# Efficiently Detecting “edges” in the time frequency plane

Given a signal $y(t)\in\mathbb{R}$ I wish to detect edge patterns. $s(f,t)$ is a time-frequency decomposition of $y(t)$ in some window $(t-n,t+n)$ so that $f$ loosely corresponds to a local frequency. Edges are located where $||s(f,t)|-|s(f+ i,t+j||>\tau$ for some threshold $\tau$ and $i,j\in \{-1,0,1\}$. I do not have a precise model or setting: at present I have been working with $s(f,t)$ being a short-time Fourier transform. My assumption is that there should only be a few such edges locations.

What measurement efficient and time efficient algorithms exist to solve this sort of problem? One can adapt methods of compressive sensing to the computed time frequency distribution but that seems wasteful: one should not have to compute an entire Fourier transform in order to discover these heavy hitters.

• Possibly this discussion on finding the discontinuities of a black-box function would be of interest. – n00b May 28 '12 at 8:55