The collision of probability, Fourier analysis, and communication-signal models.
Previous SPTK Post: I and Q Next SPTK Post: The Matched Filter
Let’s return to the probability section of the Signal Processing ToolKit posts with a look at the characteristic function, which is the Fourier transform of the probability density function. We will see it has a deep connection to the central mathematical entities of CSP, which are moments and cumulants.
Continue reading “SPTK: The Characteristic Function”“The place where I come from is a small town
They think so small, they use small words
But not me, I’m smarter than that
I worked it out
I’ve been stretching my mouth
To let those big words come right out”
‘Big Time’ by Peter Gabriel
The CSP Blog is now linked-to at the top of cyclostationarity.com, Professor Gardner’s online repository of all things cyclostationary! (See also The Literature [R1].)
Continue reading “The Big Time”“Five different voices behind him bellowed, “REDUCTO!” Five curses flew in five different directions and the shelves opposite them exploded as they hit; the towering structure swayed as a hundred glass spheres burst apart, pearly-white figures unfurled into the air and floated there, their voices echoing from who knew what long-dead past amid the torrent of crashing glass and splintered wood now raining down upon the floor…”
J. K. Rowling, Harry Potter and the Order of the Phoenix
We know that if we subject a cyclostationary signal to a squaring or delay-and-multiply operation we will obtain finite-strength additive sine-wave components at the output of the operation, where at least one of the sine waves has a non-zero frequency.
But I want to make a conjecture: All of CSP can be reduced to interpretations involving sine-wave generation by nonlinear operations. Let’s see if we can show this conjecture is true. After I make my attempt, I’ll also show what ChatGPT comes up with. Any guesses about how well it does?
Continue reading “CSP Reduction to Sine-Wave Generation”A noise-free version of the 2018 CSP Blog dataset CSPB.ML.2018R2 is posted here. This allows researchers to correctly apply propagation-channel effects to the generated signals, and to easily add their own noise at whatever level they wish.
The format of the files is the same as CSPB.ML.2018R2, and the truth parameters for each file are the same as the truth parameters for the corresponding file in CSPB.ML.2018R2, except for SNR, which is infinite.
Continue reading “CSPB.ML.2018R2.NF”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”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”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.
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”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”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.
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.
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]”The Laplace transform easily handles signals that are not Fourier transformable by introducing an exponential damping function inside the transform integral.
Previous SPTK Post: MATLAB’s resample.m Next SPTK Post: Practical Filters
In this Signal Processing ToolKit post, we look at a generalization of the Fourier transform called the Laplace Transform. This is a stepping stone on the way to the Z Transform, which is widely used in discrete-time signal processing, especially in control theory.
Continue reading “SPTK: The Laplace Transform”The cyclostationarity of frequency-shift-keyed signals depends strongly on the way the carrier phase evolves over time. Many distinct cycle-frequency patterns and spectral correlation shapes are possible.
Let’s get back to basics by looking at a large class of signals known as frequency-shift-keyed (FSK) signals. We will leave to the side, for the most part, the very large class of signals that goes by the name of continuous-phase modulation (CPM), which includes continuous-phase FSK (CPFSK), MSK, GMSK, and many more (The Literature [R188]-[R190]). Those are treated in My Papers [8], and in a future CSP Blog post.
Here we want to look at more conventional forms of FSK. These signal types don’t necessarily have a continuous phase function. They are generally easier to demodulate and are more robust to noise and interference than the more complicated CPM signal types, but generally have much lower spectral efficiency. They are like the rectangular-pulse PSK of the FSK/CPM world. But they are still used.
Continue reading “Cyclostationarity of Frequency-Shift-Keyed Signals”Sometimes MATLAB’s resample.m gives results that can be trouble for subsequent CSP.
Previous SPTK Post: Echo Detection Next SPTK Post: The Laplace Transform
In this brief Signal Processing Toolkit note, I warn you about relying on resample.m to increase the sampling rate of your data. It works fine a lot of the time, but when the signal has significant energy near the band edges, it does not.
