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| jahonen:
This calculation which takes account non-uniform spacing of sampling points could be done manually relatively easily with trapezoid rule as follows: - Take an angle a1 and a2, with values x1 and x2. Angles must be in radians. "Sampling" interval for angle should be so dense that x1 and x2 is not aliased. Function should be periodic so that first point is equal to the last point. - Calculate c11=sin(n*a1), c12=sin(n*a2), c13=cos(n*a1), c14=cos(n*a2), where n is desired harmonic number - Calculate piece area with trapezoid rule as (x1*c11+x2*c12)/2*(a2-a1) repeat same for cosine term c13 and c14. a2 and a1 should be so that a2 > a1. - Now make a1=a2 and x1=x2, get new values for a2 and x2. Repeat until all points are calculated. - Sum all sine and cosine areas together, that (should) give sin/cos coefficients for harmonic n DC term is just average of your data points, i.e. coefficients at zeroth harmonic. I don't know if that explanation is of any help but that approach should work. Regards, Janne |
| GK:
Yes, your explanation is very helpful, thanks a lot. Now that the synthesis issue is essentially overcome I can get started on bread boarding the prototype. |
| GK:
Apologies in advance for the potentially daft question, but that the DC component should be the average of my data points is obvious, but how do I incorporate that computed DC term into the computation of the Fourier coefficients such that the resultant waveform synthesized from said coefficients actually incorporates the necessary DC component? EDIT: Duh! I just realised that is of course not possible. I will have to incorporate the DC terms for each characters X and Y waveform separately into my "ROM" with a settable DC-offset for each respective coefficient summing amplifier. That's simple and straightforward enough anyhow. |
| GK:
Well here is the result - from the hand drawn character and listed X and Y data points on graph paper, through to the eventual synthesis of the waveforms in the SPICE circuit simulation, using the Fourier coefficients generated by the Excel spreadsheet DFT. Is that good or what? :D The unit I have designed will essential be a 16 (column) by 8 (row) character screen display. I'll post up further details when I have the prototype up and running with some squiggles drawn out on the CRT. |
| GK:
Figure 8! Even so the figure 8 could return a closed function by itself, the system has a blanked "retrace" interval, so closed function characters require the retrace interval tacked on as an appendage. |
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