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Cyclostationary Signal Processing – Understanding and Using the Statistics of Communication SignalsUnderstanding and Using the Statistics of Communication SignalsCyclostationary Signal Processing – Understanding and Using the Statistics of Communication Signals Skip to content Cyclostationary Signal Processing Understanding and Using the Statistics of Communication Signals Menu About All Posts My Papers The Literature Datasets Downloads Links Tricorders Vault Help Rants CotM SPTK End-of-Year Blog Notes Hey … I … Oh-oh … I’m still alive… (Alive by Pearl Jam) Hey everybody! I’m still here. I want to wish all of you a Happy New Year! I hope all your signal-processing projects succeed and your math skills grow steadily in 2025. “May your noise be additive and white, and may all your SCFs be right.” Continue reading “End-of-Year Blog Notes” Author Chad SpoonerPosted on December 23, 2024Categories Blog NotesTags Cyclostationary Signal Processing2 Comments on End-of-Year Blog Notes Interference Mitigation Course at GTRI Update December 2024: The likely date for this course at GTRI is February 4-5, 2025. Update September 2024: This course is postponed until Spring 2025. I’ll post further updates here as they become available. I’ll be part of a team of researchers and practicing engineers, led by the estimable Dr. Ryan Westafer, that will be teaching a class on radio-frequency interference mitigation in September. The class is hosted by the Georgia Tech Research Institute (GTRI) and will be held on the Georgia Tech campus on September 10-11, 2024. Continue reading “Interference Mitigation Course at GTRI” Author Chad SpoonerPosted on August 8, 2024December 23, 2024Categories Advanced CSP, FRESH Filtering, Modulation Recognition, Radio Frequency Scene Analysis, Shameless Self-PromotionTags Cyclostationarity, Cyclostationary Signal Processing, Signal ProcessingLeave a comment on Interference Mitigation Course at GTRI Two CSP-Blog Posts Turn 20,000 Oldies but goodies. It took some years, for sure, but my two most-viewed posts have gathered over 20,000 views each: Continue reading “Two CSP-Blog Posts Turn 20,000” Author Chad SpoonerPosted on July 17, 2024Categories Blog Notes, CSP Basics, Shameless Self-PromotionTags Cyclic Autocorrelation, Cyclostationarity, Cyclostationary Signal Processing, Spectral Correlation FunctionLeave a comment on Two CSP-Blog Posts Turn 20,000 Final Snoap Doctoral-Work Journal Paper: My Papers [56] on Novel Network Layers for Modulation Recognition that Generalizes Dr. Snoap’s final journal paper related to his recently completed doctoral work has been published in IEEE Transactions on Broadcasting (My Papers [56]). Continue reading “Final Snoap Doctoral-Work Journal Paper: My Papers [56] on Novel Network Layers for Modulation Recognition that Generalizes” Author Chad SpoonerPosted on July 17, 2024Categories Advanced CSP, Comments On ..., Literature, Machine Learning, Modulation Recognition, Textbook SignalsTags Cyclic Cumulants, Cyclostationary Signal Processing, Machine Learning, Modulation Recognition7 Comments on Final Snoap Doctoral-Work Journal Paper: My Papers [56] on Novel Network Layers for Modulation Recognition that Generalizes SPTK: I and Q Where does IQ (or I/Q) data come from? Previous SPTK Post: Digital Filters Next SPTK Post: TBD Let’s really get into the mathematical details of “IQ data,” a phrase that appears in many CSP Blog posts and an awful lot of machine-learning papers on modulation recognition. Just what are “I” and “Q” anyway? Continue reading “SPTK: I and Q” Author Chad SpoonerPosted on March 16, 2024March 17, 2024Categories Real-World Signals, Signal Modeling, Signal Processing ToolkitTags Signal Processing, Signal Processing Toolkit4 Comments on SPTK: I and Q Desultory CSP: What’s That Under the TV? “Alive in the Superunknown First it steals your Mind, and then it steals your … Soul” –Soundgarden An advantage of using and understanding the statistics of communication signals ™, the basics of signal processing, and the rich details of cyclostationary signal processing is that a practitioner can deal with, to some useful degree, unknown unknowns. The unknown unknowns I’m talking about here on the CSP Blog are, of course, signals. We know about the by-now-familiar known-type detection, multi-class