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Lab_1_SIGNALS_2001

Lab_1_SIGNALS_2001 - M 171L Laboratory Exercise 1 revised 1...

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M 171L Laboratory Exercise 1, revised 11/29/00 1 UNIVERSITY OF CALIFORNIA, LOS ANGELES Department of Computer Science M 171L Computer Communication Systems Laboratory Student name ___________________ Laboratory Exercise 1: Signals in Time and Frequency Domains The purpose of this lab is to introduce you to the representation of digital signals in the time and frequency domains and to determine the frequency bandwidth of each signal under consideration. In this lab you will use an oscilloscope to examine the time domain representation of the signals and a spectrum analyzer to see the components of the same signals in the frequency domain. You will relate these to the formal mathematical expressions derived from theory. Pre-Lab Assignment: The theory section on the next several pages and the theoretical calculations for your results (the shaded boxes in the Results section) must be completed correctly before you will be allowed to start the laboratory exercise. You must have your answers written in these sections before coming to the lab. They will be checked by the TA before you begin the experiment. Be prepared to answer questions about the material.
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M 171L Laboratory Exercise 1, revised 11/29/00 2 Exercise #1: Theory (Include with report) A periodic signal satisfies the condition: S ( t + T ) = S ( t ) ; - < t < + . The smallest constant value T that satisfies this equality is called the “period” of the signal. A periodic signal S ( t ) can be expressed by a Fourier-series if it is continuous and finite within the signal period. A rectangular wave is a periodic signal where the signal has a value of + A for some continuous interval during the period (the “mark”), and has a value of - A for the remainder of the period (the “space”). The “duty cycle” d of the rectangular wave is defined as the length of the positive interval divided by the period. 1) 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 A -A A -A T 2 T 2) The Fourier series for the square wave signal in (a) is:
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M 171L Laboratory Exercise 1, revised 11/29/00 3 Exercise #1: Theory (continued) (Include with report) 3) 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) If the amplitude of each signal is A max = 2V, draw the effective amplitude spectra (through the 8 th harmonic) for functions (a) and (b) above. f A rms (a) f A rms (b) 5) How does the effective amplitude spectrum of a signal change when we add a time shift or a phase shift to the signal?
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M 171L Laboratory Exercise 1, revised 11/29/00 4 Exercise #1: Theory (continued) (Include with report) 6) What are the differences between the amplitude spectrum and the effective amplitude spectrum?
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