Using Large Language Models To Understand Digital Signal Processing Algorithms

I recently needed to understand some detailed timing error detectors for a modem.

I have the books and have implemented a TED before but this algorithm (Gardner's) was new to me to I turned to my current favourite LLM (Chat-GPT v5.1) to explain the algorithm and it saved me hours of reading books. 

If you are stuck understanding an algorithm then I highly recommend this approach as it gives a detailed text based introduction and generates and runs Python code to demonstrate it.

For example: "explain the FFT algorithm" it has provided a great introduction and written a complete FFT function and then compared the results to Numpy. 

In my case, it took 3 attempts to get the code for the TED to compile (it's a complex algorithm) but Chat-GPT automatically detected the errors and kept going until the code ran successfully. 

Numerix-DSP Digital Signal Processing And Machine Learning Videos

Here is a selection of DSP and ML related videos presented by John Edwards

DSP Online Conference

2022 - Building A Tensorflow Lite Neural Network Vibration Classifier, With A Little Help From DSP

2021 - An Introduction To High Efficiency And Multi-rate Digital Filters

2020 - Frequency Domain Signal Processing

TinyML Foundation / Edge AI Foundation

2020 - “Low MIPS & Memory Machine Learning Industrial Vibration Monitoring Solution - AKA Not All AI Applications Are Cat v Dogs on Facebook ;-)

SigLib

SigLib DSP Library Introduction

SigLib Vibration Monitoring Machine Learning Demonstration

Data Science Festival 2020 - Lunch & Learn - "The Frequency Domain And How It Can Be Used To Aid Artificial Intelligence"

The 34th Annual Running Of The University Of Oxford Digital Signal Processing Course Will Be Held Online Again, In 2025

The course first moved online in 2020 and has received excellent reviews from the attendees

The course will run from Wednesday 22 Oct 2025 to Wednesday 26 Nov 2025, with live online classes one afternoon per week.

Based on the classroom course, Digital Signal Processing (Theory and Application), this online course consists of weekly live online tutorials and also includes a software lab that can be run remotely. We'll include all the same material, many of the existing labs and all the interaction of the regular course.

Online tutorials are delivered via Microsoft Teams once each week and practical exercises are set to allow you to practice the theory during the week. 

You will also have access to the course VLE (virtual learning environment) to communicate with other students, view and download course materials and tutor support is available throughout.

Code examples will be provided although no specific coding experience is required. 

The live tutorials will be on Wednesday each week from 13:00 - 14:30 and 15:00 - 16:30 (GMT) with a 30-minute break in between.

You should allow for 10 - 15 hours study time per week in addition to the weekly lessons and tutorials.

After completing the course, you should be able to understand the workings of the algorithms we explore in the course and how they can solve specific signal processing problems.

Full details are available here: https://www.conted.ox.ac.uk/courses/digital-signal-processing-online.

Copyright © 2025 Delta Numerix

The 34th Annual Running Of The University Of Oxford Live Digital Signal Processing Course, In May 2025

The 34th annual running of the University Of Oxford Live Digital Signal Processing course will be running in Oxford, UK, from Tuesday 20th to Friday 23rd May 2025.

The courses are presented by experts from industry for Engineers in industry and over the last 30 years has trained many hundreds of Engineers, from all areas of Science and Engineering.

Here is a summary of the two courses.

Digital Signal Processing (Theory and Application) - Tuesday 20th to Thursday 22nd May 2025.

https://www.conted.ox.ac.uk/courses/digital-signal-processing-theory-and-application

This course provides a good understanding of DSP principles and their implementation and equips the delegate to put the ideas into practice and/or to tackle more advanced aspects of DSP. 'Hands-on' laboratory sessions are interspersed with the lectures to illustrate the taught material and allow you to pursue your own areas of interest in DSP. The hands-on sessions use specially written software running on PCs.

Subjects include:

• Theoretical Foundations
• Digital Filtering
• Fourier Transforms And Frequency Domain Processing
• DSP Hardware And Programming
• ASIC Implementation
• Typical DSP Applications

Digital Signal Processing Implementation (algorithms to optimization) - Friday 23rd May 2025.

A one-day supplement to the Digital Signal Processing course that takes the theory and translates it into practice.

https://www.conted.ox.ac.uk/courses/digital-signal-processing-implementation-algorithms-to-optimisation

The course will include a mixed lecture and demonstration format and has been written to be independent of target processor architecture.

The course will show how to take common DSP algorithms and map them onto common processor architectures. It will also give a guide line for how to choose a DSP device, in particular how to choose and use the correct data word length for any application.

Attendee Feedback From Previous Courses:

John is like a textbook in human form ;-)  

It was informative, enjoyable and stimulating 

Excellent content, very lively thanks to the 2 excellent presenters - Anonymous

A very good introduction to DSP theory

Excellent lecturers! Really useful information and very understandable

Great mix of theory and practice

The lecturers gave a detailed and excellent explanation of the fundamental topics of DSP with real world engineering practice.