modulation-recognition, and RF scene-analysis problems, in which it is often assumed that we know the signals we are looking for, but we don’t know their times of arrival, some of their parameters, or how they might overlap in time, frequency, and space. Then there are the less-familiar problems involving unknown unknowns. Sometimes we just don’t know the signals we are looking for. We still want to do as good a job on RF scene analysis as we can, but there might be signals in the scene that do not conform to the body of knowledge we have, to date, of manmade RF signals. Or, in modern parlance, we didn’t even know we left such signals out of our neural-network training dataset; we’re a couple steps back from even worrying about generalization, because we don’t even know we can’t generalize since we are ignorant about what to generalize to. In this post I look at the broadcast TV band, seen in downtown Monterey, California, sometime in the recent past. I expect to see ATSC DTV signals (of the older 8VSB/16VSB or the newer OFDM types), and I do. But what else is there? Spoiler: Unknown unknowns. Let’s take a look. Continue reading “Desultory CSP: What’s That Under the TV?” Author Chad SpoonerPosted on February 2, 2024Categories Advanced CSP, Radio Frequency Scene Analysis, Real-World SignalsTags Cyclostationarity, Cyclostationary Signal Processing, SCF Estimation, Signal Processing, Spectral Correlation Function5 Comments on Desultory CSP: What’s That Under the TV? CSPB.ML.2023G1 Another dataset aimed at the continuing problem of generalization in machine-learning-based modulation recognition. This one is a companion to CSPB.ML.2023, which features cochannel situations. Quality datasets containing digital signals with varied parameters and lengths sufficient to permit many kinds of validation checks by signal-processing experts remain in short supply. In this post, we continue our efforts to provide such datasets by offering a companion unlabeled dataset to CSPB.ML.2023. Continue reading “CSPB.ML.2023G1” Author Chad SpoonerPosted on January 31, 2024Categories Advanced CSP, Artificial Intelligence, Machine Learning, Modulation RecognitionTags Cyclostationarity, Cyclostationary Signal Processing, Machine Learning, Modulation Recognition, Textbook Signals2 Comments on CSPB.ML.2023G1 Stupid Laws Getting In My Way A kvetch. As the generative-AI crowd continues to feast on copyrighted material of all kinds, they are getting pushback in the form of lawsuits from artists, writers, and journalists. I discussed this recently with Dan and Eunice on the CSP Blog. Open AI in particular seems to believe they have some kind of divine right to pursue whatever business they want, whether it is legal or not. Because reasons … including national security … and “meeting the needs of today’s citizens.” But probably just greed and hubris. In a statement to the UK’s House of Lords, Open AI says this, and I assume they did so with a straight face, which would have been admirably difficult: Continue reading “Stupid Laws Getting In My Way” Author Chad SpoonerPosted on January 14, 2024Categories Artificial Intelligence, Comments On ..., Machine Learning, RantsLeave a comment on Stupid Laws Getting In My Way SPTK: Digital Filters A look at general linear time-invariant filtering in the discrete-time domain. Previous SPTK Post: The Z Transform   Next SPTK Post: IQ Data Linear shift-invariant systems are often called digital filters when they are designed objects as opposed to found objects, which are models, really, of systems occurring in the natural world. A basic goal of digital filtering is to perform the same kind of function as does an analog filter, but it is used after sampling rather than before. In some cases, the digitally filtered signal is then converted to an analog signal. These ideas are illustrated in Figure 1. Figure 1. A typical role for a linear shift-invariant system, or digital filter, in signal processing. Continue reading “SPTK: Digital Filters” Author Chad SpoonerPosted on January 14, 2024March 16, 2024Categories Convolution, Signal Processing ToolkitTags Signal Processing, Signal Processing ToolkitLeave a comment on SPTK: Digital Filters Introducing Dr. John A. Snoap An expert signal processor. An expert machine learner. All in one person! I am very pleased to announce that my