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

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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)

�

� 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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