Question

At most how many extremal frequencies can be there in the error function of ideal low pass filter?

(a) L+1

(b) L+2

(c) L+3

(d) L

I had been asked this question in class test.

My doubt is from Design of Optimum Equi Ripple Linear Phase FIR Filters topic in section Digital Filters Design of Digital Signal Processing

Answer 1

Correct choice is (c) L+3

To explain I would say: We know that we can have at most L-1 local maxima and minima in the open interval 0<ω<π. In addition, ω=0 and π are also usually extrema. It is also maximum at ω for pass band and stop band frequencies. Thus the error function of a low pass filter has at most L+3 extremal frequencies.