Random frequency modulation (was [sdiy] Interesting f vs. t graphs of pitch instability)

[Scott Gravenhorst]

Tom Wiltshire <tom at electricdruid.net> wrote:
>Scott,
>
>On 7 Oct 2008, at 14:21, Scott Gravenhorst wrote:
>
>> The sample rates of the GateMan synths are 1.0MHz for the monosynth  
>> and 250KHz for
>> the poly.  The NCOs are based on a phase accumulator design, so  
>> they emulate linear
>> CV for pitch.  Because of this I had to compensate for the control  
>> voltage's action
>> as it moves through it's range.  This is done by multiplying the  
>> noise amplitude by
>> the "CV" (in quotes because it's digital, and the pitch control  
>> signal is an
>> emulation of CV, linear) so that it is scaled properly.  This gives  
>> a consistent
>> effect across the entire pitch range of the synth.
>
>This makes the pitch fluctuation a constant percentage of the pitch,  
>rather than constant number of Hertz, doesn't it?

That is correct.

>My own digital osc design is based on the Korg DWGS oscillators, a  
>phase accumulator followed by a series of bandlimited wavetables. I  
>have a 16-bit "Pitch" variable which represents 8 octaves of  
>frequency, represented logarithmically (A V/Oct CV, if you like).  
>This is then converted via a lookup table into a linear frequency  
>increment.
>So I can add the noise modulation to either the pitch variable  
>(logarithmic) or the frequency increment (linear).
>
>> What I did was to filter the noise through a simple single stage  
>> IIR filter to roll
>> off more and more high frequency energy in the noise waveform to  
>> control whether it's
>> just slow drift (very low Fc) or jumpy drift (medium Fc) or audible  
>> noise (high Fc).
>>  The lower the Fc, the slower the noise signal moves.  Lower Fc  
>> also lowers the
>> overall amplitude of the noise, so there's a multiplier value to  
>> amplify it when
>> needed.
>
>This sounds good. Single-stage IIR is something that even a dsPIC  
>should be able to handle! Will I find filter details in the Gateman  
>notes in any form I can understand?

I got the information to implement the filter from:

 http://www.dspguide.com/pdfbook.htm

Chapter 19 on recursive filters gives the details.  It's very simple and while the
"standard" form uses 2 multiply operations, it can be done without multiplies
(shifts are used instead, but there is a sacrifice in tuning resolution when doing
that.)  Be aware that the total amplitude will decrease as the bandwidth is
constricted.  In order to use the really low end, I had to use wider arithmetic for
that piece of the design.  I don't remember how much, that is also in the source,
probably somewhat cryptically.

I'm not sure how easily the Verilog will translate to assembly or C for you, but all
of the source code is on http://www.fpga.synth.net/ in the Wiki.

>> What I have can do drift times in the 10s of seconds which causes  
>> the NCOs
>> to drift slowly in and out of tune and exhibit the characteristic  
>> slow phasing we all
>> love (the monosynth has 4 NCOs, the poly has 4 NCOs per voice).
>
>How much accuracy does the filter need to be able to cope with such  
>long times? 10's of seconds at the sample rates you mentioned is a  
>LOT of samples. I'd have expected noise to build up in an IIR after  
>so long, but I'm not well versed in digital filtering.

As I mentioned above, when using a very low Fc, (or small bandwidth) the filter
won't work well if the arithmetic width is too small.  I use 18 bit signed for the
rest of the synth, but that piece is wider.  (I _think_ it's 24 bit for the noise
filter, but it could be more - it's been awhile since I've been "in" the design
code).  I originally tried just multiplying the value, but when the actual numbers
use only the lower 3 or 4 bits, you get "chunky" action, not what I wanted.  Using
more bits gives more resolution and smooths out the changes, even when the amplitude
is multiplied to "amplify" if.

>> The system stays in tune within the bounds of the noise signal  
>> because the noise
>> causes the pitch to drift back and forth across "perfect tune" by  
>> even amounts on
>> both sides of it.
>
>Yeah, isn't that a handy property of a good-quality noise signal?!

(c;  64 bit LFSR.

>> I just get a very nice in-tune, but randomly wandering phase change  
>> sound.
>
>Sounds lovely, Scott. Good work.
>
>Thanks for the useful comments too.

You're quite welcome.



-- ScottG
______________________________________________________________
-- Scott Gravenhorst
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