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20115eeM171L_2_HW 1_Fourier_1_2

20115eeM171L_2_HW 1_Fourier_1_2 - f= f= f= f= f= f= f= 5(2...

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EE M 171L, Laboratory Exercise 1 1 UNIVERSITY OF CALIFORNIA, LOS ANGELES Department of Electrical Engineering M 171L Laboratory Pre-Laboratory Home Work #1; (Due 10/04/11). Students Name____________________________ Signals in Time and Frequency Domains 1) (2) Draw plots of amplitude versus time for the following rectangular signals with period T and amplitude A : (a) Duty cycle d = 50% (also called a “square wave”) (b) Duty cycle d = 25% (a) t (b) t S ( t ) S ( t ) T 2 T T 2 T A -A -A 2) (2) The Fourier series for the square wave signal in (a) is:
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EE M 171L, Laboratory Exercise 1 2 3) (2) The Fourier series for the rectangular signal in (b) (duty cycle d = 25%) is: The effective amplitude spectrum of a signal is built from the RMS voltages of each frequency represented in the Fourier series for that signal. 4) (4) If the amplitude of each signal is A max = 2V, calculate the effective amplitudes of spectra (through the 7 th harmonic) for functions (a) and (b) above. f A rms (a) f A rms (b) f= f= f= f= f=
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Unformatted text preview: f= f= f= f= f= f= f= 5) (2) How does the effective amplitude spectrum of a signal change when we add a time shift or a phase shift to the signal? EE M 171L, Laboratory Exercise 1 3 6) (2) What are the differences between the amplitude spectrum and the effective amplitude spectrum? 7) (2) If the amplitude of the signals in (a) and (b) above is A = 2V, and each signal is sent to a 1 Ohm load, what is the power of each signal? Calculate the power by subtracting the DC offset power from the time-domain power. The power of a periodic signal equal to the power of the signal in the time-domain minus the power of the signal’s DC offset. 8) (2) How do we define the effective bandwidth of a periodic signal? 9) (2) How do we define the absolute bandwidth of a periodic signal? What are the absolute bandwidths of the signals in (a) and (b) above? (Use the calculations in the lecture notes.)...
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