signal-processing, machine-learning, and modulation-recognition collaborator and friend John Snoap has successfully defended his doctoral dissertation and is now Dr. Snoap! I started working with John after we met in the Comments section of the CSP Blog way back in 2019. John was building his own set of CSP software tools and ran into a small bump in the road and asked for some advice. Just the kind of reader I hope for–independent-minded, gets to the bottom of things, and embraces signal processing. As we interacted over email and zoom it became clear that John was thinking of making a contribution in the area of modulation recognition, and was also interested in learning more about machine learning using neural networks. Since I had been recently engaged in hand-to-hand combat with machine learners who were, in my opinion of course, injecting more confusion than elucidation into the field, I figured this might be a friendly way for me to understand machine learning better, and maybe there would be a way or two to marry signal processing with supervised learning. So off we went. Fast forward four years and we’ve published five papers, with a sixth in review, that I believe are trailblazing. John is that rare person that has mastered two very different technical areas: cyclostationary signal processing and deep learning. Because I believe that neural networks do not actually learn the things that we hope they will, but need not-so-gentle nudges toward learning the truly valuable things, a researcher with one foot firmly in the signal-processing world and the other firmly in the machine-learning world has a very bright future indeed. The title of John’s dissertation is Deep-Learning-Based Classification of Digitally Modulated Signals, which he wrote as a student in the Department of Electrical and Computer Engineering at Old Dominion University under the direction of his advisor Professor Dimitrie Popescu. Congratulations Dr. Snoap! And thank you for everything. Author Chad SpoonerPosted on November 16, 2023Categories UncategorizedTags Cyclostationary Signal Processing, Machine Learning7 Comments on Introducing Dr. John A. Snoap Infinity, Periodicity, and Frequency: Comments on a Recent Signal-Processing Perspectives Paper ([R195]) If a tool isn’t appropriate for your problem, don’t blame the tool. Find another one. Let’s take a look at a recent perspectives-style paper published in the IEEE Signal Processing Magazine called “On the Concept of Frequency in Signal Processing: A Discussion [Perspectives],” (The Literature [R195]). While I criticize the paper directly, I’m hoping to use this post to provide my own perspective, and perhaps a bit of a tutorial, on the interrelated concepts of frequency, infinity, sine waves, and signal representations. I appreciate tutorial papers in the signal-processing literature (see, for example, my positive post on Candan’s article about the Dirac delta [impulse] function), because my jaundiced view of the field is such that I think the basics, both of mathematics and communication-related signal-processing, are neglected in favor of fawning over the research flavor of the month. Over time, everybody–students, researchers, professors–is diminished because of this lack of attention to foundations. Continue reading “Infinity, Periodicity, and Frequency: Comments on a Recent Signal-Processing Perspectives Paper ([R195])” Author Chad SpoonerPosted on October 9, 2023January 8, 2024Categories Comments On ..., Literature, Mathematics, RantsTags Foundations, Fourier Series, Fourier Transform, Signal ProcessingLeave a comment on Infinity, Periodicity, and Frequency: Comments on a Recent Signal-Processing Perspectives Paper ([R195]) SPTK: The Z Transform I think of the Z transform as the Laplace transform for discrete-time signals and systems. Previous SPTK Post: Practical Filters Next SPTK Post: Digital Filters In this Signal Processing ToolKit post, we look at the discrete-time version of the Laplace Transform: The Z Transform. Continue reading “SPTK: The Z Transform” Author Chad SpoonerPosted on October 7, 2023March 17, 2024Categories Research Aids, Signal Modeling, Signal Processing ToolkitTags Signal Processing, Signal Processing Toolkit2 Comments on SPTK: The Z Transform CSPB.ML.2022R2: Correcting an RNG Flaw in CSPB.ML.2022 For completeness, I also