Set cells in matrix equal to sqrt(10^-7), when the cells of the fft of the matrix obey 20.log10(a​bs(mat_tau​))<=-20

I have a complex matrix mat_tau. I want for the cells of mat_tau which obey 20.log10(abs(mat_tau))<=-20 to equal to -70, and the same cells in ifft (mat_tau) to equal sqrt(10^-7). How can I do that?

[demos serghiou]

Sorry, I meant 20.*log10(abs(mat_tau)). Forgot the (*)

[dpb]

Setting a value in the computed value is a simple application of <logical addressing>

But since the FFT is in general complex and symmetric about the origin (DC/zero frequency), setting arbitary locations based solely on magnitude of the spectrum will undoubtedly grossly corrupt the resulting ifft from what the original input signal was.

[demos serghiou]

Thanks for the reply. I just want the noise floor components that are less or equal to -20 to be removed from the ifft and can be set as zero instead of sqrt(10^-7). Any suggestions on how to code it?

[dpb]

Doesn't matter what the value is, destroying the symmetry and values of the FFT will muck up the IFFT drastically.

Unless the input signal is composed of simple sinusoids at the precise frequencies of the FFT bins, then zero-ing out bins in the frequency domain is equivalent to convolving the signal in the time domain with a series of overlapping rectangular windows at those frequencies. This will end up causing "ringing" in the inverse FFT.

Another way to think of it is that removing a given frequency bin is the same as adding the component at that frequency but with opposite phase. This also can be seen to be a bad idea in the time domain.

Answer 1

[Nikhil]

You can use logical indexing.

mat_tau(20.*log10(abs(mat_tau))<=-20) = -70

Similarly for any matrix.