I have a smooth but rather complex curve, sampled with a good frequency. I apply the discrete Fourier transform to it using the fast Fourier transform (FFT) algorithm and get its Fourier image. I need to find peaks on the resulting Fourier transform curve, but the image I get contains a substantial amount of noise, which is a real problem because peaks can't be clearly seen. So, my question is as follows: What are the sources of noise in the Fourier transform, and how it can be reduced?
Typical plots look like this:
Initial function Initial function, narrow range Fourier transform Fourier transform, narrow range
Before transformation a constant was subtracted from the the function so that it goes to zero.