# Tracking period of quasi-periodic transient type signal in strong non-stationary interference

Consider a desired (pink) signal as well as its observation in heavy, non-stationary interference (green, this is the desired signal plus interference). As seen in the plot, the interference can also display quasi-periodic behavior. Initial filtering removed frequency bands where the interference dominated. The post-filtering desired and interfering signals share the same frequency band. Given the observations, I wish to track in real-time the period associated with the desired signal.

Given the frequency overlap, I don't see how additional linear filtering can help further mitigate interference. Also, most of the wavelet denoising approaches I have found in the literature don't have such poor signal-to-interference ratio. Other methods in the literature rely on Empirical Mode Decomposition for denoising, which seem computationally expensive and perhaps not ideally suited to real-time.

Was wondering if anyone here has some ideas for how to handle this admittedly difficult interference mitigation problem. Thanks!

• Is the period of the quasi-periodic interference the same as for the quasi-periodic desired signal? If it's different, you might try some kinda comb filter. Dec 6, 2023 at 6:00
• It's not uncommon for the periods to be "close." In such cases, (assuming precise knowledge of the interference period), the notches in the comb filter would need to be very narrow. @robertbristow-johnson: Are you aware of any efficient narrow-notch comb filter designs?
– rhz
Dec 6, 2023 at 16:36
• rhz, please take a look at the answer I pointed to. Every digital filter, FIR or IIR, is a comb filter of sorts with the comb teeth being spaced apart by the sample rate $f_\mathrm{s}$. So any digital filter design can be adapted to a comb filter design by substituting $e^{-sT}$ in for $z^{-1}$ where $\frac1T$ is the frequency spacing of the teeth in your comb filter. Now $T$ and $2T$ and $3T$ etc. must have fractional-sample precision. That's the second answer in that same question. Designing the passband of a LPF is the same design of the comb teeth shape. Dec 6, 2023 at 19:22