crash course on fourier stuff - Page 1
Forum section: electronics / general

author: Simon
author_rank: Unknown
timestamp: June 29, 2017, 08:19:18 pm
content: I'm at that point in my course where I am studying Fourier, analysis, series and the other one and I'm still not sure what each is assuming they are different.I have hundreds of pages of course material on the subject set in a highly mathematical way and no particular electronic bias (I gather Fourier is used just about everywhere and can therefore be described very abstractly which is particularly helpful if you don't want to write a module for each subject). I'm not really getting it but I'm quite aware that my course modules were not designed to make anything simple and looking further afield is encouraged.Does anyone know of a book or online articles that take some of the pain out and manage to explain things in a structured way as opposed to pages and pages of maths that seems to go on with no overall plan other than making sure it gives you everything to pick the bones out of.

author: f5r5e5d
author_rank: Frequent Contributor
timestamp: June 29, 2017, 08:36:05 pm
content: some likehttp://www.analog.com/media/en/technical-documentation/dsp-book/dsp_book_frontmat.pdfQuote

author: Simon
author_rank: Unknown
timestamp: June 29, 2017, 08:44:59 pm
content: Thank you I will give it a go.

author: Mattjd
author_rank: Regular Contributor
timestamp: June 29, 2017, 08:55:25 pm
content: I can give you a quick type up of how to use Fourier Series to analyze certain circuits.Let's say you're working on a circuit whose voltage source is non-sinusoidal (which means we cannot apply phasor analysis...but we eventually will) yet periodic like say a square wave or triangle wave. To analyze this circuit you must taking the Fourier Series representation of the function describing this square/triangle wave. Take the Fourier Series for say 4 terms. You then analyze the circuit 4 times, one for each term using phasor analysis. You can do this because of the principle of superposition (assuming linear circuit).Fourier Transform I have not learned applications for yet. I have taken complex analysis and am therefore familiar with it, but have not put it to use as I have not taken a signals course yet. Most of my experience with Fourier Series is solving Linear PDE's.

author: technogeeky
author_rank: Frequent Contributor
timestamp: June 29, 2017, 10:01:16 pm
content: Quote from: f5r5e5d on June 29, 2017, 08:36:05 pmFor reference, that link is only the table of contents of the book.This pageshows all of the contents as individual PDFs. Andthis linkis a ZIP file containing all of these PDFs.

author: Howardlong
author_rank: Super Contributor
timestamp: June 29, 2017, 10:15:57 pm
content: The text of choice for DSP IMHO is Rick Lyons' Understanding Digital Signal Processinghttps://www.amazon.co.uk/Understanding-Digital-Signal-Processing-Richard/dp/0137027419Too many texts wade through far too much willy waving academic mathematical proofs, largely irrelevant for most real engineers, and ignore practical aspects. Rick Lyons' book solves a happy medium. The author also does some Streamlining books too which offer tips and tricks to optimise algorithms in resource limited systems.Steven Smith's text is OK, especially as it's free, but I found (and still find) Lyons' text pretty much the bible of DSP for mere mortals.

author: KE5FX
author_rank: Super Contributor
timestamp: June 29, 2017, 10:35:32 pm
content: Agreed, Lyons and Smith are both good for n00bs. A less-common book that I also like a lot is Richard Newbold'sPractical Applications in Digital Signal Processing.If you're a programmer, try picking up Fourier theory this way: first write a simple pair of loops to teach yourself what convolution is by walking through a couple of arrays. Fill one array with a few dozen cycles of on-off pulses, and put a single pulse in the other. Notice that the resulting function has a peak where the two arrays' contents match. Notice the peaks and valleys that result as you 'slide' the arrays relative to each other. Congratulations, now you understand correlation.Now, correlate your square wave with an array of values obtained from a cos() waveform. Do this a few thousand times with cosine waves of various frequencies. Notice how you get peaks at odd multiples of the square wave frequency -- 1x, 3x, 5x, 7x, etc.? Congratulations, now you know what a Fourier transform does. Do the same correlation with a sine function, and the two resulting arrays will have enough information to reconstruct the original square wave.Then you get to meet Prof. Gibbs...

author: Cyberdragon
author_rank: Super Contributor
timestamp: June 30, 2017, 01:00:12 am
content: Introductory Electronics for Scientists and Engineers by Robert E. Simpson has a section on fourier equations. Although it is a very old book so it would have to be an Ebay find or something, unless there is a reprint available.

author: BrianHG
author_rank: Super Contributor
timestamp: June 30, 2017, 03:38:09 am
content: If you are familiar with the basics of what a sine and cosine function is and you want a visualization of how these are used to construct and deconstruct complex waveforms, ie synth a waveform and the reverse fourier analysis of a waveform, this mechanical fourier machine illustrates the mechanics of the math in the above .pdf documents.4 small parts: 1 history.2. Synthesis.3. Analysis.4. (Optional) In depth setup operation.Enjoy.

