How to calculate the power spectra by the power spectra?

Dear Colleagues,

If I have signals A and B, respectively, and how to calculate the power specra of A by the power spectrum of B?

Could you give me some suggestions?

Thank you very much!

Answer 1

[Vidhi Agarwal]

Hi Kathleen,

To calculate the power spectrum of a signal ( A ) using the power spectrum of another signal ( B ), below given steps might help you in getting started:

1. Compute the Fourier Transform of both signals ( A ) and ( B ) to obtain their frequency domain representations.
2. The power spectrum is the square of the magnitude of the Fourier Transform. For signal ( B ), if you already have its power spectrum, you can denote it as ( P_B(f) ).
3. If there is a known linear relationship or transformation between ( A ) and ( B ), such as a filter or a transfer function ( H(f) ), you can use this to relate the power spectra: [ P_A(f) = |H(f)|^2 \cdot P_B(f) ] Here, ( |H(f)|^2 ) is the magnitude squared of the transfer function relating ( A ) to ( B ).
4. If no such relationship is known, directly calculate the Fourier Transform of ( A ) and compute its power spectrum:

For better understanding of Fourier transform, refer to the following documentation:

• https://www.mathworks.com/help/releases/R2020a/symbolic/fourier.html

Hope that helps!