Continue reading “SPTK Addendum: Problems with resampling using MATLAB’s resample.m”‘By the pricking of my thumbs, something wicked this way comes …’ Macbeth by W. Shakespeare
I attended a conference on dynamic spectrum access in 2017 and participated in a session on automatic modulation recognition. The session was connected to a live competition within the conference where participants would attempt to apply their modulation-recognition system to signals transmitted in the conference center by the conference organizers. Like a grand modulation-recognition challenge but confined to the temporal, spectral, and spatial constraints imposed by the short-duration conference.
What I didn’t know going in was the level of frustration on the part of the machine-learner organizers regarding the seeming inability of signal-processing and machine-learning researchers to solve the radio-frequency scene analysis problem once and for all. The basic attitude was ‘if the image-processors can have the AlexNet image-recognition solution, and thereby abandon their decades-long attempt at developing serious mathematics-based image-processing theory and practice, why haven’t we solved the RFSA problem yet?’
Continue reading “Is Radio-Frequency Scene Analysis a Wicked Problem?”The next step in dataset complexity at the CSP Blog: cochannel signals.
I’ve developed another dataset for use in assessing modulation-recognition algorithms (machine-learning-based or otherwise) that is more complex than the original sets I posted for the ML Challenge (CSPB.ML.2018 and CSPB.ML.2022). Half of the new dataset consists of one signal in noise and the other half consists of two signals in noise. In most cases the two signals overlap spectrally, which is a signal condition called cochannel interference.
We’ll call it CSPB.ML.2023.
Continue reading “PSK/QAM Cochannel Dataset for Modulation Recognition Researchers [CSPB.ML.2023]”The CSP Blog recently received a comment from a signal processor that needed a small amount of debugging help with their python spectral correlation estimator code.
The code uses a form of the time-smoothing method and aims to compute and plot the spectral correlation estimate as well as the corresponding coherence estimate. What is cool about this code is that it is clear, well-organized, on github, and is written using Jupyter Notebook. Moreover, there is a Google Colab function so that anyone can run the code from a chrome browser and see the results, even a python newbie like me. Tres moderne.
Continue reading “CSP Community Spotlight: A Publicly Available python-Based SCF Estimator”And now for something completely different …
Let’s take an excursion outside of “Understanding and Using the Statistics of Communication Signals” by looking at a naturally occurring signal: the human genome.
Continue reading “Desultory CSP: The Human-Genome Edition”“That was excellently observed,” say I, when I read a passage in an author, where his opinion agrees with mine. When we differ, there I pronounce him to be mistaken.
– Jonathan Swift
Update May 2023: Added Professor Gary Smith, author of The AI Delusion, Standard Deviations, and the newer Distrust: Big Data, Data-Torturing, and the Assault on Science.
Update November 2022: Added Professor Dave and Michael Woudenberg. (How could I have forgotten Dave in the first post??)
***
A big part of the CSP Blog in the past couple years has been a critical analysis of relevant engineering literature. By ‘relevant’ I mean relevant to CSP and its main applications of presence detection, modulation recognition, parameter estimation, source separation, and array processing. So I’ve produced many ‘Comments On …’ posts lately, and this tends to solidify my reputation as a critic rather than as a creative engineer. However, the CSP and SPTK posts on the CSP Blog still vastly outnumber the ‘Comments On …’ posts. We’ll see what balance the future brings.
But if you like to see critical reviews of current science, technology, and engineering work, there are others out there doing it much better than me and doing it for much more important topics, such as artificial intelligence, particle physics, cosmology, and social media.
So here in this post I want to introduce you, should you care to view the rest of the post, to other critics that you might enjoy, and might use as a balance against the typically credulous mainstream media and those pundits, bloggers, and YouTubers that do more promoting (influencing?) than analyzing.
Continue reading “Critic and Skeptic Roundup”