correct the CSPB.ML.2022 dataset, which is aimed at facilitating neural-network generalization studies. The same random-number-generator (RNG) error that plagued CSPB.ML.2018 corrupts CSPB.ML.2022, so that some of the files in the dataset correspond to identical signal parameters. This makes the CSPB.ML.2018 dataset potentially problematic for training a neural network using supervised learning. In a recent post, I remedied the error and provided an updated CSPB.ML.2018 dataset and called it CSPB.ML.2018R2. Both are still available on the CSP Blog. In this post, I provide an update to CSPB.ML.2022, called CSPB.ML.2022R2. Continue reading “CSPB.ML.2022R2: Correcting an RNG Flaw in CSPB.ML.2022” Author Chad SpoonerPosted on October 2, 2023Categories Artificial Intelligence, Machine Learning, Modulation Recognition, Research Aids, Textbook SignalsTags Cyclostationarity, Cyclostationary Signal Processing, Machine LearningLeave a comment on CSPB.ML.2022R2: Correcting an RNG Flaw in CSPB.ML.2022 CSPB.ML.2018R2: Correcting an RNG Flaw in CSPB.ML.2018 KIRK: Everything that is in error must be sterilised. NOMAD: There are no exceptions. KIRK: Nomad, I made an error in creating you. NOMAD: The creation of perfection is no error. KIRK: I did not create perfection. I created error. I’ve had to update the original Challenge for the Machine Learners post, and the associated dataset post, a couple times due to flaws in my metadata (truth) files. Those were fairly minor, so I just updated the original posts. But a new flaw in CSPB.ML.2018 and CSPB.ML.2022 has come to light due to the work of the estimable research engineers at Expedition Technology. The problem is not with labeling or the fundamental correctness of the modulation types, pulse functions, etc., but with the way a random-number generator was applied in my multi-threaded dataset-generation technique. I’ll explain after the fold, and this post will provide links to an updated version of the dataset, CSPB.ML.2018R2. I’ll keep the original up for continuity and also place a link to this post there. Moreover, the descriptions of the truth files over at CSPB.ML.2018 are still valid–the truth file posted here has the same format as the truth files available on the CSPB.ML.2018 and CSPB.ML.2022 posts. Continue reading “CSPB.ML.2018R2: Correcting an RNG Flaw in CSPB.ML.2018” Author Chad SpoonerPosted on September 25, 2023October 14, 2023Categories Advanced CSP, Machine Learning, Modulation Recognition, Radio Frequency Scene Analysis, Research Aids, Textbook SignalsTags Cyclostationarity, Cyclostationary Signal Processing, Machine Learning6 Comments on CSPB.ML.2018R2: Correcting an RNG Flaw in CSPB.ML.2018 SPTK: Practical Filters We know that ideal filters are not physically possible. Here we take our first steps toward practical–buildable–linear time-invariant systems. Previous SPTK Post: The Laplace Transform Next SPTK Post: The Z Transform Before we translate the Laplace transform from continuous time to discrete time, deriving the Z transform, let’s take a step back and look at practical filters in continuous time. Practical here stands in opposition to ideal as in the ideal lowpass, highpass, and bandpass filters we studied earlier in the SPTK thread. Continue reading “SPTK: Practical Filters” Author Chad SpoonerPosted on September 20, 2023October 7, 2023Categories Convolution, Research Aids, Signal Processing ToolkitTags Filters, Signal Processing, Signal Processing Toolkit2 Comments on SPTK: Practical Filters The Next Logical Step in CSP+ML for Modulation Recognition: Snoap’s MILCOM ’23 Paper [Preview] We are attempting to force a neural network to learn the features that we have already shown deliver simultaneous good performance and good generalization. ODU doctoral student John Snoap and I have a new paper on the convergence of cyclostationary signal processing, machine learning using trained neural networks, and RF modulation classification: My Papers [55] (arxiv.org link here). Previously in My Papers [50-52, 54] we have shown that the (multitudinous!) neural networks in the literature that use I/Q data as input and perform modulation recognition (output a modulation-class label) are highly brittle. That is, they minimize the classification error, they converge, but they don’t generalize. A trained neural network generalizes well if