Number of filter taps in Gaussian filter design

Question

Jay 2023-9-24

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https://ww2.mathworks.cn/matlabcentral/answers/2024972-number-of-filter-taps-in-gaussian-filter-design

评论： Jay 2023-9-24

Hello,

I'm desinging a pulse shaping filter where the filter covers a span of 5 inputs symbols and 12 times of input symbol rate (e.g., 3.25 MHz). So I tried to use "gaussdesign" with parameter BT = 0.3, span = 5, and sps = 12.

I was expecting 60 coefficients which can be implemented with a polyphase FIR filter with a total 12 phases. However, the design with "gaussdesign" generated 61 taps. So what's happening here...? Am I missing something?

Thanks,

Jay

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Answer 1

Paul 2023-9-24

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https://ww2.mathworks.cn/matlabcentral/answers/2024972-number-of-filter-taps-in-gaussian-filter-design#answer_1316952

Hi Jay,

The doc page for gaussdesign states

"The number of symbols between the start and end of the impulse (span) and the number of samples per symbol (sps) determine the length of the impulse response: span×sps+1."

The impulse response for the given parameters is of length 61 and the number of delays needed to realize such a filter is 60, i.e.,

H(z) = h[0] + h[1]*z^-1 + .... h[60]*z^-60.

So there are 60 "taps," if by tap we mean "delay element."

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Paul 2023-9-24

I don't why span x sps must be even.

My guess is that it's important to have the impulse response be symmetric around the peak, which can only occur if the duration of the impulse response, span*sps + 1, is odd.

Jay 2023-9-24

One realization might be simpler than the other but both filters are implementable for sure whatever even or odd number of taps. Putting this restriction in MATLAB sounds strange to me.

Thanks Paul for the discussion. It helps.

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