author: hamster_nz
author_rank: Super Contributor
timestamp: June 30, 2017, 04:41:04 am
content: Are you looking at it for analog or digital applications? They are the same but very different, and knowing one doesn't really help with the other much (or at least for me!)the digital side is quite easy once you 'get it' and can see how the DFT/IDFT moves between the frequency/phase and time/value domains.I've not got to grips with analog the analog stuff (e.g. designing active analogue filters), but if you find a good easy reference for the analog side of thing please post it here!

author: Simon
author_rank: Unknown
timestamp: June 30, 2017, 07:06:49 am
content: Quote from: Howardlong on June 29, 2017, 10:15:57 pmThat is exactly what my course does, all I need to do is solve a few questions in my assignment just to save me the effort of buying the answer

author: alexanderbrevig
author_rank: Frequent Contributor
timestamp: June 30, 2017, 07:11:49 am
content: For me, I had read the maths and knew how to apply it. But my mental understanding of Fourier and especially the transform, changed toward intuition when I saw this:It's probably that it won't have the same effect on everyone, but I highly recommend this presentation.

author: ivaylo
author_rank: Frequent Contributor
timestamp: June 30, 2017, 07:25:48 am
content: Play with these to get a feel for what the math is doing -http://www.fourier-series.com. Some videos are cool, but if math is not your thing ignore those with people writing on boards.

author: Howardlong
author_rank: Super Contributor
timestamp: June 30, 2017, 07:55:13 am
content: Quote from: Simon on June 30, 2017, 07:06:49 amI feel your pain, or at least I did 30+ years ago. Fourier analysis was part of my EE degree course even then, but back then it was strictly batch mode, real time was a pipe dream.Hopefully they won't ask you to code up an FFT yourself. Many of us have, and once you've done it you realize why sometimes reinventing that wheel, while interesting academically, is usually a worthless exercise practically speaking when device vendors have usually already done the hard work for you, and optimized the hell out their solution at the same time.

author: blackbird
author_rank: Regular Contributor
timestamp: June 30, 2017, 12:09:24 pm
content: I can recommend 'Introductory Digital Signal Processing with Computer Applications' by Lynn and Fuerst as I have used this book (albeit in the Dutch translation) during my study with good results. This book is full of useful examples available in C, (yes even) Pascal, Matlab and Maple.

author: rstofer
author_rank: Super Contributor
timestamp: June 30, 2017, 12:57:42 pm
content: If I just needed the answer or I wanted to cross-check my understanding of the principles, I would probably use MatlabHere's a nice example of going back and forth between the time and frequency domains:https://www.mathworks.com/help/matlab/math/fourier-transforms.htmlAs I recall, this stuff was a lot less fun on a slide rule.

author: Octane
author_rank: Regular Contributor
timestamp: June 30, 2017, 03:57:13 pm
content: I like this:http://www.dspguide.com/pdfbook.htmChapters 8-12 for Fourier especially...Michael

author: RoGeorge
author_rank: Super Contributor
timestamp: June 30, 2017, 04:25:16 pm
content: Quote from: alexanderbrevig on June 30, 2017, 07:11:49 amI just watched it. Highlynotrecommended. It is "one of the most confusing seen so far" indeed, as people already wrote in the YouTube comments.

author: albert22
author_rank: Regular Contributor
timestamp: June 30, 2017, 06:49:39 pm
content: Quote from: ivaylo on June 30, 2017, 07:25:48 am+1 very useful to understand fourier transform and others.

author: chris_leyson
author_rank: Super Contributor
timestamp: July 06, 2017, 04:46:38 pm
content: Hi SimonI've just found a book on FFTs whilst tidying up, "the FFT Fundamentals and Concepts" Robert W Ramirez. Written while he was at Tektronix, link is here for PDF copywww.itermoionici.it/letteratura_files/The-FFT-Fundamentals-and-Concepts.pdf. EDIT: The pdf even has a bonus appendix on the use of windows for harmic analysis by Fred Harris, cool, there are window functions I've never even heard of. Seems my hardback copy was published in '85 and has a few extra chapters, the last one gives you a TEK basic listing for the FFT and inverse FFT. I never did get around to properly using the IEEE 488 interface on my 7854.

author: KE5FX
author_rank: Super Contributor
timestamp: July 06, 2017, 08:00:49 pm
content: Quote from: chris_leyson on July 06, 2017, 04:46:38 pmThat's a great document, I'm surprised I haven't run across it before.

author: Simon
author_rank: Unknown
timestamp: July 06, 2017, 08:02:04 pm
content: Thank you, I'll print it out at work and bind it.