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Old 06 December 2013, 00:29   #101
pandy71
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Originally Posted by mc6809e View Post
I know all about reconstruction filters. I asked the question rhetorically so as to illustrate to others that there was an ambiguity in interpreting what the stored waveform really is.
Nope - believe me, your example if antialiasing filter was used and reconstruction filter was used provide always sine - don't ignore Nyquist as it works perfectly.
Use opencalc (or excel) and verify your signal - use spline or cubic line smoothing to simulate lowpass filter.

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Originally Posted by mc6809e View Post
If the Amiga had been built with a programmable reconstruction filter that could be tuned to the waveform output frequency, then it would be a sample player.
So this is why Amiga filter begin cut energy over 4.5kHz - if you sample signal with maximum DMA OCS speed - signal will be oversampled and antialiasing not present - remember - square wave have unlimited spectrum - lowpass filtering make square no longer square bu bandlimited signal thus Nyquist criteria are meet.

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Originally Posted by mc6809e View Post
That fact that it only has a couple of gently sloping fixed low pass filters (and even one of these can be turned off) tells us that simple signal reconstruction and playback was not entirely the goal. Synthesis was also the goal.
Just take LTSpice http://www.linear.com/designtools/software/#LTspice and simulate analog circuitry behind Paula output - you will see how integrator and remain part of filter works.
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Old 06 December 2013, 02:47   #102
mc6809e
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Originally Posted by pandy71 View Post
Nope - believe me, your example if antialiasing filter was used and reconstruction filter was used provide always sine - don't ignore Nyquist as it works perfectly.
Use opencalc (or excel) and verify your signal - use spline or cubic line smoothing to simulate lowpass filter.
I understand that. But real Amigas don't have perfect and infinitely adjustable reconstruction filters with variable cutoff frequencies.

A two point square wave output at 1000 points per second requires a low pass filter with a cutoff frequency of 500 Hz to construct a sine wave. There is no such filter on the Amiga. The cutoff frequency is much higher. To get perfect reconstruction of the original signal, the cutoff frequency must be half the the output frequency and since on the Amiga the output frequency is variable, we'd also have to have a programmable filter.

Quote:
Originally Posted by pandy71 View Post
So this is why Amiga filter begin cut energy over 4.5kHz - if you sample signal with maximum DMA OCS speed - signal will be oversampled and antialiasing not present - remember - square wave have unlimited spectrum - lowpass filtering make square no longer square bu bandlimited signal thus Nyquist criteria are meet.
Oh sure. For the highest output rates, the low pass filter starts to be effective as a reconstruction filter. For lower rates, not much at all.

And maybe that's why this discussion has been so contentious. At higher output rates, the Amiga audio hardware performs more like a sample player. At lower output rates it looks more like a synthesizer. The Amiga gives us the choice.

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Originally Posted by pandy71 View Post
Just take LTSpice http://www.linear.com/designtools/software/#LTspice and simulate analog circuitry behind Paula output - you will see how integrator and remain part of filter works.
Thanks for the link!
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Old 06 December 2013, 15:36   #103
pandy71
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Quote:
Originally Posted by mc6809e View Post
I understand that. But real Amigas don't have perfect and infinitely adjustable reconstruction filters with variable cutoff frequencies.

A two point square wave output at 1000 points per second requires a low pass filter with a cutoff frequency of 500 Hz to construct a sine wave. There is no such filter on the Amiga. The cutoff frequency is much higher. To get perfect reconstruction of the original signal, the cutoff frequency must be half the the output frequency and since on the Amiga the output frequency is variable, we'd also have to have a programmable filter.
This is only partially correct - filter is present but his efficiency may be not enough to completely fulfill reconstruction requirement, also it is very important to understand that aliasing is introduced in ADC not in DAC thus even not efficient enough reconstruction filter will perform correctly if signal is without aliasing.


Quote:
Originally Posted by mc6809e View Post
Oh sure. For the highest output rates, the low pass filter starts to be effective as a reconstruction filter. For lower rates, not much at all.

And maybe that's why this discussion has been so contentious. At higher output rates, the Amiga audio hardware performs more like a sample player. At lower output rates it looks more like a synthesizer. The Amiga gives us the choice.

Thanks for the link!
Once again - aliasing is introduced when signal is sampled with to low sample rate i.e. in ADC - DAC will reproduce signal without aliasing even if reconstruction filter is not efficient enough - DAC without oversampling (Amiga case) will introduce additional loss for high frequency signal http://www.maximintegrated.com/app-n...ex.mvp/id/3853 - this can be compensated in analog reconstruction filter or compensated in digital stage (or by additional digital filter before DAC or by software filter that modify samples itself - then you need additional room (bit or 2) or you are forced to accept lower level of signal (peak and rms)).
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