Re: [music-dsp] EQ-building with fine adjustable steepness
Hello Rolf, On 27/06/2018 11:31 PM, rolfsassin...@web.de wrote: Now, I like to have an EQ with most probable flat response which is adjustable in steepness and frequency. [snip] Is there an analytic function decribing this? Check this one out: Thomas Hélie, "Simulation of Fractional-Order Low-Pass Filters." Ross. ___ dupswapdrop: music-dsp mailing list music-dsp@music.columbia.edu https://lists.columbia.edu/mailman/listinfo/music-dsp
Re: [music-dsp] EQ-building with fine adjustable steepness solution
Dear Rolf, dear All several years ago I had the same idea and solved it by using a modified Butterworth design (analog) and a Frequency Domain Least Squares (FDLS) Design for the final digital filter. (Never published it.) I just finished my first blog-post about it. (This question was a good motivation to finally start my blog and to start with Python. Thank you for that.). https://dspblog.audio-dsp.de/ A Jupyter Notebook to play around with the method in Python is provided. BTW: It also solves the problem of the bilinear transformation distortions near Nyquist. You pay with computational complexity. Best regards Joerg Am 29/06/2018 um 18:06 schrieb rolfsassin...@web.de: > Hello Robert > thanks, so this means that it will come out with a cascade anyway. Would'nt > it > then be generally better to put filters in series or use parallel band width > limited filters though? > Regards Rolf > *Gesendet:* Mittwoch, 27. Juni 2018 um 16:49 Uhr > *Von:* "robert bristow-johnson" > *An:* music-dsp@music.columbia.edu > *Betreff:* Re: [music-dsp] EQ-building with fine adjustable steepness > 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. > 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. > > > > ___ > dupswapdrop: music-dsp mailing list > music-dsp@music.columbia.edu > https://lists.columbia.edu/mailman/listinfo/music-dsp > ___ dupswapdrop: music-dsp mailing list music-dsp@music.columbia.edu https://lists.columbia.edu/mailman/listinfo/music-dsp
Re: [music-dsp] EQ-building with fine adjustable steepness
Original Message 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 -- � > 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 � > > > Gesendet: Mittwoch, 27. Juni 2018 > um 16:49 Uhr > Von: "robert bristow-johnson" > <r...@audioimagination.com> > An: music-dsp@music.columbia.edu > Betreff: Re: [music-dsp] EQ-building with fine adjustable > steepness > > > 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. > > > > 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. > > > > > > > ___ > dupswapdrop: music-dsp mailing list > music-dsp@music.columbia.edu > https://lists.columbia.edu/mailman/listinfo/music-dsp � � � -- r b-j� � � � � � � � � � � � �r...@audioimagination.com "Imagination is more important than knowledge." � � � � ___ dupswapdrop: music-dsp mailing list music-dsp@music.columbia.edu https://lists.columbia.edu/mailman/listinfo/music-dsp
Re: [music-dsp] EQ-building with fine adjustable steepness
Hello Robert thanks, so this means that it will come out with a cascade anyway. Would'nt it then be generally better to put filters in series or use parallel band width limited filters though? Regards Rolf Gesendet: Mittwoch, 27. Juni 2018 um 16:49 Uhr Von: "robert bristow-johnson" An: music-dsp@music.columbia.edu Betreff: Re: [music-dsp] EQ-building with fine adjustable steepness 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. 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. ___ dupswapdrop: music-dsp mailing list music-dsp@music.columbia.edu https://lists.columbia.edu/mailman/listinfo/music-dsp
Re: [music-dsp] EQ-building with fine adjustable steepness
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. 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. --r b-j r...@audioimagination.com "Imagination is more important than knowledge." Original message From: rolfsassin...@web.de Date: 6/27/2018 6:31 AM (GMT-08:00) To: music-dsp@music.columbia.edu Subject: [music-dsp] EQ-building with fine adjustable steepness Dear all, I registered new to the list for private interest (building self programmable music gear as hobby). Since there was activity yet, I would like to ask my question regarding equalizer builing: We know, classical EQs will work that way, that they decrease e.g 6dB/12dB/24dB per octave starting from the edge frequency. So the 6dB x X behavior seems to be fixed with a simple n-order filter. Now, I like to have an EQ with most probable flat response which is adjustable in steepness and frequency. At least the steepness schould be adjustable starting at zero. For instance I want to shape an EQ's curve from almost flat to totally steep continously such as we know it from white noise and pink noise curves. Regarding noise I am mixing this in percentages in between these cases, but it does not work with unknown signals. Is there an analytic function decribing this? In another group, the recommendation was to use a filter cascade with hi/lo behavior and overlapping the edge frequencies to get small stairs. Any more detailled / better idea to do that? Thanks in advance Rolf ___ dupswapdrop: music-dsp mailing list music-dsp@music.columbia.edu https://lists.columbia.edu/mailman/listinfo/music-dsp
