2. Consider a system with input (t) and output y(t) shown in Figure 2 x(t) y(t)...

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2. Consider a system with input (t) and output y(t) shown in Figure 2 x(t) y(t) Figure 2: Filter with input (t) and output y(t) Suppose that the system is an ideal low-pass filter with frequency response given by Fig 1, where W = 20 Assume that the input to the system is the square wave shown in Figure 3. 1 x(t) -To - To 0 - 4 64 To 5/2 Figure 3: Square Wave Recall that the Fourier series coefficients of this square wave are sin () k To t (a) Please sketch the spectral representation for x(t), showing at least 5 frequency components (i.e. 5 bars). (b) Using what you know about the ideal low-pass filter, please sketch the spectral representation for y(t). (c) Please find y(t) in terms of a constant and a cosine. (1) 2. Consider a system with input (t) and output y(t) shown in Figure 2 x(t) y(t) Figure 2: Filter with input (t) and output y(t) Suppose that the system is an ideal low-pass filter with frequency response given by Fig 1, where W = 20 Assume that the input to the system is the square wave shown in Figure 3. 1 x(t) -To - To 0 - 4 64 To 5/2 Figure 3: Square Wave Recall that the Fourier series coefficients of this square wave are sin () k To t (a) Please sketch the spectral representation for x(t), showing at least 5 frequency components (i.e. 5 bars). (b) Using what you know about the ideal low-pass filter, please sketch the spectral representation for y(t). (c) Please find y(t) in terms of a constant and a cosine. (1)