FDAtool - Scale Passband (Chebyshev)

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Jan 2011-3-24

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https://ww2.mathworks.cn/matlabcentral/answers/3902-fdatool-scale-passband-chebyshev

hello,

In Matlab when I use fdatool i see the option "Scale Passband" now this option changes the coefficients drastically, after some reading I found out the use for it but not the mathematical way to calculate it yourself.

I used for example, fs = 48000hz, fc1 = 4000, fc2 = 6000, order = 4, sidelobe attenuation = 60, scale passband is not checked. That are my FDAtool settings, now I calculated h(0) = 0.917, multiplying h(0) with the window variable (witch comes from chebwin function) gives me 0.917. this value matches FDAtool coefficients, so I can conclude that the coefficients are calculated correctly.

Now when I check the option "Scale Passband" my coefficients change, how they get the new coefficients is for me a complete riddle. Also the chebwin function doesn't calculate the new "scale bandpass" coefficients

Thank you!

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回答（1 个）

Honglei Chen 2011-3-24

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Hi Jan,

I can't really follow your example but the purpose of scale is to make sure that the center of the first passband has a magnitude response of 1.

HTH.

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Jan 2011-3-26

Can you give any more mathematical explanation? Maybe a small example?

Honglei Chen 2011-3-28

Suppose that using the regular Chebyshev window, you get your coefficients in variable b, and your pass band is centered at f0. Denote B(f0) as the magnitude frequency response of b evaluated at f0, then the scaled coefficients will be

b_scaled = b/B(f0)

Note that B_scaled(f0) = B(f0)/B(f0) = 1.

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