Any slope filter

boris81 · Jan 26, 2011, 12:34 AM

Any slope filter can be realized by cascading a bunch of 1st and 2nd order filters and punching in the correct Q factor.

For Butterworth:
1st order -> 1st order real pole filter
2nd order -> 2nd order with Q = 0.707
3rd order -> 1st + 2nd with Q = 1.
4th order -> 2nd with Q = 1.31 + 2nd with Q = 0.54
and so on..
A complete Q-factor look-up table for most common filters can be found at the end of this datasheet (p.56)

http://focus.ti.com/lit/ml/sloa088/sloa088.pdf

The KX package currently has just 2nd order filters which limits such implementations only to even order slopes. I have successfully implemented odd orders but I haven't compiled an Effects-Plugin yet.

This screenshot shows how to realize a 6th order Butterworth slope (36dB/oct) with 3 cascaded EQ Lowpass plugins.

6th order Butterworth is shown in green. 4th in red and 2nd in blue are there for reference.

Russ · Jan 26, 2011, 04:51 AM

There is a formula by RBJ (of the Audio EQ Cookbook) in the MusicDSP mailing list for calculating the Q values for each biquad section (for Butterworth LP/HP):

Q = 1 / ( 2*sin( (pi/N)*(n + 1/2) ) )
where N is the filter order, n is the section number and 0 <= n < floor(N/2)

It gives the same results as shown in that table (in reverse order).

boris81 · Jan 26, 2011, 05:21 AM

Cool! I haven't seen this formula before.

Russ · Jan 26, 2011, 05:50 AM

Hehe, actually I just noticed that the same formula is given in one of the links that you referenced (the thread at DSPRelated.com) in your other thread...

boris81 · Jan 26, 2011, 09:51 PM

I compiled a 1st order LowPass and HighPass Plugin Effect. You can cascade this with the EQ Lowpass or EQ Highpass to get any odd order filter slopes. Follow the guide in the first post or to make sure you have the correct Q values.

Get the Plugin from here:
Download LP-HP-1st.kxl

The screenshot shows the routing for 3rd order Butterworth Lowpass at 1kHz. The plots are 1st order Butterworth in blue, 2nd in red and 3rd in green.

Here is the source code if someone wants to optimize it.
http://www.datafilehost.com/download-ed8bd96e.html

Russ · Jan 26, 2011, 11:15 PM

I do not have kX installed (or Windows for that matter) at the moment, so I cannot compile anything for kX or test anything out, etc.

Looking at your source code, it seems that your microcode is using same biquad code, with a2 and b2 just set to 0.
You can save some GPRs by using code specifically for 1st order filter.

Maybe something like this:

Code:

; Difference equation
; y[n] = b0*x[n] + b1*x[n-1] - a1*y[n-1]

; LP ( b1 = b0 )
; y[n] = b0*x[n] + b0*x[n-1] - a1*y[n-1]

; HP ( b1 = (-b0) )
; y[n] = b0*x[n] - b0*x[n-1] - a1*y[n-1]

input in;
output out;
static x, b, a; ( x = previous input, b = b0, a = (-a1) )

; LP
macs 0, 0, x, b;
macmv x, in, a, out;
macs out, accum, x, b;

; HP
macsn 0, 0, x, b;
macmv x, in, a, out;
macs out, accum, x, b;

The above does not include any scaling, but that can be added (if needed) with an additional macints instruction..
I think the above should work, but again, I am not able to test (I threw it together quickly, and it is possible that I made a mistake).

[edit: oops, I swapped b0 and b1 in HP: corrected]

boris81 · Jan 27, 2011, 03:09 AM

Awesome! Thanks, Russ!!

I pretty much slapped the Demo and EQ Lowpass code together. I'm just happy it works at all. I will definitely try your optimization when I get a chance.

