In most of the posts on the CSP Blog we’ve applied the theory and tools of CSP to parameter estimation of one sort or another: cycle-frequency estimation, time-delay estimation, synchronization-parameter estimation, and of course estimation of the spectral correlation, spectral coherence, cyclic cumulant, and cyclic polyspectral functions.

In this post, we’ll switch gears a bit and look at the problem of *waveform estimation*. This comes up in two situations for me: single-sensor processing and array (multi-sensor) processing. At some point, I’ll write a post on array processing for waveform estimation (using, say, the SCORE algorithm The Literature [R102]), but here we restrict our attention to the case of waveform estimation using only a single sensor (a single antenna connected to a single receiver). We just have one observed sampled waveform to work with. There are also waveform estimation methods that are multi-sensor but not typically referred to as array processing, such as the *blind source separation problem* in acoustic scene analysis, which is often solved by principal component analysis (PCA), independent component analysis (ICA), and their variants.

The signal model consists of the noisy sum of two or more modulated waveforms that overlap in both time and frequency. If the signals do not overlap in time, then we can separate them by time gating, and if they do not overlap in frequency, we can separate them using linear time-invariant systems (filters).

Relevant FRESH filtering publications include My Papers [45, 46] and The Literature [R6].

Continue reading “Frequency Shift (FRESH) Filtering for Single-Sensor Cochannel Signal Separation”