Consider the signal x(t) = u(t + 1) 2u(t) + u(t 1) and let (a) Plot x(t) and y(t) (b) Find X(Ω) and carefully plot

Consider the signal x(t) = u(t + 1) ˆ’ 2u(t) + u(t ˆ’ 1) and let

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

(b) Find X(Ω) and carefully plot its magnitude spectrum. Is X(Ω) real? Explain. (Use MATLAB to do the plotting.)

(c) Find Y(Ω) and carefully plot its magnitude spectrum. Is Y(Ω) real? Explain. (Use MATLAB to do the plotting.)

(d) Determine from the above spectra which of these two signals is smoother. Use MATLAB to decide. Find the Fourier transform using the integration function int. Would you say that in general by integrating a signal you get rid of higher frequencies, or smooth out a signal?

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