Russ · Jan 27, 2011, 03:22 AM

BTW: I forgot to mention, you should also remove those presets since they are for the demo plugin. ...And congratulations on making your first plugin.

boris81 · Jan 27, 2011, 05:23 PM

It's a version 2 of this plugin with the optimization from Russ. This is compiled for KX-3550 x86.

macs 0, 0, x, b1;
macmv x, in, a, out;
macs out, accum, x, b0;

I'm using an extra register 'b1' to keep the Dane code the same for LP and HP. I don't plan on messing with this Plugin further unless there's a bug.
Enjoy!

If you are using the first version you might have to unregister it first. Instructions on how to do that are here:
http://www.hardwareheaven.com/effects-dsp/206708-unregistering-dsp-plugins-i-made-how.html#post1393296

The Plugin is here:
Download LP-HP-1st.kxl

And the source code:
Download fx_LP-HP-1st.zip

boris81 · Aug 31, 2011, 04:23 AM

I see the links are dead now so I will upload this Plug-in to the forum for safekeeping. You will need to delete the .TXT extension before using it.

1st Order LowPass or HighPass filter
LP-HP-1st.kxl.TXT

I also made a 2nd order Allpass filter which might be useful to someone
allpass.kxl.TXT

Enjoy!!

Jan 26, 2011, 12:34 AM	#1
boris81 HardwareHeaven Newbie Join Date: Dec 2009 Location: White Plains, NY Posts: 17 Rep Power: 0	Any slope filter Any slope filter can be realized by cascading a bunch of 1st and 2nd order filters and punching in the correct Q factor. For Butterworth: 1st order -> 1st order real pole filter 2nd order -> 2nd order with Q = 0.707 3rd order -> 1st + 2nd with Q = 1. 4th order -> 2nd with Q = 1.31 + 2nd with Q = 0.54 and so on.. A complete Q-factor look-up table for most common filters can be found at the end of this datasheet (p.56) http://focus.ti.com/lit/ml/sloa088/sloa088.pdf The KX package currently has just 2nd order filters which limits such implementations only to even order slopes. I have successfully implemented odd orders but I haven't compiled an Effects-Plugin yet. This screenshot shows how to realize a 6th order Butterworth slope (36dB/oct) with 3 cascaded EQ Lowpass plugins. 6th order Butterworth is shown in green. 4th in red and 2nd in blue are there for reference. Attached Thumbnails

Jan 26, 2011, 04:51 AM	#2
Russ HardwareHeaven Extreme Member Join Date: Jan 2005 Posts: 5,563 Rep Power: 62	Re: Any slope filter There is a formula by RBJ (of the Audio EQ Cookbook) in the MusicDSP mailing list for calculating the Q values for each biquad section (for Butterworth LP/HP): Q = 1 / ( 2sin( (pi/N)(n + 1/2) ) ) where N is the filter order, n is the section number and 0 <= n < floor(N/2) It gives the same results as shown in that table (in reverse order).

Jan 26, 2011, 05:21 AM	Thread Starter #3
boris81 HardwareHeaven Newbie Join Date: Dec 2009 Location: White Plains, NY Posts: 17 Rep Power: 0	Re: Any slope filter Cool! I haven't seen this formula before.

Jan 26, 2011, 05:50 AM	#4
Russ HardwareHeaven Extreme Member Join Date: Jan 2005 Posts: 5,563 Rep Power: 62	Re: Any slope filter Hehe, actually I just noticed that the same formula is given in one of the links that you referenced (the thread at DSPRelated.com) in your other thread...

