Techniques behind arbitrary response or "drawable" equalizers?

I need to design a filter that has arbitrary response. Basically, I want to be able to almost "draw" the equalizer curve.

What are the techniques behind (FFT-based) arbitrary response or "drawable" equalizers such as:

http://wiki.cockos.com/wiki/index.php/ReaFIR

or

http://www.elevayta.net/product4.htm

On Mon, 13 Jun 2016 21:32:12 -0700 (PDT), viljamaadsp@gmail.com wrote:

>I need to design a filter that has arbitrary response. Basically, I want to be able to almost "draw" the equalizer curve.
>
>What are the techniques behind (FFT-based) arbitrary response or "drawable" equalizers such as:
>
>http://wiki.cockos.com/wiki/index.php/ReaFIR
>
>or
>
>http://www.elevayta.net/product4.htm

Parks-McLellan/Remez Exchange, as well as other algorithms, allow the
filter definition to be defined on a grid, and portions of the grid
can be weighted or marked as "don't care" regions.  Defining the
response and the grid points can easily be done graphically, i.e.,
"drawn".

That being said, there's no guarantee that the algorithms will
converge to a solution for any arbitrary filter shape.   Similarly,
with FFT-based design methods a common problem is that the sampling in
the frequency domain does not define the response in the regions
between the samples, and undesirable effects can easily happen in the
results.

Constraining what can be "drawn" could go a long way toward increasing
confidence in the results.

tiistai 14. kes=C3=A4kuuta 2016 8.24.40 UTC+3 Eric Jacobsen kirjoitti:
> On Mon, 13 Jun 2016 21:32:12 -0700 (PDT), viljamaadsp@gmail.com wrote:
>=20
> >I need to design a filter that has arbitrary response. Basically, I want=
 to be able to almost "draw" the equalizer curve.
> >
> >What are the techniques behind (FFT-based) arbitrary response or "drawab=
le" equalizers such as:
> >
> >http://wiki.cockos.com/wiki/index.php/ReaFIR
> >
> >or
> >
> >http://www.elevayta.net/product4.htm
>=20
> Parks-McLellan/Remez Exchange, as well as other algorithms, allow the
> filter definition to be defined on a grid, and portions of the grid
> can be weighted or marked as "don't care" regions.  Defining the
> response and the grid points can easily be done graphically, i.e.,
> "drawn".
>=20
> That being said, there's no guarantee that the algorithms will
> converge to a solution for any arbitrary filter shape.   Similarly,
> with FFT-based design methods a common problem is that the sampling in
> the frequency domain does not define the response in the regions
> between the samples, and undesirable effects can easily happen in the
> results.
>=20
> Constraining what can be "drawn" could go a long way toward increasing
> confidence in the results.

I found Parks-Mccellan with LPF, HPF, BPF and Notch implementations,

http://www.iowahills.com/Example%20Code/NewParksMcClellan.txt

however, my requirements would require also a "downward peak"/cut type, spe=
cifically multiple such cuts in a group.

Any idea whether this is something the Parks-Mccellan is suited for?

On 14.06.16 06.32, viljamaadsp@gmail.com wrote:
> I need to design a filter that has arbitrary response. Basically, I want to be able to almost "draw" the equalizer curve.

Well, if your FIR convolution filter is implemented by FFT convolution 
(with overlap add) the solution is quite straight forward. Just multiply 
each value in the frequency domain by the desired gain and maybe adjust 
the phase and you are done. Strictly speaking there is no need to know 
the FIR filter kernel at all. But the overlap add method requires the 
filter kernel to drop to zero at some point. So an appropriate window 
should be applied in the time domain.
Furthermore you should be careful with jumps in the frequency response. 
They get very wide in the time domain and usually cause artifacts like 
pre echos. So you should keep your design function smooth. This is 
similar to a window function in the time domain. So having a smooth 
response might be sufficient. There is no need for an additional Hamming 
window or so. A rectangular window (to keep overlap add happy) usually 
gives the best results if dGain/dOmega and the group delay (dPhi/dOmega) 
are limited.

The more interesting question is: where does your design function come 
from? And what are the requirements of this function to selectivity.

The limiting factor for FIR filters is usually the latency. The typical 
latency of an overlap/add FIR filter is roughly in the order of the FFT 
length. While even general purpose CPUs can easily deal with 65k FFT, 
the resulting latency might be undesired.

I implemented similar things several years ago for an 32 band audio 
equalizer plug-in with group delay equalization.
http://maazl.de/project/pm123/manual/realeq/index.html
The source code is still available as part of the PM123 package
http://maazl.de/project/pm123/pm123-1.41b3-src.zip
Well adjusted the result sounds rather impressive, quite close to 
digital room correction.


Marcel

On Tuesday, June 14, 2016 at 3:49:16 PM UTC+3, Marcel Mueller wrote:
> On 14.06.16 06.32, viljamaadsp@gmail.com wrote:
> > I need to design a filter that has arbitrary response. Basically, I want to be able to almost "draw" the equalizer curve.
> 
> Well, if your FIR convolution filter is implemented by FFT convolution 
> (with overlap add) the solution is quite straight forward. Just multiply 
> each value in the frequency domain by the desired gain and maybe adjust 
> the phase and you are done. Strictly speaking there is no need to know 
> the FIR filter kernel at all. But the overlap add method requires the 
> filter kernel to drop to zero at some point. So an appropriate window 
> should be applied in the time domain.
> Furthermore you should be careful with jumps in the frequency response. 
> They get very wide in the time domain and usually cause artifacts like 
> pre echos. So you should keep your design function smooth. This is 
> similar to a window function in the time domain. So having a smooth 
> response might be sufficient. There is no need for an additional Hamming 
> window or so. A rectangular window (to keep overlap add happy) usually 
> gives the best results if dGain/dOmega and the group delay (dPhi/dOmega) 
> are limited.
>
> The more interesting question is: where does your design function come 
> from? And what are the requirements of this function to selectivity.

