Butterworth amplitude

[David_Lieberman]

I generate white noise with an amplitude of 100.  Then I pass it through a Butterworth bandpass filter with bandpass settings of 50 and 150 for the high and low frequency.  I end up with filtered noise with amplitude of 20 (more or less). 

Why does the filter drastically reduce the amplitude of the filtered noise?  I have noticed that if I increase the range of the bandpass settings (to, say, 50 to 500) the reduction in amplitude is somewhat less.  

I have tried other filters and it appears that Chebychev is slightly better, but still does not come anywhere close to the amplitude of the original signal.

I confess that my knowledge of signal processing is limited.  Can anyone help me with this problem?  Is there some parameter setting which will give me better results?

[JÞB]

White noise by definition contains a uniform spectral density.  Therefore any filtering of frequency components must, affect the total power by a ratio of the bandpass to the band width generated. (and the filter algorhithm- A chebechev IS designed with steeper roll-offs than a butterworth and accounts for your observations .  See: Fourier series.

The math is pretty involved but the consepts stem from the additive properties of wave functions.  

Your results are accurate- mathmatically.  how much "Better" would you like them to be?

Message Edited by Jeff Bohrer on 03-08-2010 02:29 PM

[Nihil]

What i do to generate white noise at a given frecuency is to take the signal from the block, filter it then pass it through a sign discriminator (which gives 1 or -1 as a result) and then multiply it for the desired amplitud. (look at the attached files) 

the filter settings are also attached as images. 

[Nihil]

oh, and if you need some formal explanation about the filter you might want to read about "shapping filters." if you need some information about it let me know and i'll find you something to make a refference to in your paper.

[David_Lieberman · Accepted solution]

thanks for your replies.

I was under the impression that white noise with amplitude of 10 when passed through a filter would result in filtered noise of amplitude 10.  But now I see why I was wrong.  White noise is the sum of sine waves of various frequencies;  thus, when you filter out some frequencies the amplitude (which is a summation) will be lower.

And thank you for the hints about normalizing the amplitude after filtering.  That is what I will do.

David

[JÞB]

Great work!