Jan 26, 2011, 09:51 PM	Thread Starter #5
boris81 HardwareHeaven Newbie Join Date: Dec 2009 Location: White Plains, NY Posts: 17 Rep Power: 0	Re: Any slope filter I compiled a 1st order LowPass and HighPass Plugin Effect. You can cascade this with the EQ Lowpass or EQ Highpass to get any odd order filter slopes. Follow the guide in the first post or to make sure you have the correct Q values. Get the Plugin from here: Download LP-HP-1st.kxl The screenshot shows the routing for 3rd order Butterworth Lowpass at 1kHz. The plots are 1st order Butterworth in blue, 2nd in red and 3rd in green. Here is the source code if someone wants to optimize it. http://www.datafilehost.com/download-ed8bd96e.html Attached Thumbnails Last edited by boris81; Jan 26, 2011 at 10:05 PM. Reason: included source code

Jan 26, 2011, 11:15 PM	#6
Russ HardwareHeaven Extreme Member Join Date: Jan 2005 Posts: 5,563 Rep Power: 62	Re: Any slope filter I do not have kX installed (or Windows for that matter) at the moment, so I cannot compile anything for kX or test anything out, etc. Looking at your source code, it seems that your microcode is using same biquad code, with a2 and b2 just set to 0. You can save some GPRs by using code specifically for 1st order filter. Maybe something like this: Code: ; Difference equation ; y[n] = b0x[n] + b1x[n-1] - a1y[n-1] ; LP ( b1 = b0 ) ; y[n] = b0x[n] + b0x[n-1] - a1y[n-1] ; HP ( b1 = (-b0) ) ; y[n] = b0x[n] - b0x[n-1] - a1y[n-1] input in; output out; static x, b, a; ( x = previous input, b = b0, a = (-a1) ) ; LP macs 0, 0, x, b; macmv x, in, a, out; macs out, accum, x, b; ; HP macsn 0, 0, x, b; macmv x, in, a, out; macs out, accum, x, b; The above does not include any scaling, but that can be added (if needed) with an additional macints instruction.. I think the above should work, but again, I am not able to test (I threw it together quickly, and it is possible that I made a mistake). [edit: oops, I swapped b0 and b1 in HP: corrected] Last edited by Russ; Jan 27, 2011 at 12:00 AM.*

Jan 27, 2011, 03:09 AM	Thread Starter #7
boris81 HardwareHeaven Newbie Join Date: Dec 2009 Location: White Plains, NY Posts: 17 Rep Power: 0	Re: Any slope filter Awesome! Thanks, Russ!! I pretty much slapped the Demo and EQ Lowpass code together. I'm just happy it works at all. I will definitely try your optimization when I get a chance.

Jan 27, 2011, 03:22 AM	#8
Russ HardwareHeaven Extreme Member Join Date: Jan 2005 Posts: 5,563 Rep Power: 62	Re: Any slope filter BTW: I forgot to mention, you should also remove those presets since they are for the demo plugin. ...And congratulations on making your first plugin.

Jan 27, 2011, 05:23 PM	Thread Starter #9
boris81 HardwareHeaven Newbie Join Date: Dec 2009 Location: White Plains, NY Posts: 17 Rep Power: 0	Re: Any slope filter It's a version 2 of this plugin with the optimization from Russ. This is compiled for KX-3550 x86. macs 0, 0, x, b1; macmv x, in, a, out; macs out, accum, x, b0; I'm using an extra register 'b1' to keep the Dane code the same for LP and HP. I don't plan on messing with this Plugin further unless there's a bug. Enjoy! If you are using the first version you might have to unregister it first. Instructions on how to do that are here: http://www.hardwareheaven.com/effects-dsp/206708-unregistering-dsp-plugins-i-made-how.html#post1393296 The Plugin is here: Download LP-HP-1st.kxl And the source code: Download fx_LP-HP-1st.zip

Aug 31, 2011, 04:23 AM	Thread Starter #10
boris81 HardwareHeaven Newbie Join Date: Dec 2009 Location: White Plains, NY Posts: 17 Rep Power: 0	Re: Any slope filter I see the links are dead now so I will upload this Plug-in to the forum for safekeeping. You will need to delete the .TXT extension before using it. 1st Order LowPass or HighPass filter LP-HP-1st.kxl.TXT I also made a 2nd order Allpass filter which might be useful to someone allpass.kxl.TXT Enjoy!!