The Fourier series coefficients of a periodic signal x(t), with fundamental frequency Ω₀= Ï€/4 are X₁= X^ˆ—_ˆ’1=j, X₅= X^ˆ—_ˆ’5= 2 and the rest are zero. Suppose x(t) is the input to a band-pass filter with the following magnitude and phase responses

Let y(t) be the output of the filter.

(a) Determine the Fourier series of x(t) in the trigonometric form

and then find the steady-state response of y(t).

(b) Find the Fourier transform of x(t) and y(t) and carefully plot their magnitudes and phases.

Transcribed Image Text:

|H(j2)| : ZH(jN) = -2 -1.5n X cos(k2ot + ZXµ) k=0