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[Csnd] on filters.....

Date2009-02-24 11:55
FromFederico Vanni
Subject[Csnd] on filters.....
hi list,

two important question:

1)
i know that a cut frequncy of a filter
corresponds to its -3 dB point. So in a frequency
responce of a first order filter
we get - 3 dB point and, after, the rolloff of a -6 dB for each octave.

If we use a second order filter we know that the rolloff of -6 dB
becomes -12 dB... BUT... does the -3 dB becames -6 dB????


2)
in the 'reson' opcode, does the iscale value of 2
means an output signal with the same RMS value
of the input one?

Thanks a lot
fv







Date2009-02-24 23:09
FromRichard Dobson
Subject[Csnd] Re: on filters.....
Federico Vanni wrote:
> 
> hi list,
> 
> two important question:
> 
> 1)
> i know that a cut frequncy of a filter
> corresponds to its -3 dB point. So in a frequency
> responce of a first order filter
> we get - 3 dB point and, after, the rolloff of a -6 dB for each octave.
> 
> If we use a second order filter we know that the rolloff of -6 dB
> becomes -12 dB... BUT... does the -3 dB becames -6 dB????
> 
> 


No. The  -3dB point is part of the standard description of a filter (of 
whatever kind): the bandwidth of a bandpass filter is defined  as the 
width (in Hz) of the response between the two -3dB points. As the 
resonance (Q) increases (in the case of a recursive filter such as 
reson), those points move closer together. Slightly more complex to 
describe in relation to something such as a lowpass but the principle is 
the same: there may be a resonant peak, but the -3dB point is, by 
definition, where the nominally flat passband response (discounting any 
ripple) has reduced by  that amount. It is not applied only to filters - 
the -3dB points are still a standard element of the description of the 
overall frequency response of an amplifier.




> 2)
> in the 'reson' opcode, does the iscale value of 2
> means an output signal with the same RMS value
> of the input one?
> 


That's the general idea; but how close you get to that depends a lot on 
the nature of the input  (the documentation says it works as described 
when used with a white noise input).  I haven't analysed reson that 
closely, someone who has will be able to give a more comprehensive answer.

Why -3dB? Partly convention, but it does relate to rms measurements and 
such things as summing to unity amplitude (as in a constant-power pan). 
  With a sinusoid at digital peak amplitude (= 0dBFS), the corresponding 
rms level is -3dB  (=0.707, or sqrt(2)/2).


Richard Dobson