[sdiy] Generating a large number of CV outputs

[Roman Sowa]

Unfiltered, steppy, non-oversampled DAC oputput does contain higher 
images of the signal repeated at sampling frequency multiples. If there 
was no images up there, the waveform would not look steppy at all but 
smooth. However, the images do not carry the same power as fundamental 
one, like it would be the case if the samples were very short pulses, 
not steps. The upper images of such steps fade away pretty quickly with 
frequency and even the first one isn't that big either.

If we subtract wanted smooth signal from steppy DAC output, all we get 
is the sampling noise in a form of modulated up and down ramps, almost 
like sawtooth wave of frequency equal to sampling frequency. So this 
will produce images centered at multiples of sampling frequency, with 
amplitude decreasing in a rate of 1/n where n is multiple of sampling 
frequency. The power of first image will be determined by individual 
sample step sizes. In that pathological case of toggling between min and 
max value, resulting "ramp" amplitude is also full scale, so the images 
will be screaming. But in case of regular music signal this will be 
couple of %. Although something like crash cymbal will produce many big 
steps, creating enormous power in upper spectrum.

And since the images are still there, it only takes one nonlinearity in 
the output stage to intermodulate upper unwanted frequencies and 
downshift them to audio range, causing whistles and buzzes all over the 
audio spectrum.

Roman

W dniu 2023-12-14 o 22:27, Gordonjcp pisze:
> On Thu, Dec 14, 2023 at 03:53:39PM +0000, Mike Bryant wrote:
>> If by 'continuous' you mean DC, then there is an image before filtering - at the sampling rate :-)
>>
> 
> No. If you've got a DC output from a DAC, it's just that - DC. There's no change in level. You're writing the same value to it over and over, and it does not change.
> 
> The output from a DAC is continuous. It does not have steps. It has steep slopes, but not steps. Even then, that's not going to allow the sample rate to leak out particularly. If you pick a pathological case where your DAC is swinging fully positive for one sample time and fully negative the next, you'll get a signal at half the sample rate. Even though that's a squarewave right at Nyquist, it still won't alias, because the harmonics are being generated *after* the discrete-time part.
> 
> So I'm having a hard time seeing where these images could come from, or how you'd ever detect them. You definitely couldn't hear them.
>