The output of an ideal low-pass filter is

(a) Assume the filter input is a periodic signal x[n]. What is its fundamental frequency ω₀? What is the fundamental period N₀?

(b) When the filter is low-pass with H(e^j0) = H(e^jω0) = H(e^ˆ’jω0) = 1 and H(e^j2ω0) = H(e^{ˆ’j2ω0}) = 1/2 determine the Fourier series for the  input x[n].

Transcribed Image Text:

y[n] = 1+(2/k) cos(0.2t kn) 0 < n < ∞. k=1 |