ECE3340 Numerical Methods |
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Fourier Tutorial Series - 1
graphics for space-dependent functions
ECE 3340 & generic Han Q. Le (c)
1. Review previous
1.1 From HW
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1.2 Different coefficients
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1.3 Still different coefficients
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1.4 Fourier morphing
2-set morph
Code
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3-set morph
Code
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2. Fourier series
See Lecture on Fourier
Some demo
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3. Numerical demos
3.1 House
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A function
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3.2 Castle
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3.2 Multivalue-function: Heart
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Fourier synthesis function V2
test previous
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3.3 Multivalue-function: pine tree
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4. The nature of different-frequency contribution
Why need many frequencies? A look at how each frequency contributes to an image.
4.1 image to be studied
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observe each additional step of each Fourier Component
Code
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4.2 related app
See app page 2.
5. Waveform - pulse synthesis
Below are Fourier coefficients for a few common waveforms. You can adapt these things for your HW, however, you must understand the different codes (functions) and their intended applications. There are those written for graphics output, and those for numerical output.
5.1 Square wave
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5.1.1 Integral
To obtain a Fourier coefficient:
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For coding, use this:
5.1.2 For computation
Demo only. You SHOULD extract, modify, adapt, do whichever needed for your own work.
Code
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5.2 Sawtooth
Code
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5.2.1 Integral
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For coding, use this:
5.2.2 For computation
Demo only. You SHOULD extract, modify, adapt, do whichever needed for your own work.
Code
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5.3 Triangle
Code
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5.3.1 Integral
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For coding, use this:
5.3.2 For computation
Demo only. You SHOULD extract, modify, adapt, do whichever needed for your own work.
Code
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5.4 Exponential
Code
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5.4.1 Integral
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For coding, use this:
5.4.2 For computation
Demo only. You SHOULD extract, modify, adapt, do whichever needed for your own work.
Code
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5.5 Common utilities for the 4 waveforms
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Example:
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6. Concept of bandwidth and pulse duration
6.1 Exponential pulse
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Code
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6.2 Gaussian pulse
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Code
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6.3 Square pulse
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Code
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6.4 Triangle (symmetric ramp) pulse
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Code
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HW on pulse shape
pulse: raised cosine, sech, trapeze.
Pre-classwork and HW project
Each generates a line art graphics that can be done
with Fourier synthesis. Two options:
A- multi-line artwork (minimum 2 non-constant lines)
B- 2 or more single-line artworks and morph them
You have some data in a csv file. Analyze it.