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RE: All FIR filters are fatally flawed.

It makes no sense to say that this ringing is non-harmonic. The filter is not adding any frequency components that were not in the original signal.

It makes perfect sense. The fact that the frequency of the ringing is not an integer multiple of the frequency of the signal, by definition, makes it enharmonic. The fact that none of the frequencies output by the filter match the frequency of the input signal, at any time, by definition, makes the output of the filter enharmonic and off pitch. The fact the filter is outputting non-zero samples during periods of time where the input samples are zero, by definition, means the filter is adding frequency components not in the original signal.

The input signal consists of three segments. The first and third are silence and the second consists of two complete cycles of a sine wave. The instantaneous slope at every point of the input signal, plus/minus the quantization error, matches the instantaneous slope at each corresponding point in those idealized segments. The fact the filter sees all frequencies between 0 and Fs/2 is a problem with the filter and not the input signal. The fact that the filter computes each sample point as a weighted average of surrounding samples is a problem with the filter, not the input.

You don’t really need to see the input sample points to conclude the output of DAC W in response to a 10KHz trill is pure fiction.

Here is the same signal processed by DAC A.


Here is the exact same signal, i.e., the exact same frequency, processed by DAC N, a NOS DAC with a minimal, non-brick wall, analog reconstruction filter.


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