Number of filter taps in Gaussian filter design

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

Answer 1

[Paul]

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."

[Jay]

Thanks Paul for the explaination!

You answer makes sense but I have a follow up question. Why "span x sps" is always supposed to be even in the filter design? As an example, let's consider the case where I need to design 3 symbol span with 25 samples per symbol, then the gaussdesign does not allow this because 3x25 is not an even. Any explanation on this as well?

Thanks for your time and answer.

[Paul]

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]

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.