Let the signal x(t) r(t 1) 2r(t) r(t 1) and y(t) dx(t) dt (a) Plot x(t) and y(t) (b) Find X() and carefully plot its magnitude spectrum Is X() real Explain (c) Find Y()(use properties of Fourier transform) and carefully plot its magnitude spectrum Is Y() real Explain (d) Determine from the above sp...

a The triangular pulse xt is even xt rt 1 2rt rt 1 and its derivat ...

Let the signal x(t) = r(t + 1) 2r(t) + r(t 1) and y(t) =

Question:

Let the signal x(t) = r(t + 1) − 2r(t) + r(t − 1) and y(t) = dx(t)/dt.

(a) Plot x(t) and y(t)

(b) Find X(Ω) and carefully plot its magnitude spectrum. Is X(Ω) real? Explain.

(d) Determine from the above spectra which of these two signals is smoother. Use MATLAB integration function int to find the Fourier transforms. Plot 20 log₁₀|Y(Ω)|and 20 log₁₀|X(Ω)|and decide. Would you say in general that computing the derivative of a signal generates high frequencies, or possible discontinuities?

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