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1. Consider a continuous-time ideal high-pass filter that removes all frequencies below a given cut-off frequency, and allows all frequencies at or above that cut-off frequency to pass through the system unchanged. That is, the filter will keep frequency w if w] 2we and remove frequency w if ww Let the cutoff frequency we have value 2π. (a) Sketch this filter's frequency response H(ju). (b) Let x(t) 4-3 cos(3m) + 6eMt. Find ak, the Fourier series coefficients of x(t) (c) Now, let r(t) (defined as in part b) be the input to this high-pass filter. Let y(t) represent the filter's output, and let bk represent the Fourier series coefficients of y(t) Write an expression for bk (d) Write an expression for y(t)
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