crash course on fourier stuff

[Simon]

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.

[f5r5e5d]

some like http://www.analog.com/media/en/technical-documentation/dsp-book/dsp_book_frontmat.pdf

This book was written for scientists and engineers in a wide variety of fields: physics,
bioengineering, geology, oceanography, mechanical and electrical engineering, to name
just a few. The goal is to present practical techniques while avoiding the barriers of
detailed mathematics and abstract theory. To achieve this goal, three strategies were
employed in writing this book:
First, the techniques are explained, not simply proven to be true through mathematical
derivations. While much of the mathematics is included, it is not used as the primary
means of conveying the information. Nothing beats a few well written paragraphs
supported by good illustrations.
Second, complex numbers are treated as an advanced topic, something to be learned
after the fundamental principles are understood. Chapters 1-29 explain all the basic
techniques using only algebra, and in rare cases, a small amount of elementary
calculus. Chapters 30-33 show how complex math extends the power of DSP,
presenting techniques that cannot be implemented with real numbers alone. Many
would view this approach as heresy! Traditional DSP textbooks are full of complex
math, often starting right from the first chapter.
xiii
Third, very simple computer programs are used. Most DSP programs are written in
C, Fortran, or a similar language. However, learning DSP has different requirements
than using DSP. The student needs to concentrate on the algorithms and techniques,
without being distracted by the quirks of a particular language. Power and flexibility
aren't important; simplicity is critical. The programs in this book are written to teach
DSP in the most straightforward way, with all other factors being treated as secondary.
Good programming style is disregarded if it makes the program logic more clear. For
instance:
ë a simplified version of BASIC is used
ë line numbers are included
ë the only control structure used is the FOR-NEXT loop
ë there are no I/O statements
This is the simplest programming style I could find. Some may think that this book
would be better if the programs had been written in C. I couldn't disagree more.

[Simon]

Thank you I will give it a go.

[Mattjd]

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.

[technogeeky]

some like http://www.analog.com/media/en/technical-documentation/dsp-book/dsp_book_frontmat.pdf

For reference, that link is only the table of contents of the book. This page shows all of the contents as individual PDFs. And this link is a ZIP file containing all of these PDFs.

[Howardlong]

The text of choice for DSP IMHO is Rick Lyons' Understanding Digital Signal Processing https://www.amazon.co.uk/Understanding-Digital-Signal-Processing-Richard/dp/0137027419

Too 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.

[KE5FX]

Agreed, Lyons and Smith are both good for n00bs.  A less-common book that I also like a lot is Richard Newbold's Practical 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...

[Cyberdragon]

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.

[BrianHG]

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.

[hamster_nz]

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!

[Simon]

Too many texts wade through far too much willy waving academic mathematical proofs, largely irrelevant for most real engineers, and ignore practical aspects.

That 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

[alexanderbrevig]

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.

[ivaylo]

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.

[Howardlong]

Too many texts wade through far too much willy waving academic mathematical proofs, largely irrelevant for most real engineers, and ignore practical aspects.

That 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

I 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.

[blackbird]

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.

[rstofer]

If I just needed the answer or I wanted to cross-check my understanding of the principles, I would probably use Matlab

Here's a nice example of going back and forth between the time and frequency domains:

https://www.mathworks.com/help/matlab/math/fourier-transforms.html

As I recall, this stuff was a lot less fun on a slide rule.

[Octane]

I like this:

http://www.dspguide.com/pdfbook.htm

Chapters 8-12 for Fourier especially...

Michael

[RoGeorge]

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.

I just watched it. Highly not recommended. It is "one of the most confusing seen so far" indeed, as people already wrote in the YouTube comments.

[albert22]

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.

+1 very useful to understand fourier transform and others.

[chris_leyson]

Hi Simon
I'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 copy www.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.

[KE5FX]

Hi Simon
I'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 copy www.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.

That's a great document, I'm surprised I haven't run across it before.   

[Simon]

Thank you, I'll print it out at work and bind it.