Talk:Chebyshev filter

Untitled

are chebyshev filters the same as IIS filters?

is the comb filter a sort of chebyshev filter?

does the chebyshev filter work with delayed signal input from its output?

what is the chebyshev filter actually good for? (applications)

--Abdull 17:58, 18 Jun 2005 (UTC)

1. Never heard of an IIS filter
2. I highly doubt it. Maybe they are related in some trivial way
3. All filters delay the signal
4. They are used anywhere a steep cutoff is required with minimal parts and ripple doesn't matter.  :-) I know they are used in analog to digital converters for one thing. - Omegatron 15:54, July 19, 2005 (UTC)

A chebyshev filter is a modern filter which (like all continuous-time filters)can be implemented as an IIR (infinite impulse response) discrete-time filter. It is based on chebyshev polynomials. Its characteristic in the complex frequency domain is composed of poles lying in the left half-plane and distributed along an ellipse centered at the origin and with zeroes at infinity. The butterworth characteristic can be seen as a special case of the chebyshev since its poles are distributed at uniform angles along a circle. What I would like to know is if the poles of a chebyshev filter are distributed according to some simple rule, for example do vectors from the origin to poles carve out equal segment areas of the ellipse as is the case of the butterworth?

As can be seen from the equation on the article page, the poles can be thought of as uniformly distributed on a circle, and this circle then stretched in each dimension to give an ellipse. Oli Filth 22:35, 10 November 2006 (UTC)

A comb filter is very different from the chebyshev in that its characteristic is composed of finite zeroes, and poles at infinity. It can be implemented as an FIR discrete-time filter.--T. Groover, MSEE

New LC realization section

Yo I added this section but someone please check for validity. I am not a EE major (I'm in aerospace) but I gleaned the equations off of the 2nd reference on the bottom (which I also added). If someone could check it out for accuracy, etc., that'd be great

Subheight640 15:37, 27 July 2007 (UTC)

Missing j in Inverse Cheb. Lowpass Zeros?

I think the zeros of the inverse Cheb. should be something like sn = j/cos(Pi/2 * (2*m+1)n), that means imaginary not real. In other words the j is missing. What do You think? I'll change it now. —Preceding unsigned comment added by 213.178.172.228 (talk • contribs) 13:11, 13 September 2007

Poor Explanation...

There is beauty in the Chebyshev filter but if you read this article you wouldn't know it. I don't have a clue how to manipulate the math graphics, but if I did I could create a much more clear explanation. Basically you want to substitute arcsinh(1/e) with a constant variable, say 'a'. Then you split up the real and imaginary parts of the pole locations into x and y respectively. Then you can show how (x/sinh(a))^2 + (y/cosh(a))^2 = 1. This equation clearly shows that the chebyshev poles are on an ellipse. It can then be compared to the Butterworth filter which has its poles on a circle.

In the Chebyshev filter, the terms roll-off is not defined properly and also the link with it shows the wrong meaning. —Preceding unsigned comment added by 115.187.16.1 (talk) 05:37, 5 April 2009 (UTC)

It has been on my to do list for a long time to write a roll-off article. I will get round to it one day. If you want a tutorial on the math markup take a look at Help:Displaying a formula. SpinningSpark 13:45, 11 April 2009 (UTC)

Questions and comments

1. I understand there are two types of the same filter. I am unable to picture the difference in implementation to obtain the ripple in the passband or stopband.

2. It would be nice to add a section with an active implementation of the filter as well as an implementation for a digital filter.

3. In the example for the Cauer circuit, C_{1 shunt} = G₁, _{L2 top} = G₂ or L_{1 shunt} = G₁, C_{1 top} = G₂. Should it be "L_{1 shunt} = G₁, C_{1 top} = G₂" or "L_{1 shunt} = G₁, C_{2 top} = G₂" to maintain consistency?

4. I assume R_db and ε are two arbitrary values decided by the designer of the filter. Could the designer say that R_db=5dB and ε=0.5?

ICE77 (talk) 22:39, 13 July 2011 (UTC)

5. I was trying to design a Chebyshev filter using the Cauer topology equations. I tried to obtain G₁ and realized that the hyperbolic cosine of f_H is a number that approaches infinity. I chose my cutoff frequency to be 10kHz but also tried for lower values down to 100Hz. I don't see how the filter can be designed with the provided expression for G₁.

ICE77 (talk) 19:36, 18 July 2011 (UTC)

In "Cauer topology":

Inductor or capacitor values of a nth-order Chebyshev filter may be calculated from the following equations:

$G_{1}={\frac {2A_{1}\cosh(f_{H})}{Y}}$

...

f_H, the 3 dB frequency is calculated with: $f_{H}=f_{C}\cosh \left({\frac {1}{n}}\cosh ^{-1}{\frac {1}{\varepsilon }}\right)$

f_H is argument of cosh function, so f_H must be dimensionless, but it has dimension of Hz. So the equations are not right. Maksim-e (talk) 14:44, 30 July 2011 (UTC)

Yes, something's not right here ...

