# How to take the FFT of an undersampled signal

I am sampling a 5mhz blocks at an IF of 40 MHZ. I am sampling at 11MHz per bandpass sampling theory, but when I run the FFT I get all the aliases.

So I am trying to figure out how to constrain the fft interpretation to the appropriate bands.

IE i may be sampling the band from 80-85MHz by mixing it down to 37.5-42.5 MHZ and sampling at 11 MHZ. How do I take the FFT and plot it showing the peaks appropriately?

A compressed sensing technique is called "iterative hard thresholding." It's represented by $x^{n+1} = H_K(x^n + FFT(y-FFT^{-1}(x^n))$ where $H_K$ is a nonlinear operator that takes the largest $k$ terms, $y$ your measurements in the time domain, and $x$ your reconstruction in the Fourier domain.