Thank you for visiting the CSP blog.

The purpose of this blog is to talk about cyclostationary signals and cyclostationary signal processing (CSP). I’ve been working in the area for nearly thirty years, and over that time I’ve received a lot of requests for help with CSP code and algorithms. I thought it was time to put some of the basics out on the web so everybody could benefit. And I’m hoping to learn from you too.

In future posts, I’ll be showing how to create simple cyclostationary signals, write code for basic CSP estimators and detectors, and discuss papers in the literature.

What is cyclostationarity? It is a property of a class of mathematical models for a large number of signals in the world, most notably man-made modulated radio-frequency signals, like those used by cell phones, broadcast AM/FM/TV, satellites, WiFi modems, and many more systems. The mathematical models can be quite accurate, so we also say that cyclostationarity is a property of the real-world signals themselves.

The key aspect of the model is that cyclostationary signals have probabilistic parameters that vary periodically with time. Traditionally, signals are treated as stationary, which means their parameters do not vary with time. What are these ‘probabilistic parameters?’ Quantities like the mean value, the variance, and higher-order moments. These quantities are defined for both the time-domain signal and for its frequency-domain representation. So we have ‘temporal moments‘ and ‘spectral moments.’ The second-order spectral moment is also called the spectral correlation function (SCF). The SCF is central to many CSP algorithms; a display of the SCF is shown above for a simple bandlimited binary phase-shift keyed (BPSK) signal.

The well-known noise- and interference-tolerance properties of CSP algorithms follow from the periodically time-varying nature of the signals’ parameters.

The most common difficulty I’ve encountered is when a researcher is developing a CSP estimator and is having trouble applying it to their data set. The researchers almost always skip the step of first applying the estimator to a signal with a perfectly known cyclostationary parameters. So, in the next post I’ll describe how to make the simplest digital CS signal, which has known temporal and spectral moments of all orders, so that we can test CSP estimators by comparing their output to the known correct result.

I encourage readers to point out my errors in the comments of my posts and to suggest topics they would like to see covered in future posts. Also, let me know about your application and interests so I can continue to learn too.

I hope you enjoy your time here at the CSP Blog!

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Just stumbled upon your blog. My bad, I suppose, that I didn’t know it existed. I think I’ll learn a lot from it. Keep up the good work!

Bet regards,

Menguc

Great blog! Coming from a non signal processing background, I was having hard time to learn the basics of cyclostationary. Your blog helped me a lot!

Glanced through this and It great to see your amazing work. We all knew you were brilliant nearly 40 years ago.

Thank you so much Professor Lewis! I see you have risen to the top of your field–congratulations! We have both come a long way from those pizza days…

I’m fascinated by the world of CSP. Do you have any recommended lectures or video series for a beginner to gain some intuition of the topics?

Hello B and welcome to the CSP Blog!

I’m so enamored with the written word that I haven’t even thought about a move into video, such as a YouTube channel, or recorded any lectures. My own style of learning is such that I seek out written work much more often than I seek out audio or video work. For example, I really don’t like podcasts–I’d rather read the transcript. Much faster, and I can more easily go back and forth, reread passages, etc.

However, I did a lecture for the Green Bank Observatory [Radio Astronomy] during the pandemic, over Zoom, and they ended up posting it to YouTube:

https://youtu.be/JTfxzHJyuaQ

Well, this

isone of the objectives of the CSP Blog. I do believe it is effective if you start from the first post and proceed chronologically. You can do that by making use of this link.