ICE77 (talk) 18:04, 11 August 2011 (UTC)

I've figured out the problems and I think I can add a reference. I don't have time right now, but hopefully in the next few days I'll be able to update this to the correct values. Wa03 (talk) 23:29, 30 June 2012 (UTC)

Isn't this simply because the equations are describing a normalized filter? That is, a prototype filter referenced to f_H = 1 Hz. SpinningSpark 00:37, 1 July 2012 (UTC)

Yes it is. I've updated the equations to be correct and added a reference from which I took the equations. I'm not sure where the f_H equation comes from, so I left it in for now. It probably would be a good idea to link to the prototype filter pages. It's not referenced to f_C = 1 Hz, though. It's ω_C = 1 rad/sec. Wa03 (talk) 15:50, 2 July 2012 (UTC)

Missleading picture

Hey, I am a little confused about the picture of the frequency response of the chebychev filter type 1. If you plot the response in dB it is impossible that the blue line is 1 / sqrt( 1 + eps^2), because it is clearly a positive value. It looks like the scale of the gain isn't in dB, but in the "normal" absolute value of the transfer function. Maybe it should be chanced. 91.66.179.181 (talk) 12:06, 30 August 2012 (UTC)

The blue line is the gain in dB for G=1/√2 with G as defined in the text. It is not the actual value of the blue line plot, which is -3 dB. The graph is definitely in dB; if it were linear the excursions would be considerably more pronounced. 16:25, 30 August 2012 (UTC)

Gain on complex plane images

Why do the gain images show twice the number of poles and zeros compared to the transfer function? All poles and zeros appear duplicated with the sign of the real part of the duplicate flipped. Olli Niemitalo (talk) 08:55, 30 October 2016 (UTC)

The answer is not simple. The gain is not simply the absolute value of the transfer function (I have changed that statement in the article). The gain function is the absolute value of the steady-state output amplitude divided by the amplitude of a steady-state input. So if you want to calculate the gain using the transfer function, you input a signal for which σ is zero, get the output signal, which, as time increases, may settle into a steady state, then you divide those steady-state amplitudes and take the absolute value. It is a theorem that the result you get will be the absolute value of the transfer function evaluated at j ω. The output will only settle to a steady state if the poles of the transfer function all have σ less than zero. The gain function poles will be the poles of the transfer function, AND the mirror images of the poles of the transfer function, with the ω axis forming the mirror. In other words if σ+ j ω is a pole of the transfer function, then both σ+ j ω and -σ+ j ω will be poles of the gain function. PAR (talk) 15:25, 2 November 2016 (UTC)

Generalised Chebyshev Filters

Could a section on generalised Chebyshev, a.k.a "quasi-elliptical", filters could be added to this article, please? MyOtherHead (talk) 01:52, 17 May 2017 (UTC)

LPF: Gain=1 at w=0

It is clear from the Chebyshev transfer function that, at w=0, Gain=1 (0 dB) always. On the first plot, < The frequency response of a fourth-order type I Chebyshev low-pass filter with ε = 1 > , Gain=-3 dB instead of 0, at w=0. For instance, if n is even, the ripples are upwards and the cutoff frequency is at Gain=1 (0 dB). If n is odd, the ripples are downwards and the cutoff frequency is at G=1/sqrt(1 + eps^2). KerimF (talk) 20:42, 29 December 2018 (UTC)

Only the odd Chebychev polynomials go to 0 at $\omega =0$. See Chebyshev polynomials#Examples. For a fourth-order filter,

$T_{4}(x)=8x^{4}-*x^{2}+1$

$T_{4}(0)=1$

$G(0)={1 \over {\sqrt {2}}}$

or 3 dB, as correctly shown on the plot. SpinningSpark 00:24, 30 December 2018 (UTC)

I agree with you, SpinningSpark. So I wonder how we could relate the response of real Chebyshev active filters to the transfer function. For example, the initial gain (at w=0) of chebyshev Sallen-Key active filters is the same, say “K”, for “n” pair or odd. And the gain difference in the passband is the side, above or below K, on which the ripples are; it is above “K” if “n” is pair and below “K” if n is odd.KerimF (talk) 08:52, 2 January 2019 (UTC)

Clearly, you need to scale the response to the boundary conditions of the filter you have actually built. Remember, passive LC network is not the only way of implementing this function. One can also implement as active (Sallen-Key) elements, or entirely in the digital domain in a DSP for instance. In just about every implementation except passive LC, the overall gain is just another parameter under the control of the designer. SpinningSpark 13:32, 2 January 2019 (UTC)

Thank you. KerimF (talk) 01:49, 3 January 2019 (UTC)

Consistency

In the first chapter "Type I Chebyshev filters (Chebyshev filters)" δ stands for the passband ripple in dB, while in the later chapter "Implementation" it's called R_dB. This could be because of different literature, but it should be consistent.

WP:SOFIXIT. SpinningSpark 17:33, 11 January 2019 (UTC)