8. Consider the continuous-time epcriodic signal x(1) and the periodic signal il) defined by -1 I- E2). 0, othcrwise (a) Compute the l'ourier transform X(j27 F) of x(1) and the Fourier scries cocfficients C of fr). (b Using the results in (a) verify the relationship c - X(j2zk/Th) /To. to Pla X(j2x Ð| and lal on one plot and ZX(j2x F) and Zq on another plot to illustrate the rtsult in part (b). An aperiodic signalTf)

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8. Consider the continuous-time aperiodic signal 1) and the periodic signal i()
defined by
() -
and i() -
Tt-2).
otherwise
(a) Compute the Fourier transform X(j27 F) of x(1) and the Fourier serics cocfficients
q of f().
(b Using the results in (a) verify the relationship - X(j2zk/Th) /To.
(O Plat IX(j2n FD| and Ical on one plot and ZX(j2nF) and Zg on another plot to
illustrate the result in part (b).
An aperiodic signal x(1) - 2xinc(21) is multiplied by a periodic rectungular pulse truin
s() with fundamental frequency Fo - 4 Hz and the fundamental rectangular pulse
given by
1. -1/80 re 1/80
0. othcrwisc
pi) -
to obtain a signal x,t) - x(tis().
(a Compute and plot the CTIT X2) over the F< 80 range in Hr.
by Compute and plot the CTIS cocfficients Over the A 80 range in Hz.
(C) Compute X (j2F) using ( and plot it ver the F 80 range in H.
10. In this problem we illustratc the numerical cvalualion ofDTES using MATLAR.
(a) Write a funcion dif( which compates the DTT cocflicients Tof a
pcriodic signal.
b) Write a furction aFnOi- which computes the inycrse DTES
Verify that your funcions are sorking comuctly by replicating the nauls in
Example 1
Determinc and plot the maer tede and phae spera of the fowina de
scquence
hp
fg
f10
f11
f12
Transcribed Image Text:E-00 8. Consider the continuous-time aperiodic signal 1) and the periodic signal i() defined by () - and i() - Tt-2). otherwise (a) Compute the Fourier transform X(j27 F) of x(1) and the Fourier serics cocfficients q of f(). (b Using the results in (a) verify the relationship - X(j2zk/Th) /To. (O Plat IX(j2n FD| and Ical on one plot and ZX(j2nF) and Zg on another plot to illustrate the result in part (b). An aperiodic signal x(1) - 2xinc(21) is multiplied by a periodic rectungular pulse truin s() with fundamental frequency Fo - 4 Hz and the fundamental rectangular pulse given by 1. -1/80 re 1/80 0. othcrwisc pi) - to obtain a signal x,t) - x(tis(). (a Compute and plot the CTIT X2) over the F< 80 range in Hr. by Compute and plot the CTIS cocfficients Over the A 80 range in Hz. (C) Compute X (j2F) using ( and plot it ver the F 80 range in H. 10. In this problem we illustratc the numerical cvalualion ofDTES using MATLAR. (a) Write a funcion dif( which compates the DTT cocflicients Tof a pcriodic signal. b) Write a furction aFnOi- which computes the inycrse DTES Verify that your funcions are sorking comuctly by replicating the nauls in Example 1 Determinc and plot the maer tede and phae spera of the fowina de scquence hp fg f10 f11 f12
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