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Complementary narrow-band peak-notch filters pair design

Started by roman rumian 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