The Signal-Processing Equivalent of Resume-Padding? Comments on “A Robust Modulation Classification Method Using Convolutional Neural Networks” by S. Zhou et al.

Does the use of ‘total SNR’ mislead when the fractional bandwidth is very small? What constitutes ‘weak-signal processing?’

Or maybe “Comments on” here should be “Questions on.”

In a recent paper in EURASIP Journal on Advances in Signal Processing (The Literature [R165]), the authors tackle the problem of machine-learning-based modulation recognition for highly oversampled rectangular-pulse digital signals. They don’t use the DeepSig data sets, but their data-set description and use of ‘signal-to-noise ratio’ leaves a lot to be desired. Let’s take a brief look. See if you agree with me that the touting of their results as evidence that they can reliably classify signals with SNRs of -10 dB is unwarranted and misleading.

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SPTK: Examples of Random Variables in Communication-Signal Contexts

Some examples of random variables encountered in communication systems, channels, and mathematical models.

Previous SPTK Post: Random Variables Next SPTK Post: Random Processes

In this Signal Processing ToolKit post, we continue our exploration of random variables. Here we look at specific examples of random variables, which means that we focus on concrete well-defined cumulative distribution functions (CDFs) and probability density functions (PDFs). Along the way, we show how to use some of MATLAB’s many random-number generators, which are functions that produce one or more instances of a random variable with a specified PDF.

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SPTK: Random Variables

Our toolkit expands to include basic probability theory.

Previous SPTK Post: Complex Envelopes Next SPTK Post: Examples of Random Variables

In this Signal Processing ToolKit post, we examine the concept of a random variable.

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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.

Previous SPTK Post: The Moving-Average Filter    Next SPTK Post: Random Variables

In this Signal-Processing Toolkit post, we review the signal-processing steps needed to convert a real-valued sampled-data bandpass signal to a complex-valued sampled-data lowpass signal. The former can arise from sampling a signal that has been downconverted from its radio-frequency spectral band to a much lower intermediate-frequency spectral band. So we want to convert such data to complex samples at zero frequency (‘complex baseband’) so we can decimate them and thereby match the sample rate to the signal’s baseband bandwidth. Subsequent signal-processing algorithms (including CSP of course) can then operate on the relatively low-rate complex-envelope data, which is beneficial because the same number of seconds of data can be processed using fewer samples.

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SPTK: The Moving-Average Filter

A simple and useful example of a linear time-invariant system. Good for smoothing and discovering trends by averaging away noise.

Previous SPTK Post: Ideal Filters             Next SPTK Post: The Complex Envelope

We continue our basic signal-processing posts with one on the moving-average, or smoothing, filter. The moving-average filter is a linear time-invariant operation that is widely used to mitigate the effects of additive noise and other random disturbances from a presumably well-behaved signal. For example, a physical phenomenon may be producing a signal that increases monotonically over time, but our measurement of that signal is corrupted by noise, interference, or flaws in measurement. The moving-average filter can reveal the sought-after trend by suppressing the effects of the unwanted disturbances.

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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.

Previous SPTK Post: Convolution       Next SPTK Post: The Moving-Average Filter

We continue with our non-CSP signal-processing tool-kit series with this post on ideal filtering. Ideal filters are those filters with transfer functions that are rectangular, step-function-like, or combinations of rectangles and step functions.

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Spectral Correlation and Cyclic Correlation Plots for Real-Valued Signals

Spectral correlation surfaces for real-valued and complex-valued versions of the same signal look quite different.

In the real world, the electromagnetic field is a multi-dimensional time-varying real-valued function (volts/meter or newtons/coulomb). But in mathematical physics and signal processing, we often use complex-valued representations of the field, or of quantities derived from it, to facilitate our mathematics or make the signal processing more compact and efficient.

So throughout the CSP Blog I’ve focused almost exclusively on complex-valued signals and data. However, there is a considerable older literature that uses real-valued signals, such as The Literature [R1, R151]. You can use either real-valued or complex-valued signal representations and data, as you prefer, but there are advantages and disadvantages to each choice. Moreover, an author might not be perfectly clear about which one is used, especially when presenting a spectral correlation surface (as opposed to a sequence of equations, where things are often more clear).

