Compute Modified Periodogram Using Generated C Code

Create a function periodogram_data.m that returns the modified periodogram power spectral density (PSD) estimate of an input signal using a window. The function specifies a number of discrete Fourier transform points equal to the length of the input signal.

type periodogram_data

function [pxx,f] = periodogram_data(inputData,window)
%#codegen
nfft = length(inputData);
[pxx,f] = periodogram(inputData,window,nfft);
end

Use codegen (MATLAB Coder) to generate a MEX function.

• The %#codegen directive in the function indicates that the MATLAB® code is intended for code generation.

• The -args option specifies example arguments that define the size, class, and complexity of the inputs to the MEX-file. For this example, specify inputData as a 1024-by-1 double precision random vector and window as a Hamming window of length 1024. In subsequent calls to the MEX function, use 1024-sample input signals and windows.

• If you want the MEX function to have a different name, use the -o option.

• If you want to view a code generation report, add the -report option at the end of the codegen command.

codegen periodogram_data -args {randn(1024,1),hamming(1024)}

Code generation successful.

Compute the PSD estimate of a 1024-sample noisy sinusoid using the periodogram function and the MEX function you generated. Specify a sinusoid normalized frequency of $2\pi /5$ rad/sample and a Hann window. Plot the two estimates to verify they coincide.

N = 1024;
x = 2*cos(2*pi/5*(0:N-1)') + randn(N,1);
periodogram(x,hann(N))
[pxMex,fMex] = periodogram_data(x,hann(N));
hold on
plot(fMex/pi,pow2db(pxMex),':','Color',[0 0.4 0])
hold off
grid on
legend('periodogram','MEX function')