[music-dsp] Re: <no subject>

[Payan, Remi]

OK Iain,
next time I'll read all my e-mails before answering :o)
Sorry :o)

Cheers,
Remi

-----Original Message-----
From: Iain Sandoe [mailto:iain at sandoe.co.uk]
Sent: Tuesday, April 24, 2001 7:41 PM
To: music-dsp at shoko.calarts.edu
Subject: [music-dsp] Re: <no subject>


 
> While playing around with fft in matlab,
> I've realized that if you take a real function,
> transform it, play around with it and then use
> the inverse transform, you no longer have a real
> function. My question is, what do you do?

well, assuming that you *want* a real result... ;-)

the transform of a real signal is hermitian (in the general case) - that is
the positive frequency components are conjugates of the negative.

If you want to end up with a real signal after your 'messing around' - you
must preserve this situation (and adjust negative freq components by the
appropriate factor).

three other things:

1/ transforms are not perfect (there will be some small amount of rounding
error) - you may end up with small (e.g. 1^-6 * signal, for floats)
imaginary components after the inverse transform - these should not worry
you too much.

2/ If you are _just_ intending to work with real functions - you can, if you
wish, ignore the negative freqs during the processing - and then, just
before the inverse transform, - copy conjugate values from the positive ones
you've been playing with.

3/ make sure you deal properly with the d.c. component and the Fs/2
component.

----

There are lots of more efficient ways of doing these things.. but I'm taking
the Keep It Simple approach .. ;)

Iain

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