I have data in which the signal we want is a few gaussian peaks superposed on a noisy background in which some of the 'noise' is periodic. Simply suppressing the associated fourier modes is effective (e.g., a 'notch filter') but also suppresses the signal, since it has some power associated with those frequencies.
What is a good approach for removing these periodic signals without removing the corresponding signal?
This figure shows the data (top; with X-axis labeled by pixel #) and the absolute value of its fourier transform (bottom; X-axis is pixel frequency) with relevant regions identified.
An approach I've considered is least-squares fitting a series of sine functions with frequencies limited to the identified range and the signal-containing region masked out, but this is computationally expensive and it is difficult to automatically identify the affected frequency range.