1st order -3dB/octave at cut-off
2nd order -6dB/octave at cut-off
3rd order -12dB/octave at cut-off
4th order -24dB/octave(?) at cut-off

1st=> cascade into 2nd order=> cascade into 3rd order=> .... into N-th order

Note: all this ASSUMES it's a passive filter.

With active filters using op-amps, you can get
1st order -20dB/per Decade at cut-off
2nd order -40dB/per Decade at cut-off
There is typically resonance emphasis (gain hump) prior to cut-off.
And if you go beyond what's called Barkhausen's Criteria,
then your active op-amp filter turns into one heck of a wild 
oscillator (which has an awful sound to it). Found out 1st hand.

Have fun with your filter exporations. Happy hunting.


Cheers,
-Partev


=================================================================================




--- richarddobson@blueyonder.co.uk wrote:

From: Richard Dobson 
To: csound@lists.bath.ac.uk
Subject: [Csnd] Re: on filters.....
Date: Tue, 24 Feb 2009 23:09:25 +0000

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




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_____________________________________________________________
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  Partev Barr Sarkissian wrote:
> 1st order -3dB/octave at cut-off
> 2nd order -6dB/octave at cut-off
> 3rd order -12dB/octave at cut-off
> 4th order -24dB/octave(?) at cut-off
> 

We have to be careful not to conflate two distinct measures. The slope 
of a filter response is really the asymptote of that response in 
mathematical terms (it defines the maximum slope the response will 
reach), and particularly for the lower-order filters  is a slope arrived 
at very gradually, it is not reached immediately at the cut-off (or 
centre) frequency (which is to say that low-order filter responses have 
rounded curves rather than tight corners). The -3dB points are however 
specific, and disregard slope as such entirely - they simply define at 
what point in the response that response has fallen by 3dB.

By convention, the scope is described simply as XdB/octave  (or decade), 
  signifying the absolute slope. Mathematically, slopes can be positive 
(ascending) or negative (descending), but in the case of a bandpass 
filter we can have one of each, so specifying any sign is ambiguous.

Since slopes  emerge from the maths of the filter definition (or the 
physics of analogue components), we also discover that 6dB/octave is the 
minimum slope we can have, as given by a 1st-order filter. Making a 
filter with a 3dB/octave slope  (such as we might want for pink noise) 
is actually very difficult (see all the literature from Robin Whittle on 
making pink noise for example).

In short - the -3dB point is one measure of a filter, and the (signless) 
slope is another, following the basic rule of 6dB per order. So the 
slope-per-order sequence is 6,12,18,24.

Richard Dobson

ok, it is clear... thank you very much.
fv


Il giorno 25/feb/09, alle ore 10:33, Richard Dobson ha scritto:

>  Partev Barr Sarkissian wrote:
>> 1st order -3dB/octave at cut-off
>> 2nd order -6dB/octave at cut-off
>> 3rd order -12dB/octave at cut-off
>> 4th order -24dB/octave(?) at cut-off
>
> We have to be careful not to conflate two distinct measures. The  
> slope of a filter response is really the asymptote of that response  
> in mathematical terms (it defines the maximum slope the response  
> will reach), and particularly for the lower-order filters  is a  
> slope arrived at very gradually, it is not reached immediately at  
> the cut-off (or centre) frequency (which is to say that low-order  
> filter responses have rounded curves rather than tight corners).  
> The -3dB points are however specific, and disregard slope as such  
> entirely - they simply define at what point in the response that  
> response has fallen by 3dB.
>
> By convention, the scope is described simply as XdB/octave  (or  
> decade),  signifying the absolute slope. Mathematically, slopes can  
> be positive (ascending) or negative (descending), but in the case  
> of a bandpass filter we can have one of each, so specifying any  
> sign is ambiguous.
>
> Since slopes  emerge from the maths of the filter definition (or  
> the physics of analogue components), we also discover that 6dB/ 
> octave is the minimum slope we can have, as given by a 1st-order  
> filter. Making a filter with a 3dB/octave slope  (such as we might  
> want for pink noise) is actually very difficult (see all the  
> literature from Robin Whittle on making pink noise for example).
>
> In short - the -3dB point is one measure of a filter, and the  
> (signless) slope is another, following the basic rule of 6dB per  
> order. So the slope-per-order sequence is 6,12,18,24.
>
> Richard Dobson
>
>
>
>
>
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