All CSP Blog Posts

SPTK (and CSP): Random Processes

The merging of conventional probability theory with signal theory leads to random processes, also known as stochastic processes. The ideas involved with random processes are central to cyclostationary signal processing.

SPTK: The Analytic Signal and Complex Envelope

In signal processing, and in CSP, we often have to convert real-valued data into complex-valued data and vice versa. Real-valued data is in the real world, but complex-valued data is easier to process due to the use of a substantially lower sampling rate.

SPTK: Ideal Filters

Ideal filters have rectangular or unit-step-like transfer functions and so are not physical. But they permit much insight into the analysis and design of real-world linear systems.

All BPSK Signals

An analysis of DeepSig’s 2016.10A data set, used in many published machine-learning papers, and detailed comments on quite a few of those papers.

CSP Resources: The Ultimate Guides to Cyclostationary Random Processes by Professor Napolitano

My friend and colleague Antonio Napolitano has just published a new book on cyclostationary signals and cyclostationary signal processing: Cyclostationary Processes and Time Series: Theory, Applications, and Generalizations, Academic Press/Elsevier, 2020, ISBN: 978-0-08-102708-0. The book is a comprehensive guide to the structure of cyclostationary random processes and signals, and it … Continue reading “CSP Resources: The Ultimate Guides to Cyclostationary Random Processes by Professor Napolitano”

For the Beginner at CSP

Here is a list of links to CSP Blog posts that I think are suitable for a beginner: read them in the order given. How to Obtain Help from the CSP Blog Introduction to CSP How to Create a Simple Cyclostationary Signal: Rectangular-Pulse BPSK The Cyclic Autocorrelation Function The Spectral … Continue reading “For the Beginner at CSP”

On The Shoulders

What modest academic success I’ve had in the area of cyclostationary signal theory and cyclostationary signal processing is largely due to the patient mentorship of my doctoral adviser, William (Bill) Gardner, and the fact that I was able to build on an excellent foundation put in place by Gardner, his … Continue reading “On The Shoulders”

100,000 Page Views!

The CSP Blog has reached 100,000 page views! Also, a while back it passed the “20,000 visitors” milestone. All of this for 53 posts and 10 pages. More to come! I started the CSP Blog in late 2015, so it has taken a bit over three years to get to … Continue reading “100,000 Page Views!”

MATLAB’s SSCA: commP25ssca.m

In this short post, I describe some errors that are produced by MATLAB’s strip spectral correlation analyzer function commP25ssca.m. I don’t recommend that you use it; far better to create your own function.

How we Learned CSP

We learned it using abstractions involving various infinite quantities. Can a machine learn it without that advantage?

CSP Patent: Tunneling

Tunneling == Purposeful severe undersampling of wideband communication signals. If some of the cyclostationarity property remains, we can exploit it at a lower cost.

CSP Blog Highlights

Welcome to the CSP Blog! To help new readers, I’m supplying here links to the posts that have gotten the most attention over the lifetime of the Blog. Omitted from this list are the more esoteric topics as well as most of the posts that comment on the engineering literature. … Continue reading “CSP Blog Highlights”

Automatic Spectral Segmentation

Radio-frequency scene analysis is much more complex than modulation recognition. A good first step is to blindly identify the frequency intervals for which significant non-noise energy exists.

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 is its idea that broad … Continue reading “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.”

Machine Learning and Modulation Recognition: Comments on “Convolutional Radio Modulation Recognition Networks” by T. O’Shea, J. Corgan, and T. Clancy

Update October 2020: Since I wrote the paper review in this post, I’ve analyzed three of O’Shea’s data sets (O’Shea is with the company DeepSig, so I’ve been referring to the data sets as DeepSig’s in other posts): All BPSK Signals, More on DeepSig’s Data Sets, and DeepSig’s 2018 Data … Continue reading “Machine Learning and Modulation Recognition: Comments on “Convolutional Radio Modulation Recognition Networks” by T. O’Shea, J. Corgan, and T. Clancy”

The Periodogram

The periodogram is the scaled magnitude-squared finite-time Fourier transform of something. It is as random as its input–it never converges to the power spectrum.

