[LAD] Quick question on theory

[Fons Adriaensen]

On Wed, Aug 20, 2008 at 10:15:25AM +0200, Arnold Krille wrote:


White noise contains all frequencies with equal power, but
only *in a statistical sense*, this is, in the average.
Any finite length of a white noise signal can have a fully
random spectrum if you analyse it with a resolution
corresponding to the lenght.

> Anyway, thinking about this I realized that I have maybe found a good way to 
> reduce the noise in my data-samples while still preserving the steep 
> (delta-peak-like) rising slope that is the real information... Maybe I 
> shouldn't just do lowpass filtering but dft -> suppress/reduce the amplitude 
> of frequencies with random phase -> back dft.
> Only drawback is that this is _far_ slower then 1st order butterworth 
> lowpass...

When compared to any delta you may choose, half the power of any random
noise will be in-phase with it, and half will be in quadrature.

The same is in general true of any sufficiently complex audio 
signal (i.e. not for synthesised waveforms, single tones on
some instruments, etc.).

So it will be quite difficult to remove noise from real-life
signals in this way. 

Since random noise defeats any attempt to define it locally,
the only way to remove noise from an audio signal is by using
statistical features of the signal.


Ciao,


-- 
FA

Laboratorio di Acustica ed Elettroacustica
Parma, Italia

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