This session closes the gap and clears up much confusion between classroom DSP theories and actual DSP implementation.

Very good session, with in-depth discussion on the math and background.

These courses will be held at the University of Oxford, UK

Copyright © 2025 Delta Numerix

Understanding First Order Filters

While sorting through some very old papers I came across a solution to an interesting problem that I I struggled with when I was learning DSP. I have no idea where the original problem came from so I've replicated it here, as best I can remember, along with the solution:

The following first order direct form II filter :

                 w(n)
x(n) -->+-------------------+-->y(n)
        ^         |         ^
        |       +----+      |
        |       |z^-1|      |
        |       +----+      |
        |         |         |
        |         v         |
        ----*-----------*----
           a1  w(n-1)  b1

Is defined by the following equations:

y(n) = w(n) + b1.w(n-1)     (1)

w(n) = x(n) + a1.w(n-1)     (2)

Question: Show the difference equation in terms of y and x ?

Hint: Rearranging to a direct form I filter structure will help.

Solution

Diagramatically

The original system is a Linear Time Invariant (LTI) system so the feedforward and feedback sections can be swapped without changing the system response:

x(n) -------------+-------------->y(n)
         |        ^        |
       +----+     |      +----+
       |z^-1|     |      |z^-1|
       +----+     |      +----+
         |        |        |
         v        |        v
         ----*----+----*----
            b1        a1

Hence:

y(n) = x(n) + b1.x(n-1) + a1.y(n-1)

Mathematically

From (2):

w(n-1) = x(n-1) + a1.w(n-2)     (3)

Substituting (2) and (3) into (1), to compute the output:

y(n) = x(n) + a1.w(n-1) + b1.[x(n-1) + a1.(w(n-2)]     (4)

Rearranging to combine w terms:

y(n) = x(n) + b1.x(n-1) + a1.[w(n-1) + b1.w(n-2)]     (5)

From (1):     y(n-1) = w(n-1) + b1.w(n-2)     (6)

Substituting (6) into (5) gives:

y(n) = x(n) + b1 x(n-1) + a1 y(n-1)

Copyright © 2025 Delta Numerix

Using Generative AI And Large Language Models (LLMs) To Write DSP Code - Autumn 2024 Update

Having previously written a couple of blog posts regarding the use of LLMs to write DSP code, I've spent the last few months working on a project that has shown the landscape has changed dramatically.

The previous blog posts are here:

Using Generative AI And Large Language Models (LLMs) To Write DSP Code

Are Chat-GPT and Google Bard The New Frontier For Writing DSP Code?

At the start of the project, Claude 3.5 Sonnet was a step up from Chat-GPT 3 and Gemini really didn't cut the mustard at all. Then Chat-GPT 4o was released and this is a game changer, it has much more knowledge about the nuances of signal processing libraries such as scipy.signal and while it still struggles sometimes to write C code, I find it is by far the best option.

While I am lucky enough to have paid access to Chat-GPT 4o, not everyone does however there is an option through GitHub Marketplace that should work for most people. The nice thing about this is that you can easily try different LLMs but I find sticking to GPT 4o is the best option for me.

Copyright © 2024 Delta Numerix

Why Mel-frequency Cepstrum Analysis Is Not Always The Ideal Solution For Vibration Analysis

The Mel-frequency Cepstrum (MFC) and it's associated outputs, the Mel-frequency Cepstral Coefficients (MFCCs), are commonly used for speech applications such as speaker and speech recognition, using neural networks. Unfortunately, the nature of the MFC means that it is not always ideally suited to applications such as vibration analysis and predictive maintenance

The MFC uses logarithmicaly spaced frequency banks to replicate how the human ear hears sound. This approach can lead to very large savings in the number of MIPS required for the recognition part of speaker and speech recognition. Unfortunately, this logarithmic frequency space hides frequencies that are closely spaced meaning that this approach is sub-optimal for applications such as machine vibration analysis, where small variations in vibrational frequency can indicate problems with the machine, particularly the bearings.

The following diagram shows a simple Mel-spaced filterbank, with 12 separate filters:

As can be seen from the diagram, resolution of close by frequencies is a particular problem for higher frequency harmonics, where the filters have a wider bandwidth.

The problem can also be seen in the following two images, which are sampled from identical machines running with two different error modes. It can be seen that it is the higher frequency peaks (1 kHz to 2 kHz) that vary the most and this is just the region, for this Mel-spaced filterbank, where the filter bandwidths start to get exessively wide.

Vibration Mode #1

Vibration Mode #2

The solution to this problem is to use a regular Fast Fourier Transform (FFT) for the front-end processing of these types of applications and use spectral analysis of the anticpated vibration modes to observe the frequency resolution required and this will then define the FFT size required for the application.

The SigLib Digital Signal Processing and Machine Learning library includes examples for machine vibration monitoring. These can be found here.

Copyright © 2024 Delta Numerix