[Fpga-synth] phLUTe

[Magnus Danielson]

From: Scott Gravenhorst <music.maker at gte.net>
Subject: Re: [Fpga-synth] phLUTe
Date: Mon, 31 Mar 2008 17:24:17 -0700
Message-ID: <200804010024.m310OHDx014314 at linux7.lan>

> "The making of synthesizers in FPGAs." wrote:
> >Eric Brombaugh wrote:
> >
> >>>> 2) I haven't used LaGrange interpolators before. Do you have a link or 
> >>>> reference to the structure you used here?
> >>> I found this very complete and extremely helpful:
> >>>
> >>> http://www.acoustics.hut.fi/~vpv/publications/vesan_vaitos/ch3_pt2_lagrange.pdf
> >>>
> >>> As you can tell from that sample, the tuning is precise enough for music.
> >> 
> >> Yes - those seem to work just fine. In my wireless communications work I 
> >> use something called a 'Farrow Interpolator' - it's got decent SNR and 
> >> distortion characteristics but it's fairly resource intensive (read 
> >> 'complicated'). I'm interested in learning simpler structures.
> >
> >Hah! Reading through that paper I see in section 3.3.7 that the Farrow 
> >structures I've been using for lo these many years are considered a form 
> >of LaGrange interpolation. Learn something new every day.
> 
> And the LaGrange interpolator I used is actually just a linear interpolator.  The way it works
> sort of reminds me of a potentiometer...
> 
> >I typically use a 3rd order Farrow with 8-tap FIR structures driving the 
> >polynomial chain (see figure 3.14). That eats up a lot of gates.
> 
> Ah, yes, I saw the higher order one, they're required when the signal frequency is a bigger
> proportion of the sample rate.  My sample rate vs my signal frequency was compatible with the
> performance of the much simpler 1st order interpolator, the sample rate is 100KHz and the
> application stays at 5KHz or below. 

Actually, I have been running this as a thesis for some time... that some of
the problems we experience is due to the fact that the low sample rate vs
usefull signal space curves the response-field so much that you run into
troubles. The smaller the relative frequency is... the more like linear analog
it should behave.

Some of the more advanced filter-mappings (Bilinear for instance) causes some
hurdles, but if you run higher sample frequency... simpler mappings may be
used instead as distorsion in response becomes smaller.

In effect, how much simpler does my model becomes if I double the sample rate?
What if I double it again?

For a certain sound quality, I think the processing drops below linear increase
in samplerate at some point. Question is where at the knee we are...

What if we where running at say 1 MHz?

It is kind of interesting actually.

Cheers,
Magnus