Cyclic Polyspectra

Higher-order statistics in the frequency domain for cyclostationary signals. As complicated as it gets at the CSP Blog.

Comments on “Cyclostationary Correntropy: Definition and Application” by Fontes et al

I recently came across a published paper with the title Cyclostationary Correntropy: Definition and Application, by Aluisio Fontes et al. It is published in a journal called Expert Systems with Applications (Elsevier). Actually, it wasn’t the first time I’d seen this work by these authors. I had reviewed a similar … Continue reading “Comments on “Cyclostationary Correntropy: Definition and Application” by Fontes et al”

Blog Notes and New-Post Poll

The CSP Blog has been up for about a year, and September 2016 was its best month: record numbers of visitors, page views, and views per visitor. Thanks to all of my readers!

100-MHz Amplitude Modulation? Comments on “Sub-Nyquist Cyclostationary Detection for Cognitive Radio” by Cohen and Eldar

I came across a paper by Cohen and Eldar, researchers at the Technion in Israel. You can get the paper on the Arxiv site here. The title is “Sub-Nyquist Cyclostationary Detection for Cognitive Radio,” and the setting is spectrum sensing for cognitive radio. I have a question about the paper … Continue reading “100-MHz Amplitude Modulation? Comments on “Sub-Nyquist Cyclostationary Detection for Cognitive Radio” by Cohen and Eldar”

Cyclostationarity of Digital QAM and PSK

PSK and QAM signals form the building blocks for a large number of practical real-world signals. Understanding their probability structure is crucial to understanding those more complicated signals.

Signal Processing Operations and CSP

How does the cyclostationarity of a signal change when it is subjected to common signal-processing operations like addition, multiplication, and convolution?

The Cycle Detectors

CSP shines when the problem involves strong noise or cochannel interference. Here we look at CSP-based signal-presence detection as a function of SNR and SIR.

CSP-Based Time-Difference-of-Arrival Estimation

Time-delay estimation can be used to determine the angle-of-arrival of a signal impinging on two spatially separated signals. This estimation problem gets hard when there is cochannel interference present.

Square-Root Raised-Cosine PSK/QAM

SRRC PSK and QAM signals form important components of more complicated real-world communication signals. Let’s look at their second-order cyclostationarity here.

Blog Notes

In the near future, I’ll post on two new topics: Time-Delay Estimation and the Cyclic Polyspectrum. The blog is getting good traffic: But not many comments. So, feel free to comment on this post with your suggestions on topics that you’d like to see discussed on the CSP blog. Now is … Continue reading “Blog Notes”

Conjugation Configurations

Using complex-valued signal representations is convenient but also has complications: You have to consider all possible choices for conjugating different factors in a moment.

Cyclic Temporal Cumulants

Cyclic cumulants are the amplitudes of the Fourier-series components of the time-varying cumulant function for a cyclostationary signal. They degenerate to conventional cumulants when the signal is stationary.

Textbook Signals

Yes, the CSP Blog uses the simplest idealized cyclostationary digital signal–rectangular-pulse BPSK–to connect all the different aspects of CSP. But don’t mistake these ‘textbook’ signals for the real world.

The Spectral Coherence Function

Cross correlation functions can be normalized to create correlation coefficients. The spectral correlation function is a cross correlation and its correlation coefficient is called the coherence.

Signal Selectivity

We can estimate the spectral correlation function of one signal in the presence of another with complete temporal and spectral overlap provided the signal has a unique cycle frequency.

The Spectral Correlation Function

Spectral correlation in CSP means that distinct narrowband spectral components of a signal are correlated-they contain either identical information or some degree of redundant information.

Welcome to the CSP Blog!

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. … Continue reading “Welcome to the CSP Blog!”

4 thoughts on “All CSP Blog Posts”

        1. WordPress gave me a hint on how to restore the pretty version, which I’ve done, but at the expense of disallowing sharing of the posts and the “Like” button. I don’t care about “Likes,” so that’s fine, and people can always email or text the URLs themselves, so this workaround is fine indefinitely.

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