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SPTK: Convolution and the Convolution Theorem

Convolution is an essential element in everyone’s signal-processing toolkit. We’ll look at it in detail in this post.

Previous SPTK Post: Interconnection of Linear Systems      Next SPTK Post: Ideal Filters

This installment of the Signal Processing Toolkit series of CSP Blog posts deals with the ubiquitous signal-processing operation known as convolution. We originally came across it in the context of linear time-invariant systems. In this post, we focus on the mechanics of computing convolutions and discuss their utility in signal processing and CSP.

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Are Probability Density Functions “Engineered” or “Hand-Crafted” Features?

The Machine Learners think that their “feature engineering” (rooting around in voluminous data) is the same as “features” in mathematically derived signal-processing algorithms. I take a lighthearted look.

One of the things the machine learners never tire of saying is that their neural-network approach to classification is superior to previous methods because, in part, those older methods use hand-crafted features. They put it in different ways, but somewhere in the introductory section of a machine-learning modulation-recognition paper (ML/MR), you’ll likely see the claim. You can look through the ML/MR papers I’ve cited in The Literature ([R133]-[R146]) if you are curious, but I’ll extract a couple here just to illustrate the idea.

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Stationary Signal Models Versus Cyclostationary Signal Models

What happens when a cyclostationary time-series is treated as if it were stationary?

In this post let’s consider the difference between modeling a communication signal as stationary or as cyclostationary.

There are two contexts for this kind of issue. The first is when someone recognizes that a particular signal model is cyclostationary, and then takes some action to render it stationary (sometimes called ‘stationarizing the signal’). They then proceed with their analysis or algorithm development using the stationary signal model. The second context is when someone applies stationary-signal processing to a cyclostationary signal model, either without knowing that the signal is cyclostationary, or perhaps knowing but not caring.

At the center of this topic is the difference between the mathematical object known as a random process (or stochastic process) and the mathematical object that is a single infinite-time function (or signal or time-series).

A related paper is The Literature [R68], which discusses the pitfalls of applying tools meant for stationary signals to the samples of cyclostationary signals.

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DeepSig’s 2018 Data Set: 2018.01.OSC.0001_1024x2M.h5.tar.gz

The third DeepSig data set I’ve examined. It’s better!

Update February 2021. I added material relating to the DeepSig-claimed variation of the roll-off parameter in a square-root raised-cosine pulse-shaping function. It does not appear that the roll-off was actually varied as stated in Table I of [R137].

DeepSig’s data sets are popular in the machine-learning modulation-recognition community, and in that community there are many claims that the deep neural networks are vastly outperforming any expertly hand-crafted tired old conventional method you care to name (none are usually named though). So I’ve been looking under the hood at these data sets to see what the machine learners think of as high-quality inputs that lead to disruptive upending of the sclerotic mod-rec establishment. In previous posts, I’ve looked at two of the most popular DeepSig data sets from 2016 (here and here). In this post, we’ll look at one more and I will then try to get back to the CSP posts.

Let’s take a look at one more DeepSig data set: 2018.01.OSC.0001_1024x2M.h5.tar.gz.

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More on DeepSig’s RML Data Sets

The second DeepSig data set I analyze: SNR problems and strange PSDs.

I presented an analysis of one of DeepSig’s earlier modulation-recognition data sets (RML2016.10a.tar.bz2) in the post on All BPSK Signals. There we saw several flaws in the data set as well as curiosities. Most notably, the signals in the data set labeled as analog amplitude-modulated single sideband (AM-SSB) were absent: these signals were only noise. DeepSig has several other data sets on offer at the time of this writing:

In this post, I’ll present a few thoughts and results for the “Larger Version” of RML2016.10a.tar.bz2, which is called RML2016.10b.tar.bz2. This is a good post to offer because it is coherent with the first RML post, but also because more papers are being published that use the RML 10b data set, and of course more such papers are in review. Maybe the offered analysis here will help reviewers to better understand and critique the machine-learning papers. The latter do not ever contain any side analysis or validation of the RML data sets (let me know if you find one that does in the Comments below), so we can’t rely on the machine learners to assess their inputs. (Update: I analyze a third DeepSig data set here.)

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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.

