# Complementary narrow-band peak-notch filters pair design

Started by May 3, 2016
```Hello,

I am searching for examples (reference - papers, books) of narrow-band
peak-notch filters pairs design having complementary frequency
characteristics.
By "complementary" I mean a characteristic of notch having -40..80 dB at
some f0 frequency, 0dB in others, and peak filter having floor at
-40..80 but 0dB at f0.
Cascade connection of both should give -40..80 dB horizontal line.
Such a pair are used in application where we need to insert some control
signal at some not important, or not used frequency sub-band.

Kind regards

Roman
```
```On Tuesday, May 3, 2016 at 6:13:13 AM UTC-7, roman rumian wrote:

> I am searching for examples (reference - papers, books) of narrow-band
> peak-notch filters pairs design having complementary frequency
> characteristics.

Maybe I miss the point, but I think if you take one, say f(x), and compute 1-f(x)
(scaled appropriately) you should get what you want.

In more usual cases, this allows for low-pass and high-pass complementary
filters, but it should work fine for peak/notch, too.

Well, it does require careful design of the filter in the first place, but you
can't get away from that.  The notch filter has to be very close to 1 away
from the notch, which might otherwise not be a requirement.
```
```On Tuesday, May 3, 2016 at 9:13:13 AM UTC-4, roman rumian wrote:
> Hello,
>
> I am searching for examples (reference - papers, books) of narrow-band
> peak-notch filters pairs design having complementary frequency
> characteristics.
> By "complementary" I mean a characteristic of notch having -40..80 dB at
> some f0 frequency, 0dB in others, and peak filter having floor at
> -40..80 but 0dB at f0.
> Cascade connection of both should give -40..80 dB horizontal line.
> Such a pair are used in application where we need to insert some control
> signal at some not important, or not used frequency sub-band.
>
> Kind regards
>
> Roman

```
```On Tuesday, May 3, 2016 at 9:13:13 AM UTC-4, roman rumian wrote:
>
> I am searching for examples (reference - papers, books) of narrow-band
> peak-notch filters pairs design having complementary frequency
> characteristics.
> By "complementary" I mean a characteristic of notch having -40..80 dB at
> some f0 frequency, 0dB in others, and peak filter having floor at
> -40..80 but 0dB at f0.
> Cascade connection of both should give -40..80 dB horizontal line.
> Such a pair are used in application where we need to insert some control
> signal at some not important, or not used frequency sub-band.
>

Roman, other than the constant gain difference, why doesn't the "Peaking EQ" in the Audio EQ Cookbook http://www.musicdsp.org/files/Audio-EQ-Cookbook.txt fit your requirement?

r b-j
```
```On Tue, 03 May 2016 17:57:44 -0700, herrmannsfeldt wrote:

> On Tuesday, May 3, 2016 at 6:13:13 AM UTC-7, roman rumian wrote:
>
>> I am searching for examples (reference - papers, books) of narrow-band
>> peak-notch filters pairs design having complementary frequency
>> characteristics.
>
> Maybe I miss the point, but I think if you take one, say f(x), and
> compute 1-f(x)
> (scaled appropriately) you should get what you want.
>
> In more usual cases, this allows for low-pass and high-pass
> complementary filters, but it should work fine for peak/notch, too.
>
> Well, it does require careful design of the filter in the first place,
> but you can't get away from that.  The notch filter has to be very close
> to 1 away from the notch, which might otherwise not be a requirement.

I think there's a lot more ways to get notch and peak filters than there
are to get ones that necessarily do what you want.

Start with one denominator, then find a pair of numerators that work
right...

--

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com
```
```On 3.5.16 16:13, roman rumian wrote:
> Hello,
>
> I am searching for examples (reference - papers, books) of narrow-band
> peak-notch filters pairs design having complementary frequency
> characteristics.
> By "complementary" I mean a characteristic of notch having -40..80 dB at
> some f0 frequency, 0dB in others, and peak filter having floor at
> -40..80 but 0dB at f0.
> Cascade connection of both should give -40..80 dB horizontal line.
> Such a pair are used in application where we need to insert some control
> signal at some not important, or not used frequency sub-band.
>
> Kind regards
>
> Roman

Have you considered that the bandwidth of the control signal must
be compatible with the notch width? A steep notch will ring in a
way similar to an equally steep peak.

--

-TV

```
```Hi Robert,

W dniu 2016-05-04 o 16:21, robert bristow-johnson pisze:
(...)
> Roman, other than the constant gain difference, why doesn't the "Peaking EQ" in the Audio EQ Cookbook http://www.musicdsp.org/files/Audio-EQ-Cookbook.txt fit your requirement?
>
> r b-j

yes, you are right, but sorry, I badly defined my need.
I have a design method of such a filters pair, but need literature
references for our new publication.

BTW, your Cookbook is excellent, I used it many times - THANK YOU ! :-)

Roman
```
```W dniu 2016-05-04 o 18:27, Tim Wescott pisze:
(...)
> I think there's a lot more ways to get notch and peak filters than there
> are to get ones that necessarily do what you want.
>
> Start with one denominator, then find a pair of numerators that work
> right...

Thank you Tim. :-)

Maybe this way ?

notch:
[num]= [1    -1.98288773985790   0.99999800000100];
[den] = [1    -1.98269143377535   0.99980001000000];

peak:
[num] = [1    -1.98269143377535   0.99980001000000];
[den] =  [1    -1.98288773985790   0.99999800000100];

;-)

Roman
```
```W dniu 2016-05-04 o 02:57, herrmannsfeldt@gmail.com pisze:
(...)
> Maybe I miss the point, but I think if you take one, say f(x), and compute 1-f(x)
> (scaled appropriately) you should get what you want.
>
> In more usual cases, this allows for low-pass and high-pass complementary
> filters, but it should work fine for peak/notch, too.
>
> Well, it does require careful design of the filter in the first place, but you
> can't get away from that.  The notch filter has to be very close to 1 away
> from the notch, which might otherwise not be a requirement.

Hermann,

yes, you hit the point. As the notch is close to 1.0 the numerical
precision and stability issue are the problem.

Thank you. :-)

Roman

```