it can maintain high classification performance even if some of the probability density functions for the data’s random variables differ from the training inputs (in the lab) relative to the application inputs (in the field). The problem is also called the dataset-shift problem or the domain-adaptation problem. Generalization is my preferred term because it is simpler and has a strong connection to the human equivalent: we can quite easily generalize our observations and conclusions from one dataset to another without massive retraining of our neural noggins. We can find the cat in the image even if it is upside-down and colored like a giraffe. Continue reading “The Next Logical Step in CSP+ML for Modulation Recognition: Snoap’s MILCOM ’23 Paper [Preview]” Author Chad SpoonerPosted on August 15, 2023September 22, 2023Categories Advanced CSP, Artificial Intelligence, Higher-Order Cyclostationarity, Machine Learning, Modulation Recognition, Textbook SignalsTags Cyclic Cumulants, Cyclostationarity, Cyclostationary Signal Processing, Machine Learning4 Comments on The Next Logical Step in CSP+ML for Modulation Recognition: Snoap’s MILCOM ’23 Paper [Preview] A Gallery of Cyclic Cumulants The third in a series of posts on visualizing the multidimensional functions characterizing the fundamental statistics of communication signals. Let’s continue our progression of galleries showing plots of the statistics of communication signals. So far we have provided a gallery of spectral correlation surfaces and a gallery of cyclic autocorrelation surfaces. Here we introduce a gallery of cyclic-cumulant matrices. When we look at the spectral correlation or cyclic autocorrelation surfaces for a variety of communication signal types, we learn that the cycle-frequency patterns exhibited by modulated signals are many and varied, and we get a feeling for how those variations look (see also the Desultory CSP posts). Nevertheless, there are large equivalence classes in terms of spectral correlation. That simply means that a large number of distinct modulation types map to the exact same second-order statistics, and therefore to the exact same spectral correlation and cyclic autocorrelation surfaces. The gallery of cyclic cumulants will reveal, in an easy-to-view way, that many of these equivalence classes are removed once we consider, jointly, both second- and higher-order statistics. Continue reading “A Gallery of Cyclic Cumulants” Author Chad SpoonerPosted on August 14, 2023July 19, 2024Categories Advanced CSP, Higher-Order Cyclostationarity, Modulation Recognition, Research AidsTags Cyclic Cumulants, Cyclostationarity, Cyclostationary Signal ProcessingLeave a comment on A Gallery of Cyclic Cumulants CSP Blog Interview: Why We Still Need Human Signal Processors with Engineers E. Akamai and D. Peritum What do practicing engineers think of using large-language models like ChatGPT in their research, development, and writing tasks? And is there a future for humans in signal processing? Let’s switch things up a bit here at the CSP Blog by presenting an interview on a technical topic. I interview two characters you might recall from the post on the Domain Expertise Trap: Engineers Dan Peritum and Eunice Akamai. With the splashy entrance of large-language models like ChatGPT into everyday life and into virtually all aspects of science, engineering, and education, we all want to know how our jobs and careers could be affected by widespread use of artificial intelligence constructs like ChatGPT, Dall-E, and Midjourney. In this interview with a couple of my favorite engineers, I get a feel for how non-AI researchers and developers think about the coming changes, and of course how they view the hype, distortions, and fabrications surrounding predictions of those changes. You can find photos of the interviewees and brief biographies at the end of the post. The interview transcript is carefully contrived lightly edited for believability clarity. Continue reading “CSP Blog Interview: Why We Still Need Human Signal Processors with Engineers E. Akamai and D. Peritum” Author Chad SpoonerPosted on July 3, 2023September 3, 2024Categories Artificial Intelligence, Interviews, Machine Learning, Rants, Research AidsTags ChatGPT, Cyclostationary Signal Processing, Signal Processing1 Comment on CSP Blog Interview: Why We Still