Fourier Transform

Fourier Transform is difficult for me. How can i practic this?

Reply to
polian22
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I have some "Gut-Level Fourier Transforms" tutorials at:

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There is also an extensive tutorial section in the Help system of my Daqarta software. That section is available on-line at

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But you are welcome to download the program itself at

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Daqarta includes a signal generator and FFT spectrum analyzer, plus a waveform (scope) display, so you can experiment with the effects of different waveforms, window functions, quantization levels, noise, dither, etc for some "hands on" leaning. Daqarta is nominally $29 shareware, but that's only if you need to analyze external signals via the sound card inputs. The output functions and all the display modes keep on working after the trial period expires. You are welcome to use it this way for free, for as long as you like. You will not only have a powerful signal generator, but a handy learning tool.

Best regards,

Bob Masta D A Q A R T A Data AcQuisition And Real-Time Analysis

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Scope, Spectrum, Spectrogram, Signal Generator Science with your sound card!

Reply to
Bob Masta

Given a periodic waveform, draw or plot it on a sheet of paper... not a computer screen. Step back and look at it. If it seems to be, on avearge, above or below zero, guess the average value. That is the DC term, the first (actually, the 0th) Fourier component.

You can usually spot a basic repetitive period visually. Now, on a separate piece of paper, draw a sine wave of that "fundamental" period. Hold the sine wave paper under the waveform paper and slide it horizontally. You are trying to visualise how much your input waveform resembles the perfect sine. The best horizontal alignment is the phase of the fundamental (1st) Fourier component, and the relative height of the match is its amplitude.

You can do the higher harmonics this way. Draw a 2F sinewave and see if there'd anything in your original waveform that visually matches up with 2F.

The Fourier math is just a way of accurately quantizing the "resemblence" of your waveform to a set of possible perfect sines. The math is similar to your visual process is actually doing: multiply the input waveform by a sine wave, point by point, and see if the summed products are nonzero, and then how big the sum is.

When you slide the pieces of paper, you are finding the phase where the match is best. The mathematical discrete Fourier operation separates the "match" into sine and cosine components, 0 and 90 degrees, whose sum will be that same best-match phase angle. It's really the same thing; it's just that the mathematical method is too dumb to do the visual slide-for-best-match, so it has to do the math twice, at 0 and 90 degrees.

So: Fourier analysis is a formal way of saying how much a waveform looks like DC, then how much is looks like a low frequency sine, then how much it looks like a 2x sine, etc. The formal mathematical expression of the step-by-step procedure is called a "transform" and is compact but not totally obvious, so take it one step at a time.

John

Reply to
John Larkin

Follow-up: I just uploaded Daqarta v3.03.2, which fixes a bug in v3.03(a) that caused incompatibility with certain recent sound cards/chipsets that declare input and output as separate devices (instead of the more-traditional separate lines on the same device). Also, the earlier v3.03 had a defective build that disabled the free trial system. Sorry for any inconvenience.

Best regards,

Bob Masta D A Q A R T A Data AcQuisition And Real-Time Analysis

formatting link
Scope, Spectrum, Spectrogram, Signal Generator Science with your sound card!

Reply to
Bob Masta

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