# Threshold for peak detection of noisy signal in frequency domain

I have a noisy signal (Gaussian Noise) with a known SNR and known Noise variance. This signal contains a number of Frequency components. My ultimate objective is to detect the components of the signal. What is the Threshold formula should I use to detect the peaks of the signal in frequency domain given a certain Pfa (probability of false alarm)?

The following plot is an example of my objective. I want a Threshold that separates my useful components from the noise components (Let's say between 0.6 and 1)

• It looks to me you can get rid of the noise by mirroring the spectrum about 20.5 Hz and subtracting. I suppose this is not actual data but a modeling artifact, say complex quadrature signal in real noise. Jan 18, 2019 at 9:47
• @OlliNiemitalo I didnt get your point. However, this plot is just a sample example. In other cases, the peaks could be spread along the full band. I tried npwgnthresh function in matlab but it didnt give me good threshold Jan 18, 2019 at 20:55