What do you mean by design function?

Also, I thought that manipulating FFT bins that way poses problems:
https://groups.google.com/forum/#!topic/comp.dsp/ZRehYt2SlE0

What about window size? How large must it be?

On Tuesday, June 14, 2016 at 9:31:27 AM UTC-4, Matti Viljamaa wrote:
> On Tuesday, June 14, 2016 at 3:49:16 PM UTC+3, Marcel Mueller wrote:
> > On 14.06.16 06.32, viljamaadsp@gmail.com wrote:
> > > I need to design a filter that has arbitrary response. Basically, I want to be able to almost "draw" the equalizer curve.
> > 


N Track Studio audio editor has a very nice drawable EQ function that is overlayed on a spectrum analyzer.

I don't know how  it is implemented.

M

On 14.06.16 15.31, Matti Viljamaa wrote:
> What do you mean by design function?

The desired filter response.

> Also, I thought that manipulating FFT bins that way poses problems:
> https://groups.google.com/forum/#!topic/comp.dsp/ZRehYt2SlE0

Yes, that's why I recommended at least a rectangular window.
But this only is reasonable if the target response is reasonable smooth. 
Jumps from 0 to 1 are /not/ smooth.

Of course, you can use any fancy target response and turn it into a 
implementable filter kernel by a window function. But the window 
function will /somehow/ make the response smooth. But if you do not 
require impossible results, there is no need for further smoothing. This 
gives you more control than a window function.
Window functions are fine to tune just the stop band attenuation. But if 
you want to get close to a desired response, they might not hit the nail 
on the head. Like a blur filter they smooth everything. Even the parts 
that do not cause much harm.

> What about window size? How large must it be?

Well, the window size should always match the FIR kernel length. ;-)
And within the context of overlap add processing kernel length < FFT 
size. In other words, each iteration creates as many samples of output 
as the difference of the FFT size and the kernel length.
And the FFT size mainly determines the latency. It could be decreased to 
some degree with a Block Convolver.

Choosing an appropriate kernel length for a given response is a bit more 
complicated. This is mainly dominated by the maximum gain and phase 
change rate over frequency. A phase change rate is basically a group 
delay and just moves the filter kernel to one of the edges. While a gain 
change rate reduces the damping of sinc functions with neighbor 
frequencies. I.e. it raises the kernel values at the edges. Both makes 
the values far away from the center less negligible.

But it is quite easy to get the real filter response. Just do an FFT of 
the filter kernel including the window function.
And if you want to get the response at frequencies between the bins, 
just add zeros to the kernel an repeat with a larger FFT.


Marcel

viljamaadsp@gmail.com writes:

> I need to design a filter that has arbitrary response. Basically, I want to be able to almost "draw" the equalizer curve.
>
> What are the techniques behind (FFT-based) arbitrary response or "drawable" equalizers such as:
>
> http://wiki.cockos.com/wiki/index.php/ReaFIR
>
> or
>
> http://www.elevayta.net/product4.htm

This sounds like a good fit (no pun intended) for FDLS (Frequency Domain
Least Squares). You could compute the phase from the magnitude: the
input to FDLS requires both (complex).
-- 
Randy Yates, DSP/Embedded Firmware Developer
Digital Signal Labs
http://www.digitalsignallabs.com

viljamaadsp@gmail.com wrote:
> I need to design a filter that has arbitrary response. Basically, I want to be able to almost "draw" the equalizer curve.
>
> What are the techniques behind (FFT-based) arbitrary response or "drawable" equalizers such as:
>
> http://wiki.cockos.com/wiki/index.php/ReaFIR
>
> or
>
> http://www.elevayta.net/product4.htm
>


I could easily be wrong, but many of those plugins are just four, five,
six filters in series. Each is simply an IIR with gain/cut, Q or
low shelf/high shelf, possibly with order for shelving filters.

I can't speak exactly to ReaFIR.

This is a blog from Justin Frankel and he calls ReaFIR "FFT EQ",
as if he were simply "stomping buckets" in the FFT.

http://www.blorp.com/index.php?viewstart=320

It is from ten years ago.

Perhaps you can contact him? If I read that right, he's the
author. And perhaps a question the the REAPER  forum is
in order.



-- 
Les Cargill

On Tuesday, June 14, 2016 at 4:59:24 PM UTC-5, Randy Yates wrote:

> This sounds like a good fit (no pun intended) for FDLS (Frequency Domain
> Least Squares). You could compute the phase from the magnitude: the
> input to FDLS requires both (complex).

VLV apparently did a lot of experimentation applying FDLS to arbitrary frequency responses, creating the phase response from the log of the magnitude response. He reported that minimum-phase was, in general, not sufficient to guarantee a good fit. I don't know what the criterion for a good fit is, or even if such a criterion exists, but in my experience FDLS works best approximating LTI frequency responses known to have originated in digital or analog rational transfer functions.

I wish that Vladimir were here to elaborate.

Greg Berchin