Time (s)');

ylabel('Autocorrelation Function');

title('Autocorrelation Function of Signal with Noise');

[madhan ravi]

What’s delta()? Default delta() requires RF OCB Toolbox

[Sonia]

How can it be an example value for delta?

[madhan ravi]

https://in.mathworks.com/help/symbolic/sym.dirac.html

Answer 1

[Brahmadev]

Hi @Sonia,

I understand that you would like to calculate the autocorrelation using the Dirac Delta function, you can use the 'dirac' function. Please refer to the documentation below for more information.

https://www.mathworks.com/help/symbolic/sym.dirac.html

Hope this helps in resolving your query!