Need Human Signal Processors with Engineers E. Akamai and D. Peritum Simply Avert Your Eyes Everything is just fine. The IEEE sent me their annual report for 2022. I was wondering how they were responding to the poor quality of many of their published papers, including faked papers and various paper retractions. Let’s take a quick look. Continue reading “Simply Avert Your Eyes” Author Chad SpoonerPosted on June 29, 2023Categories Comments On ..., Literature, Research AidsTags Cyclostationarity, Cyclostationary Signal Processing, Signal Processing3 Comments on Simply Avert Your Eyes Latest Paper on CSP and Deep-Learning for Modulation Recognition: An Extended Version of My Papers [52] Another step forward in the merging of CSP and ML for modulation recognition, and another step away from the misstep of always relying on convolutional neural networks from image processing for RF-domain problem-solving. My Old Dominion colleagues and I have published an extended version of the 2022 MILCOM paper My Papers [52] in the journal MDPI Sensors. The first author is John Snoap, who is one of those rare people that is an expert in signal processing and in machine learning. Bright future there! Dimitrie Popescu, James Latshaw, and I provided analysis, programming, writing, and research-direction support. Continue reading “Latest Paper on CSP and Deep-Learning for Modulation Recognition: An Extended Version of My Papers [52]” Author Chad SpoonerPosted on June 20, 2023Categories Advanced CSP, Higher-Order Cyclostationarity, Literature, Machine Learning, Modulation Recognition, Research Aids, Textbook SignalsTags Cyclic Cumulants, Cyclostationarity, Cyclostationary Signal Processing, Machine Learning9 Comments on Latest Paper on CSP and Deep-Learning for Modulation Recognition: An Extended Version of My Papers [52] Posts pagination Page 1 Page 2 … Page 8 Next page Search the CSP Blog Search for: Search Support the CSP Blog and Keep it Ad-FreeFollow Blog via Email Enter your email address to follow this blog and receive notifications of new posts by email. Email Address Follow Your Host at the CSP BlogChad Spooner on Epistemic Bubbles: Comments on “Modulation Recognition Using Signal Enhancement and Multi-Stage Attention Mechanism” by Lin, Zeng, and Gong.March 5, 2025Welcome to the CSP Blog Abdul! I appreciate your comment. Can you check your email for a question I asked… abdul wahid on Epistemic Bubbles: Comments on “Modulation Recognition Using Signal Enhancement and Multi-Stage Attention Mechanism” by Lin, Zeng, and Gong.March 3, 2025you reviewed my paper and rejected it. and i am proud of it. you gave me very postive reviews and… Chad Spooner on Introducing Dr. John A. SnoapFebruary 21, 2025Thanks Todd! Todd Reinking on Introducing Dr. John A. SnoapFebruary 21, 2025Dr. Snoap's dissertation was released from "embargo" February 2025 and is available at: https://digitalcommons.odu.edu/ece_etds/256/ Chad Spooner on Final Snoap Doctoral-Work Journal Paper: My Papers [56] on Novel Network Layers for Modulation Recognition that GeneralizesFebruary 15, 2025new approach requires a BOI filter I take it the "new approach" is what we have been calling the "novel… student on Final Snoap Doctoral-Work Journal Paper: My Papers [56] on Novel Network Layers for Modulation Recognition that GeneralizesFebruary 14, 2025For me, the key question is why the new approach requires a BOI filter while the cumulant-net does not. It… Chad Spooner on Final Snoap Doctoral-Work Journal Paper: My Papers [56] on Novel Network Layers for Modulation Recognition that GeneralizesFebruary 13, 2025student: Welcome to the CSP Blog! No, I don't have any plans to open source the networks that Dr. Snoap… student on Final Snoap Doctoral-Work Journal Paper: My Papers [56] on Novel Network Layers for Modulation Recognition that GeneralizesFebruary 13, 2025I’m currently experiencing some difficulties implementing the network. Would you mind letting me know if you have any plans to… Chad Spooner on The Cyclic Autocorrelation for Rectangular-Pulse BPSKFebruary 10, 2025Welcome to the CSP Blog Ivan! And thanks much for the question. I also use circular shifts to approximate a… Ivan Ivanov on The Cyclic Autocorrelation for Rectangular-Pulse BPSKFebruary 8, 2025Dr. Spooner, In some examples (https://pysdr.org/content/cyclostationary.html, https://github.com/krono-i2/gr-CycloDSP) , the