2. Consider a 4-periodic signal y(t) defined as 0 < t < 1 2 t 1 < t <3 y(t) 1 3 < t < 4 Vt g(t+4) (a) Sketch y(t) over t

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2 Consider A 4 Periodic Signal Y T Defined As 0 T 1 2 T 1 T 3 Y T 1 3 T 4 Vt G T 4 A Sketch Y T Over T 1 (447.26 KiB) Viewed 43 times

2. Consider a 4-periodic signal y(t) defined as 0 < t < 1 2 t 1 < t <3 y(t) 1 3 < t < 4 Vt g(t+4) (a) Sketch y(t) over two periods. (b) Without using direct integration (that is, use properties!), determine the (complex exponential) Fourier series Y of signal y(t). What is wo? [Note: if needed, you can use integration to find X₁] (c) Use MATLAB to plot the Fourier series magnitude and phase spectra over -K ≤ k ≤ K, where K is some suitably chosen positive constant. (d) Similar to the example provided in class, synthesize and (MATLAB) plot the K = 5, K = 10, and K = 25 truncated Fourier series yk (t) over two periods. t²