How to add odd number and even number polynomial series with different sampling time

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phoenix 2018-12-30

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https://ww2.mathworks.cn/matlabcentral/answers/437695-how-to-add-odd-number-and-even-number-polynomial-series-with-different-sampling-time

回答： Walter Roberson 2019-1-2

How to add B1 and B2 having different sampling time:

B1=B(1,1)z^-0+B(3,1)z^-2+..........+B(201,1)z^-200 
B2=B(2,1)z^-1+B(4,1)z^-3+..........+B(202,1)z^-201

and represent the transfer function as T(z)=(B1+B2)/B1 and plot the frequency response in Matlab.

B(1,1),B(2,1),B(3,1)....are the polynomial coefficients.

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Answer 1

Walter Roberson 2019-1-2

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How to add B1 and B2 having different sampling time:

Resample them both to the lcm (lowest common multiple) of the two sampling rates.

and represent the transfer function as T(z)=(B1+B2)/B1

It is not obvious to me that that makes sense to do. In transfer functions, z is input frequency, and sampling rate is the same as frequency, so talking about B1 and B2 having different sampling rates would sound to be equivalent to saying that B1(z) and B2(z) are being evaluated at different z, which would make it difficult to establish a meaning for T(z).