I believe this is relevant:

   =20
https://secure.wikimedia.org/wikipedia/en/wiki/Noise_shaping#Noise_shaping_=
and_1-bit_converters

    https://secure.wikimedia.org/wikipedia/en/wiki/Delta-sigma_modulation

 From my understanding the interpolation is basically density modulation=20
where the incoming sample value is the density, and the high frequency=20
1-bit output is averaged/low-pass filtered for the audio output.  The=20
precise pulse position is driven by error feedback so that every bit=20
reduces the quantization noise in the passband, while pushing that noise=20
above the hearing threshold into the (internal analog filter's) stopband.

I think all you have to do is arrange the right system clock value and=20
setup your ISR to push per-sample data into the FIFO  (which will happen=20
at the sample rate as the FIFOs get consumed and the ISR called). The=20
sampling rate is set by your system clock (or external clock pin),=20
divided by the DAC divisor, and then the mandatory upsampling divisor of=20
256.  So you must carefully set the system clock if you expect to=20
correctly play "normal" audio data at {8,16,22.05,32,44.1,48} ksamples/s.

If you are doing arbitrary frequency synthesis, generally you accumulate=20
a phase term by adding a fractional ((desired_freq / sampling_rate) *=20
(units_per_cycle)) "tuning" term to a fixed-point counter on every=20
sample.   The integer part of the counter is the index into your table. =20
The number of fractional bits sets your frequency precision.  The=20
combination of input tuning value and sample rate determines the phase=20
jitter.  As always, a low-pass filter of your choosing after the analog=20
output will mop up any frequency spikes above the desired frequency, but=20
the phase noise can remain.

Most people use 1/256th of a circle as the unit and use the integer byte=20
to index their waveform table.  As you know, a truncated table is used=20
for symmetrical waveforms such as the sine wave with the high bits of=20
the index used to negate/invert the returned value.


Joe Koberg




On 2011-01-18 18:40, IVP wrote:
> Hi all,
>
> could someone expound a little about interpolation, more
> particularly as implemented on the dsPIC
>
> Here's the relevant section of the 33F64GP802 data sheet
>
> Section 33. Audio Digital-to-Analog Converter (DAC)
>
> http://ww1.microchip.com/downloads/en/DeviceDoc/70211B.pdf
>
> I've had a look around Microchip and found
>
> Piecewise Linear Interpolation
>
> http://ww1.microchip.com/downloads/en/AppNotes/00942A.pdf
>
> which uses a table, not hardware
>
> and generally,
>
> http://en.wikipedia.org/wiki/Upsampling
>
> http://en.wikipedia.org/wiki/Sample_rate_conversion
>
> For example, I have a data table which holds 16-bit values for a
> sine wave, in degree steps (included below if anyone wants it)
>
> Now, if I wanted to output a 1Hz sine wave, that would mean
> retrieving new data each 1/360th (2.78ms) of a second. If it
> was a 1kHz sine wave output, then new data each 1/360,000th
> (2.78us)
>
> Section 33 says -
>
> "The digital interpolation filter up-samples the input signal to
> create additional interpolated data points. The over-sampling
> ratio is 256:1, or 256x the incoming sampling rate. For example,
> a 100 ksps input signal (the maximum sampling rate) produces
> 25.6M data points per second"
>
> So my retrieval rate from a data store is the 'sampling rate' ?
>
> If I interpret correctly,
>
> Table 33-1 shows that if this were data for a variable or irregular
> wave (eg speech or music), the over-sampling clock is set to the
> maximum frequency component. eg for a digitised 44.1kHz signal,
> the over-sampling clock would need to be set to (256 * 44100),
> or 11.289600MHz
>
> To make full use of the interpolation then, is it simply necessary
> to have an over-sampling clock that is only as fast as the highest
> component or should it be *at least* as fast as the highest
> component ?
>
> IOW, if the over-sampling clock is fast enough (256kHz) to
> interpolate data for a 1kHz signal, then how does it interpolate
> just 256 intermediate points at 1Hz ?
>
> Joe
>
> ;0 - 90 degrees, 16-bit decimal
> ;
> ;Signed
> ;
> ;0x7FFF =3D Most positive output voltage
> ;0x0000 =3D Midpoint output voltage
> ;0xFFFF =3D Value just below midpoint
> ;0x8000 =3D Minimum output voltage
>
> ;1st quadrant ->  table
> ;2nd quadrant ->  reverse table
> ;3rd quadrant ->  -table
> ;4th quadrant ->  reverse -table
>
> ;Unsigned
> ;
> ;0xFFFF =3D Most positive output voltage
> ;0x8000 =3D Midpoint output voltage
> ;0x7FFF =3D Value just below midpoint
> ;0x0000 =3D Minimum output voltage
> ;
> ;1st quadrant ->  table + 32768
> ;2nd quadrant ->  reverse (table + 32768)
> ;3rd quadrant ->  32767 - table
> ;4th quadrant ->  reverse (32767 - table)
>
> sine90:  .word     0                          ; 0
>           .word   570, 1143, 1713, 2287, 2857  ; 1 -  5
>           .word  3424, 3994, 4561, 5124, 5688  ; 6 - 10
>           .word  6252, 6812, 7369, 7926, 8480  ;11 - 15
>           .word  9031, 9581,10125,10669,11206  ;16 - 20
>           .word 11744,12275,12802,13327,13848  ;21 - 25
>           .word 14365,14877,15384,15886,16384  ;26 - 30
>           .word 16875,17364,17845,18324,18796  ;31 - 35
>           .word 19261,19720,20175,20621,21063  ;36 - 40
>           .word 21498,21924,22347,22763,23169  ;41 - 45
>           .word 23569,23966,24349,24729,25099  ;46 - 50
>           .word 25466,25820,26168,26508,26839  ;51 - 55
>           .word 27164,27482,27786,28085,28376  ;56 - 60
>           .word 28658,28930,29195,29451,29697  ;61 - 65
>           .word 29933,30162,30381,30592,30791  ;66 - 70
>           .word 30981,31165,31335,31499,31649  ;71 - 75
>           .word 31794,31928,32049,32164,32269  ;76 - 80
>           .word 32364,32449,32524,32587,32642  ;81 - 85
>           .word 32688,32721,32747,32760,32767  ;86 - 90
--=20
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