# [PD] tabread4~ "broken" interpolation algorithm - was Re:, Max Smoother Audio than Pd?

Matteo Sisti Sette matteosistisette at gmail.com
Thu Apr 1 18:28:28 CEST 2010

```Charles Henry escribió:
>
> When it comes to the general class of functions with flat spectra, the
> only difference is in phase, right?
> But the error is the same in time domain as in frequency domain thanks
> to the isometric property of the Fourier transform.  Our interpolation
> is the same as a convolution, so we're still just multiplying our
> spectra and the phase comes out differently in each frequency.

I'm not sure I understand what you're saying here about the phase, buy I
think the misleading part of youre reasoning is that you take a concept
that makes sense in the context of stochastic processes, namely assuming
a "flat spectrum", and acritically apply it in the context of
deterministic signals where it has a completely different meaning.

You're trying to restrict the analysis to a convenient (but reasonable)
class of signals, and to assume that the signal to be interpolated, x,
belongs to that class. Right?

It doesn't make any sense, as far as I can see, to assume that the
signal being interpolated belongs to the class of function whose
spectrum has a flat modulus (and any phase).
Why not assuming then, for example, that x(t) is a constant?
(please don't take my tone as sarchastic)

What does make some sense (it is a strong hypothesis but discussing its
plausibility would bring the discussion to a much higher level) is to
treat the signal x as a stochastic process with a given power spectrum -
such as flat, or pink.

But that means that the quantity you're minimizing is no longer an
integral of the signal minus some other signal all squared: it is the
expectation of something.

The power spectrum of a stochastic process x(t) is not the fourier
transform of x(t), it is the fourier transform of tha autocorrelation
function of x (or something like that).

--
Matteo Sisti Sette
matteosistisette at gmail.com
http://www.matteosistisette.com

```