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Chebyshev v Butterworth Filter Design

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Elias Altrabshah

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In parts A and B we design a 9th order Chebvshev filter. However, I'm stuck with part C.

Can you confirm/disprove my method as being correct steps in solving the problem please?

1. Already determined is that we require a 9th order system. So we evaluate the Chebyshev polynomial up to this order.

2. It is required to look at the attenuation within the stop band, so we define the Ls(dB) equation for both filters.

3. As they are in measured in dB we subtract the Ls of the Cheybshev from the Ls of the Butterworth

4. Finally perform the algebraic manipulation for confirm the relationship

I'm at step 4, but can tell its all about to kick off when the Chebyshev polynomials are inserted to the equation.

Thank you in advance

Elias

11281595_10152872092801027_2014970034_o.jpg
 

LvW

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Perhaps the following can help for solving step 4:

For the Butterworth as well as Chebyshev approximation there is a formula that gives you the required filter order n as a function of w (ripple), as (stopband attenuation, ws (stopband freqency).
These formulas contain the log function (for Butterworth) and the arcosh function (for Chebyshev). If desired, I can provide you with the formulas.
Inserting the actual n value (n=9) it should be possible to find the difference in stopband attenuation for both approximations at a certain stop band frequency.
 

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