# FIR Filters: determining optimal number of taps and phase slope

As a design input for an low-pass FIR filter I have 6dB@1.6kHz, 24 dB/oct, sample frequency 48kHz. I need to specify phase response, and for that I need a phase slope. I have found, from Julius O. Smith web page, that the phase slope = (N-1)/2 where N is number of taps. What is the way to determine the optimal number of taps? I am aware of Kaiser formula, but I don't have ripple, passband and stopband frequencies that figure in the formula. I need the number of taps to calculate phase slope. Is there any other way to calculate, specify phase from my input requirements?

• There is no formula, it's just trial and error (and experience). Also note that your specs are very minimalistic, e.g. what behavior do you expect in the pass band, etc.? – Matt L. May 25 '15 at 15:25
• Please indicate if you are referring to a low-pass filter. Also, since you mention a constant group delay ("phase slope"), then another requirement should be phase linearity (not all FIR filters have linear phase). – Juancho May 25 '15 at 16:44
• That's the spec I have. There is a reference curve in Smaart v.7 and I am uploading coefficients to the filter so I can see how well it matches curve. Maybe the question how to find phase slope is good too. From Julius O. Smith site I have found that phase slope is (N-1)/2, N - number of taps. – Nebojsa May 25 '15 at 17:06
• For a linear phase filter, the group delay (phase slope) is indeed $(N-1)/2$, but the question is if linear phase is a requirement or not. – Matt L. May 25 '15 at 18:26
• @MattL. Yes, linear phase is requirement. – Nebojsa May 26 '15 at 13:11