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| Home Brew Analog Computer System |
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| jahonen:
I think since you have only few coefficients to determine, it could be feasible to just use discretized Fourier analysis to find out the required coefficients. That is easily done by basically multiplying the desired signal against sine and cosine terms, and then summing the results and I think that the results should be multiplied by the time step used (dt). Regards, Janne |
| GK:
Hmmm.... I half follow, but wouldn't I need a great deal more data points for my desired waveform to do any kind of moderately accurate DFT calculation on it? At the moment the waveforms are derived from my hand-drawn figures on graph paper. The coordinate values are entered into the spreadsheet and the smoothing function of Excels chart plotter gives a smooth, continuous function. Is it in some way possible to have Excels chart plotter output "smoothed" functions with the n-th fold increase in data points to a data file rather than a chart diagram? I think my spreadsheet as is would be perfectly adequate if only I could get my hands on that cited Dec. 1947 issue of Electronics. Those guys back in 1958 did the same Fourier synthesis with impressive/adequate accuracy with pen and paper! There is obviously some kind of (most likely quite simple and straightforward) systematic methodology required in adjusting the coefficient values to eventually arrive at the desired result. Googling for hits on "Graphical Fourier Analysis" has been less than enlightening so far. The knowledge seems to be arcane now. |
| GK:
In case anyone wants to have a play, my spreadsheet is attached. The aim of the game is to tweak the coefficient values in orange cells B3 through K3 until the blue synthesized waveform plotted on the chart matches the desired function plotted in pink. Have fun! ;D |
| jahonen:
I did give it a go. I think you only need so much samples so that you don't alias. Then just calculate the Fourier integrals piecewise numerically. That is the approach I did here. FFT is optimized for speed, but I don't think that is the main objective here. For best results, the angle spacing should be uniform, or the difference in angle taken into account for each interval. I did just enter a experimental number of 0.05 which I used to scale down the sums so that results were in the same ballpark you had. Result seems to be vertically offset because I didn't immediately find DC term. I leave it for your judgement if it is any better. Less work for sure. Regards, Janne |
| GK:
Fantastic. Thanks! I really had no idea that an DFT could be done so effectively on my crude and limited set of data points. It's > 1am and I'm new to this Fourier transformation stuff, but how does one go about computing the DC term? This was an issue in that 1958 character generator design, as the toroidal transformers with the series-connected secondaries used to sum the sin and cos terms could not of course pass the DC terms. This caused some wonkyness in the on-screen positioning of some characters relative to the others. However I won't have that issue with my DC-coupled op-amp based summers, so if I can compute the DC terms for each waveform I'll be able to generate an all over better and more accurate display. |
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