Frequency response of Resample

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Dear Igoristas,

 

A question from a user who is not very good at DSP: What is the frequency response of the Resample function with the default Hanning window? I'd like an analytical solution but googling did not get me very far.

A MWE:

#include <power spectral density>
 
Function MWE()
    //Generate white noise data
    Variable rate = 1e3 // e.g. 1kHz
    Make/O/N=1e6 data = gnoise(1)
    setscale/P x, 0, 1/rate, data
    
    //Generate PSD
    fPowerSpectralDensity(data,256,"Hann",1)
    
    //Downsample and generate PSD of downsampled data
    Variable factor=2
    Duplicate/O data, data_res
    Resample/DOWN=(factor) data_res //Hann window default
    fPowerSpectralDensity(data_res,256/factor,"Hann",1)
End

 

Basically, I'd like to know the frequency-dependent ratio between data_psd and data_res_psd for a given sampling rate and a given factor, analytically. Can somebody please point me in the right direction?