Two bandpass filters have impulse responses h1n 04n cospi n

Two bandpass filters have impulse responses h_1[n] = (0.4)^n cos(pi n/3)u[n] and h_2[n] = (0.8)^n cos(3pi n/4)u[n]. Without computing the DTFT, find the center frequency of each, and determine which one has the bigger bandwidth. Explain your answers. Are they FIR or HR filters? What order is the filter?

Solution

h1(z) = 1/ ( 1- 0.4e(pi/3) z^-1 + 1/  ( 1+ 0.4e(pi/3) z^-1 )

centre frequency = 2.5

h2(z) =  1/ ( 1- 0.8e(3pi/4) z^-1 + 1/  ( 1+ 0.8e(3pi/4) z^-1 )

centre frequency = 1.25

h1(z) has higher bandwidth

secod order of the system\'

it is FIR filters