time shift of x(t) is performed via circular shift. Is this… CSP Blog Post Categories Advanced CSP (61) Artificial Intelligence (5) Audio Signal Processing (1) Blog Notes (22) Comment of the Month (1) Comments On ... (34) Compressive Sensing (1) Convolution (7) CSP Basics (28) first post (1) FRESH Filtering (3) Higher-Order Cyclostationarity (32) Impulsive Noise (3) Interviews (1) Literature (48) Machine Learning (38) Mathematics (1) Modulation Recognition (22) Polyspectrum (7) Radio Frequency Scene Analysis (44) Rants (21) Real-World Signals (31) Research Aids (82) Resolution Analysis (7) RML (7) Shameless Self-Promotion (2) Signal Modeling (57) Signal Processing Toolkit (22) Signal Separation (1) Spectrum Estimation (32) TDOA (1) Textbook Signals (57) Uncategorized (5) Recent Posts End-of-Year Blog Notes December 23, 2024 Interference Mitigation Course at GTRI August 8, 2024 Two CSP-Blog Posts Turn 20,000 July 17, 2024 Final Snoap Doctoral-Work Journal Paper: My Papers [56] on Novel Network Layers for Modulation Recognition that Generalizes July 17, 2024 SPTK: I and Q March 16, 2024 Most Popular Posts The Cyclic Autocorrelation Function The Cycle Detectors For the Beginner at CSP The Spectral Coherence Function CSP Estimators: The FFT Accumulation Method CSP CategoriesCSP Categories Select Category Advanced CSP  (61) Artificial Intelligence  (5) Audio Signal Processing  (1) Blog Notes  (22) Comment of the Month  (1) Comments On …  (34) Compressive Sensing  (1) Convolution  (7) CSP Basics  (28) first post  (1) FRESH Filtering  (3) Higher-Order Cyclostationarity  (32) Impulsive Noise  (3) Interviews  (1) Literature  (48) Machine Learning  (38) Mathematics  (1) Modulation Recognition  (22) Polyspectrum  (7) Radio Frequency Scene Analysis  (44) Rants  (21) Real-World Signals  (31) Research Aids  (82) Resolution Analysis  (7) RML  (7) Shameless Self-Promotion  (2) Signal Modeling  (57) Signal Processing Toolkit  (22) Signal Separation  (1) Spectrum Estimation  (32) TDOA  (1) Textbook Signals  (57) Uncategorized  (5) Blogroll Wikipedia Gaussian Waves Complex to Real The Gritty Engineer Why Evolution is True Sean Carroll (the Physicist) My LinkedIn Profile Sean Carroll: The Biggest Ideas in the Universe Professor Dave Explains Inside the Score Veritasium Wave Walker DSP Gary Marcus–AI We Can Trust Sabine Hossenfelder's Physics Blog CSP Blog Archives CSP Blog Archives Select Month December 2024  (1) August 2024  (1) July 2024  (2) March 2024  (1) February 2024  (1) January 2024  (3) November 2023  (1) October 2023  (3) September 2023  (2) August 2023  (2) July 2023  (1) June 2023  (2) May 2023  (2) April 2023  (1) March 2023  (5) February 2023  (1) January 2023  (3) December 2022  (1) November 2022  (3) September 2022  (2) August 2022  (2) June 2022  (2) May 2022  (3) April 2022  (2) February 2022  (2) January 2022  (1) November 2021  (3) October 2021  (2) September 2021  (2) August 2021  (1) July 2021  (2) June 2021  (1) May 2021  (3) April 2021  (2) February 2021  (2) January 2021  (2) December 2020  (1) November 2020  (2) September 2020  (1) August 2020  (1) July 2020  (1) April 2020  (3) March 2020  (4) February 2020  (1) January 2020  (1) December 2019  (4) August 2019  (1) July 2019  (3) April 2019  (2) March 2019  (2) February 2019  (1) January 2019  (1) October 2018  (1) September 2018  (1) August 2018  (1) June 2018  (2) February 2018  (1) December 2017  (1) November 2017  (2) September 2017  (1) August 2017  (1) June 2017  (1) May 2017  (1) April 2017  (2) March 2017  (1) February 2017  (1) January 2017  (2) December 2016  (2) November 2016  (2) October 2016  (1) September 2016  (1) August 2016  (2) June 2016  (2) May 2016  (2) April 2016  (1) March 2016  (1) February 2016  (3) January 2016  (4) December 2015  (1) November 2015  (3) September 2015  (6) Site NavigationAbout All Posts My Papers The Literature Datasets Downloads Links Tricorders Vault Help Rants CotM SPTK About All Posts My Papers The Literature Datasets Downloads Links Tricorders Vault Help Rants CotM SPTK Cyclostationary Signal Processing cropped-four_hoccs_line.jpg Cyclostationary Signal Processing cropped-four_hoccs_line.jpg / Proudly powered by WordPress Theme: Twenty Sixteen.   Loading Comments...   Write a Comment... 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