[music-dsp] Filter Q and bandwidth

[robert bristow-johnson]

> ----- Original Message -----
> From: "robert bristow-johnson" <rbj at audioimagination.com>
> To: "A discussion list for music-related DSP" <music-dsp at music.columbia.edu>
> Subject: Re: [music-dsp] Filter Q and bandwidth
> Date: Thu, 29 Mar 2007 18:24:40 -0400
> 
> 
>                           | j*w/w0 |^2
>      H(j*w) = --------------------------------------- = (Q^2)/2
>                | 1 + (1/Q)*(j*w/w0) + (j*w/w0)^2 |^2
> 
> 
>                                1
>      H(j*w) = --------------------------------------- = (Q^2)/2
>                  | -j*w0/w + (1/Q) + j*w/w0 |^2
> 
> 
>                           Q^2
>      H(j*w) = ---------------------------- = (Q^2)/2
>                |1 + j*Q*(w/w0 - w0/w)|^2
> 
> 
>                           Q^2
>      H(j*w) = ------------------------------ = (Q^2)/2
>                |1 + j*2*Q*sinh(ln(w/w0))|^2
> 


of course, all of the above were meant to be expressed as |H(j*w)|^2 .


--

r b-j                  rbj at audioimagination.com

"Imagination is more important than knowledge."