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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