# A Challenge for the Machine Learners

## UPDATE

I’ve decided to post the data set I discuss here to the CSP Blog for all interested parties to use. See the new post on the Data Set. If you do use it, please let me and the CSP Blog readers know how you fared with your experiments in the Comments section of either post. Thanks!

# 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 $n$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? Comments on “Energy-Efficient Processor for Blind Signal Classification in Cognitive Radio Networks,” by E. Rebeiz et al.

Let’s talk about another published paper on signal detection involving cyclostationarity and/or cumulants. This one is called “Energy-Efficient Processor 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 distinguished by the use of a single number: the fourth-order cumulant with two conjugated terms. This kind of cumulant is referred to as the $(4, 2)$ cumulant here at the CSP Blog, and in the paper, because the order is $n=4$ and the number of conjugated terms is $m=2$.