Suppose that the input x(t) to an ideal frequency selective filter is the square wave depi...

Suppose that the input x(t) to an ideal frequency selective filter is the square wave depicted in Figure 1. The Fourier series representation of this waveform is

(a) Determine the fundamental frequency ω0

(b) Determine the Fourier coefficients ak for this signal.

(c) State whether or not it is possible that the corresponding output of the LTI system could be the signal

If it is impossible, state why. If it is possible, determine the frequency response H (jω) of an ideal frequency-selective filter (lowpass, highpass, or bandpass) such that the output is as specified. Draw a carefully labeled sketch of H (jω) showing the gain and cutoff frequencies for the filter.

(d) Repeat part (c) when the desired output is

Figure 1: