[music-dsp] Bandlimiting, Aliasing and Reconstructed Signals

robert bristow-johnson rbj at audioimagination.com
Thu Dec 23 11:41:42 EST 2010

On Dec 23, 2010, at 8:56 AM, Charles Turner wrote:

> Here's my limit case: let's assume some typical laptop with CD- 
> quality sound generation capability with a sample rate of 44.1khz  
> and sample size of 16 bits. I create a sinusoidal waveform on the  
> computer with a period of 4,410hz. I choose to create this waveform  
> by feeding 4,410 divisions of the unit circle into a sine function.  
> In other words, I calculate a unique value for each sample of the  
> period at the sample rate of the laptop's D->A converter.

On Dec 23, 2010, at 11:31 AM, Nigel Redmon wrote:

>> 1) Is the synthesized signal aliased? If so, how can we anti-alias  
>> it?
> Technically, there's always aliasing--it's a matter of whether it's  
> in the audio band, and in your example it isn't.

Nigel, i think there is a semantic problem here.  there is a  
conceptual (and real) difference between what an "image" is and what  
an "alias" is.  images are not exactly the same thing as aliases.   
*some* images *become* aliases because they fold over the Nyquist  
frequency.  but this simple sine is not such a case.

>> 2) Is the signal band-limited? If not, do we want it to be, and how  
>> do we do it?
> It is band-limited.

and sufficiently bandlimited that there are no aliases.

>> As this waveform is sent out the DAC, I assume it's subjected to a  
>> zero order hold of approximately 0.023 milliseconds
> Maybe, but the DAC will make up for it--no need to worry about how  
> the DAC does it. For instance, if it uses ZOH, which causes high- 
> freq droop, it will make up for it.

if it is a "conventional" DAC (this would be the convention of 1985  
and earlier) that is not oversampled, then either the processing  
before the DAC (some digital filter) or after the DAC (an analog  
filter) will make up for it.


r b-j                  rbj at audioimagination.com

"Imagination is more important than knowledge."

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