[sdiy] Harmonic bandwidth

[Nicholas Gregorich]

Ben Lincoln wrote:
> On Wed, January 9, 2008 10:35 am, Nicholas Gregorich said:
> 
>> Hmmm, are you using 100Hz as the fundamental? If so the 32nd harmonic is
>> only 3.2kHz. Would inaccuracies due to sample rate become important at
>> this low of a frequency? The 32nd harmonic is 40dB below the fundamental
>> as well.
> 
> I was wondering about what effect different resolutions and sampling rates
> might have on the effect as well. I tried downconverting Tom's sounds to
> 8-bit 11 KHz and didn't hear any difference (other than it sounding
> lower-quality). I don't have audio software at work but was going to try
> using lower-resolution sine waves as the input, rather than adjusting the
> output after the fact, to see if that amplified the effect.
> I have a feeling that while they're both important, the resolution might
> play a larger role than the sampling rate. 65536 potential states for the
> wave to be in at any given sample seems to me like it could lead to a lot
> of inaccuracy when compared to a true sine wave.
> 

When I did my test in MATLAB the data was generated and summed in 64-bit 
floating point and re-quantized to 16 bits for stuffing into the soundcard.

I don't think bit depth has much to do with the differences heard 
between the two samples [I also don't think its a sample rate 
"problem"]. I studied the effects of quantizing a sinusoid with no 
headroom [best case scenario] and I was shocked at how low the bit depth 
could be without ANY audible effect. I was studying quantizing as an 
audio effect and to get the desired results the bit depth had to be 
below 8 bits, or maybe even 6 bits. I think the reasoning is 
quantization error is output as white noise which is not objectionable 
to the human ear. It wasn't until the output waveform looked nearly 
square that the effect became very pronounced.

I guess I should round up those results and post them, but in the mean 
time I'm intrigued with this random phase peculiarity! :)

Nick.