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Subject: Re: [music-dsp] EQ-building with fine adjustable steepness
From: ***@web.de
Date: Fri, June 29, 2018 12:06 pm
To: music-***@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
<b>Betreff:</b> Re: [music-dsp] EQ-building with fine adjustable steepness</div>
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<div>So with a one-pole LPF with its corner frequency set very low, you wI'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>
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<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. If you have more space between the pole and zero frequency, then
the slope is higher.</div>
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r b-j ***@audioimagination.com
"Imagination is more important than knowledge."