Update June 2020

I’ll be adding new papers to this post as I find them. At the end of the original post there is a sequence of date-labeled updates that briefly describe the relevant aspects of the newly found papers. Some machine-learning modulation-recognition papers deserve their own post, so check back at the CSP Blog from time-to-time for “Comments On …” posts.

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SPTK: Frequency Response of LTI Systems

The frequency response of a filter tells you how it scales each and every input sine-wave or spectral component.

Previous SPTK Post: LTI Systems             Next SPTK Post: Interconnection of LTI Systems

We continue our progression of Signal-Processing ToolKit posts by looking at the frequency-domain behavior of linear time-invariant (LTI) systems. In the previous post, we established that the time-domain output of an LTI system is completely determined by the input and by the response of the system to an impulse input applied at time zero. This response is called the impulse response and is typically denoted by h(t).

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SPTK: Linear Time-Invariant Systems

LTI systems, or filters, are everywhere in signal processing. They allow us to adjust the amplitudes and phases of spectral components of the input.

Previous SPTK Post: The Fourier Transform         Next SPTK Post: Frequency Response

In this Signal Processing Toolkit post, we’ll take a first look at arguably the most important class of system models: linear time-invariant (LTI) systems.

What do signal processors and engineers mean by system? Most generally, a system is a rule or mapping that associates one or more input signals to one or more output signals. As we did with signals, we discuss here various useful dichotomies that break up the set of all systems into different subsets with important properties–important to mathematical analysis as well as to design and implementation. Then we’ll look at time-domain input/output relationships for linear systems. In a future post we’ll look at the properties of linear systems in the frequency domain.

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SPTK: The Fourier Transform

An indispensable tool in CSP and all of signal processing!

Previous SPTK Post: The Fourier Series      Next SPTK Post: Linear Systems

This post in the Signal Processing Toolkit series deals with a key mathematical tool in CSP: The Fourier transform. Let’s try to see how the Fourier transform arises from a limiting version of the Fourier series.

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SPTK: The Fourier Series

A crucial tool for developing the temporal parameters of CSP.

Previous SPTK Post: Signal Representations            Next SPTK Post: The Fourier Transform

This installment of the Signal Processing Toolkit shows how the Fourier series arises from a consideration of representing arbitrary signals as vectors in a signal space. We also provide several examples of Fourier series calculations, interpret the Fourier series, and discuss its relevance to cyclostationary signal processing.

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SPTK: Signal Representations

A signal can be written down in many ways. Some of them are more useful than others and can lead to great insights.

Previous SPTK Post: Signals                    Next SPTK Post: Fourier Series

In this Signal Processing ToolKit post, we’ll look at the idea of signal representations. This is a branch of signal-processing mathematics that expresses one signal in terms of one or more signals drawn from a special set, such as the set of all sine waves, the set of harmonically related sine waves, a set of wavelets, a set of piecewise constant waveforms, etc.

Signal representations are a key component of understanding stationary-signal processing tools such as convolution and Fourier series and transforms. Since Fourier series and transforms are an integral part of CSP, signal representations are important for all our discussions at the CSP Blog.

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Signal Processing Toolkit: Signals

Introducing the SPTK on the CSP Blog. Basic signal-processing tools with discussions of their connections to and uses in CSP.

Next SPTK Post: Signal Representations

This is the inaugural post of a new series of posts I’m calling the Signal Processing Toolkit (SPTK).  The SPTK posts will cover relatively simple topics in signal processing that are useful in the practice of cyclostationary signal processing. So, they are not CSP posts, but CSP practitioners need to know this material to be successful in CSP. The CSP Blog is branching out! (But don’t worry, there are more CSP posts coming too.)

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The Ambiguity Function and the Cyclic Autocorrelation Function: Are They the Same Thing?

To-may-to, to-mah-to?

Let’s talk about ambiguity and correlation. The ambiguity function is a core component of radar signal processing practice and theory. The autocorrelation function and the cyclic autocorrelation function, are key elements of generic signal processing and cyclostationary signal processing, respectively. Ambiguity and correlation both apply a quadratic functional to the data or signal of interest, and they both weight that quadratic functional by a complex exponential (sine wave) prior to integration or summation.

Are they the same thing? Well, my answer is both yes and no.

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