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Subject: Re: [music-dsp] EQ-building with fine adjustable steepness

From: rolfsassin...@web.de

Date: Fri, June 29, 2018 12:06 pm

To: music-dsp@music.columbia.edu

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�

        > Hello Robert

        >

        > thanks, so this means that it will come out with a cascade anyway. 
Wouldn't it then be generally better to put filters in series or use parallel 
band width limited filters though?

        �

        it's harder to design the response when the filters are in parallel.� 
especially when the target response is in dB, because in cascade, the frequency 
responses of the different sections in dB *add*.

        �

        so a single, first-order section looks like:

        

        � H_n(z) = (z-q_n)/(z-p_n)

        �

        and the cascade will be:

        

        � H(z) = H_1(z) . H_2(z) . H_3(z) ... H_N(z)

        �

        p_n are the poles and q_n are the zeros

        �

        the corner frequency associated with each pole wp_n = arccos(2 - (p_n + 
1/p_n)/2)� and same for q_n� but the corner for p_n bends down and the corner 
for q_n bends up.

        �

        if the slope is monotonically descending then wp_1 < wq_1 < wp_2 < wq_2 
< ...

        �

        you want to space the pole frequencies wp_n equally in log frequency.� 
that is

        �

        � �log(wp_2) - log(wp_1) = log(wp_3) - log(wq_2)

        �

        and similarly for the zero frequencies.� but the relative placement of 
the zeros to their poles will determine the slope.

        �

        if� wq_n is close to wp_n, then the slope will be closer to zero.� if 
wq_n is close to wp_(n+1), then the slope will be closer to -6 dB per octave.

        �

        if you really wanna put this in parallel, then you have to do Heaviside 
partial fraction expansion.� sometimes that is a female canine, but since there 
are no double poles, this might be pretty straight forward.

        �

        r b-j

        �

> <div>&nbsp;

> <div name="quote" style="margin:10px 5px 5px 10px; padding: 10px 0 10px 10px; 
> border-left:2px solid #C3D9E5; word-wrap: break-word; -webkit-nbsp-mode: 
> space; -webkit-line-break: after-white-space;">

> <div style="margin:0 0 10px 0;"><b>Gesendet:</b>&nbsp;Mittwoch, 27. Juni 2018 
> um 16:49 Uhr<br/>

> <b>Von:</b>&nbsp;&quot;robert bristow-johnson&quot; 
> &lt;r...@audioimagination.com&gt;<br/>

> <b>An:</b>&nbsp;music-dsp@music.columbia.edu<br/>

> <b>Betreff:</b>&nbsp;Re: [music-dsp] EQ-building with fine adjustable 
> steepness</div>

>

> <div name="quoted-content">

> <div>So with a one-pole LPF with its corner frequency set very low, you 
> wI&#39;ll get a -6 sB slope, which is twice the slope that you desire for 
> pink noise.if you follow that with a zero, the slope will bend back to zero 
> slope.</div>

>

> <div>&nbsp;</div>

>

> <div>So repeating and alternating poles and zeros, will get you a slope 
> somewhere between 0 and -6 dB per octave. If you start with a pole on the 
> left and follow it shortly with a zero, it will be closer to zero.&nbsp; If 
> you have more space between the pole and zero frequency, then
the slope is higher.</div>
>

> <div>&nbsp;</div>

> </div>

> </div>

> </div>

> </div></div></body></html>

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> music-dsp@music.columbia.edu

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�
�
�


--



r b-j� � � � � � � � � � � � �r...@audioimagination.com



"Imagination is more important than knowledge."

�
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