[sdiy] More Xilinx 3E board comments

[Eric Brombaugh]

Magnus Danielson wrote:
> From: James Patchell <patchell at cox.net>
>   
>> For instance...You could easily build up a bank of 512 NCO sawtooth 
>> oscilators...and it would barely be a hicup...with a sample rate of 
>> 97656.25hz @ clk=50MHz...
>>     
> Actually, you could go 36 bit for free, since those blockrams is really 36 bit
> x 512. Running a 36-bit DDS at 50 MHz is trivial. However, you really consume
> 2 blockrams if you want to go to 512 oscillators. You need to store the
> increments somewhere. Still, keeping down at 50 MHz makes is yawn.
>   
I've been doing a lot of work with audio-frequency NCOs over the last 
few months (see my DVCO project page at 
http://kbadc.synth.net/dvco.html) and I can confidently say that using 
the NCO phase output as a sawtooth wave will work well only up to about 
2kHz unless your sample rate is extremely high. Beyond that, aliasing of 
the higher-order harmonics of the sawtooth are a serious problem. I've 
got some samples on the site of a 20Hz-20kHz sweep of sawtooth and 
square at a ~60kHz sample rate that illustrate this.

Although I was working mostly at 192kHz sample rates recently, I did 
some simulations to analyze this and even with a 1.5MHz sample rate the 
sawtooth still sounds nasty. The higher harmonics fall off at 1/n, so 
they're not down more than about 45dB when they bounce off of Nyquist 
and come screaming back down on you. Square waves are just as bad. Using 
lowpass filters to cut the harmonics helps a little, but not enough for 
a really clean sound.

Fortunately, triangle waves are fairly nice, and sine waves are very 
well behaved because neither of them have the sharp edges found in the 
saw and square. Sharp edges are very sensitive to phase jitter at the 
sample rate. Both triangles and sines are simple to implement in 
software and hardware: For triangles, just use the top two bits of the 
NCO phase to mirror and invert the lower-order phase bits. For 
sinewaves, use the triangle values to address a linear->sine lookup 
table in block RAM. Block RAM limits you to a maximum of 4096 
points/wave, but you can do interesting interpolation stuff to increase 
the apparent phase resolution.

There's a reason why so much research has been expended on generating 
bandwidth-limited classical synth waveforms. The easy solutions don't 
sound good and the ones that sound good take a lot of resources.

Eric

PS - I can't wait until after DAFX'06 when Antti's paper on oscillators 
goes up in the proceedings (Assuming that's where he's getting 
published). I've dug up a lot of material on this topic, but I'd really 
like to see his overview of the current technology.