A while back I was working with some machine-learning researchers on the problem of carrier-frequency-offset (CFO) estimation. The CFO is the residual carrier frequency exhibited by an imperfectly downconverted radio-frequency signal. I’ll describe it in more detail below. The idea behind the collaboration was to find the SNR, SINR, block-length, etc., ranges for which machine-learning algorithms outperform more traditional approaches, such as those involving exploitation of cyclostationarity. If we’re going to get rid of the feature-based approaches used by experts, then we’d better make sure that the machines can do at least as well as those approaches for the problems typically considered by the experts.

# Cumulants

# Can a Machine Learn the Fourier Transform?

Update: See Part 2 of this post at this link. If you want to leave on comment, leave it on Part 2. Comments closed on this Part 1 post.

# More on Pure and Impure Sine Waves

Remember when we derived the cumulant as the solution to the pure th-order sine-wave problem? It sounded good at the time, I hope. But here I describe a curious special case where the interpretation of the cumulant as the pure component of a nonlinearly generated sine wave seems to break down.

# Cumulant (4, 2) is a Good Discriminator?

Let’s talk about another published paper on signal detection involving cyclostationarity and/or cumulants. This one is called “*Energy-Efficient ProcessorÂ **for Blind Signal Classification in Cognitive Radio Networks*,” (The Literature [R69]), and is authored by UCLA researchers E. Rebeiz and four colleagues.

My focus on this paper it its idea that broad signal-type classes, such as direct-sequence spread-spectrum (DSSS), QAM, and OFDM can be reliably distinguishedÂ by the use of a single number: the fourth-order cumulant with two conjugated terms. This kind of cumulant is referred to as the cumulant here at the CSP Blog, and in the paper, because the order is and the number of conjugated terms is .