Wayne Foletta wrote:

>Mike Keitz is right on the fundamentals of simple resampling - linear
>interpolation does work. You only need to use more complex DSP routines
>if you want to account for sampling aperture (sinc 1/fs rolloff) and
>sample resolution. If the human eye is the observer, 8 bits and linear
>resampling is transparent


Surely the ideal way to do a general resample of the data is via Fourier
Transforms? A fourier transform of your n sample points gives you the
amplitudes of the n/2 freqencies the data contains. You can regenerate data
between samples by summing the sine and cosine values of each of these
freqencies at the given time you need a new data-point.

The fourier transform contains ALL the information contained in the
original data, so what you regenerate will be (calculation accuracy
permitting) as correct as it can be.

So each time you want to shuffle the data down the buffer, you need to do
an FT and an inverse FT (lots of trig calculations for each point.) The
Fast Fourier algorithm will simplify the first part (anyone implemented an
FFT on a PIC?). You might speed up the second part with trig look-up tables.

I think this is going to be SLOW.

I also think that any other resampling approach MUST fail, because other
interpolation methods will introduce contributions that are not present in
the data (like aliasing errors). After a few shuffles, this random garbage
will swamp the original data. (Even with FFT's your rounding errors are
cumulative.) The samples representing early data in your buffer (the ones
that have been shuffled the most) will bear no resemblance to the original
data. Very pretty, but worse than useless because they will be misleading.

There is a more general problem with data sampling:

Unfortunately, with a small fixed number (n) of samples you can only keep
information about a small (n/2) fixed number of freqencies in your data.
These will be equally spaced in the spectrum up to half your sampling rate.
Clearly you want to stop sampling before the highest frequency contained in
the data (half the current sampling rate) falls below the highest frequency
you're interested in. You won't know when this is, unless you already know
something about the data. But if you already know what freqencies you want
to sample you can just pick the right sampling rate from the start! If you
don't know anything about the data (frequency-wise) then you can NEVER be
sure that you've sampled at a freqency that captures the features you might
be looking for.

Any comments anyone?


Alec


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