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.

Introduction to CSP

How to Create a Simple Cyclostationary Signal: Rectangular-Pulse BPSK

The Cyclic Autocorrelation Function

The Spectral Correlation Function

The Cyclic Autocorrelation for BPSK

The Spectral Correlation Function for BPSK

The Frequency-Smoothing Method of Spectral Correlation Estimation

The Time-Smoothing Method of Spectral Correlation Estimation

The Spectral Coherence Function

Estimation Quality: The Resolution Product

Blind Cycle-Frequency Estimation: The SSCA

Blind Cycle-Frequency Estimation: The FAM

Computational Costs of Second-Order Estimators

The Periodogram

Signal Selectivity

The Cycle Detectors

A Gallery of Spectral Correlation

Verification Guide for Second-Order Estimation

This list leaves out all the posts on higher-order cyclostationarity, all the posts on machine learning, all the posts that present reviews of published technical papers, and a lot of advanced or niche topics. See the Highlights post for a guide to those posts, or just load cyclostationary.blog and read from the bottom up!

A Gallery of Cyclic Correlations

There are some situations in which the spectral correlation function is not the preferred measure of (second-order) cyclostationarity. In these situations, the cyclic autocorrelation (non-conjugate and conjugate versions) may be much simpler to estimate and work with in terms of detector, classifier, and estimator structures. So in this post, I’m going to provide plots of the cyclic autocorrelation for each of the signals in the spectral correlation gallery post. The exceptions are those signals I called feature-rich in the spectral correlation gallery post, such as LTE and radar. Recall that such signals possess a large number of cycle frequencies, and plotting their three-dimensional spectral correlation surface is not helpful as it is difficult to interpret with the human eye. So for the cycle-frequency patterns of feature-rich signals, we’ll rely on the stem-style (cyclic-domain profile) plots in the gallery post.

Continue reading

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 advisor Lewis Franks, and key Gardner students such as William (Bill) Brown.

Continue reading

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!

yearly_totals

I started the CSP Blog in late 2015, so it has taken a bit over three years to get to 100,000 views. I don’t know if that should be considered fast or slow. But I like it anyway.

I want to thank each and every one of the visitors to the CSP Blog. It has reached so many more people that I though it ever would when I started it.

Thank you for all your clicks, comments, emails, and downloads! If you’d like, leave a comment to this post if you have an idea for a post you’d like to see.

Below the fold, some graphics that show the vital statistics of the CSP Blog as of the 100,000 page-view milestone.

Continue reading

Can a Machine Learn a Power Spectrum Estimator?

I continue with my foray into machine learning (ML) by considering whether we can use widely available ML tools to create a machine that can output accurate power spectrum estimates. Previously we considered the perhaps simpler problem of learning the Fourier transform. See here and here.

Along the way I’ll expose my ignorance of the intricacies of machine learning and my apparent inability to find the correct hyperparameter settings for any problem I look at. But, that’s where you come in, dear reader. Let me know what to do!

Continue reading

How we Learned CSP

This post is just a blog post. Just some guy on the internet thinking out loud. If you have relevant thoughts or arguments you’d like to advance, please leave them in the Comments section at the end of the post.

How did we, as people not machines, learn to do cyclostationary signal processing? We’ve successfully applied it to many real-world problems, such as weak-signal detection, interference-tolerant detection, interference-tolerant time-delay estimation, modulation recognition, joint multiple-cochannel-signal modulation recognition (My Papers [25,26,28,38,43]), synchronization (The Literature [R7]), beamforming (The Literature [R102,R103]), direction-finding (The Literature [R104-R106]), detection of imminent mechanical failures (The Literature [R017-R109]), linear time-invariant system identification (The Literature [R110-R115]), and linear periodically time-variant filtering for cochannel signal separation (FRESH filtering) (My Papers [45], The Literature [R6]).

How did this come about? Is it even interesting to ask the question? Well, it is to me. I ask it because of the current hot topic in signal processing: machine learning. And in particular, machine learning applied to modulation recognition (see here and here). The machine learners want to capitalize on the success of machine learning applied to image recognition by directly applying the same sorts of techniques used there to automatic recognition (classification) of the type of a captured man-made electromagnetic wave.

Continue reading

Useful Signal Processing Blogs or Websites?

Update November 1, 2018: A site called feedspot (blog.feedspot.com) contacted me to tell me I made their “Top 10 Digital Signal Processing Blogs, Websites & Newsletters in 2018” list. Weirdly, there are only eight blogs in the list. What’s most important for this post is the other signal processing blogs on the list. So check it out if you are looking for other sources of online signal processing information. Enjoy!  blog.feedspot.com/digital_signal_processing_blogs

***             ***             ***

Some of my CSP posts get a lot of comments asking for help, and that’s a good thing. I continue to try to help readers to help themselves. Throughout my posts, I link terms and methods to webpages that provide tutorial or advanced information, and most of the time that means wikipedia.

But I’d like to be able to refer readers to good websites that discuss related aspects of signal processing and communication signals, such as filtering, spectrum estimation, mathematical models, Fourier analysis, etc. I’ve had little success with the Google searches I’ve tried.

Continue reading

Comments on “Detection of Almost-Cyclostationarity: An Approach Based on a Multiple Hypothesis Test” by S. Horstmann et al

I recently came across the conference paper in the post title (The Literature [R101]). Let’s take a look.

The paper is concerned with “detect[ing] the presence of ACS signals with unknown cycle period.” In other words, blind cyclostationary-signal detection and cycle-frequency estimation. Of particular importance to the authors is the case in which the “period of cyclostationarity” is not equal to an integer number of samples. They seem to think this is a new and difficult problem. By my lights, it isn’t. But maybe I’m missing something. Let me know in the Comments.

Continue reading

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 that I’ll ask below.

Continue reading