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Unformatted text preview: EE 2200 / Spring 2010: Section TWO 1 ECE 2200 / Spring 2010 SECTION Two (Week 3: Feb 8-11) 1. Problem P-2.21 in text. 2. Consider the system that with input u u ( t ) = cos( at ) produces the output y y ( t ) = u ( t )(cos( bt )) Given that the magnitude spectrum of y has lines at only four frequencies: 16 . 8 and 17 . 6 MHz, determine a and b . 3. The signal x ( t ) has the two-sided spectrum representation shown in Figure 1. (i) Write an equation for x ( t ) as a sum of cosines. (ii) Is x ( t ) a periodic signal? If so, determine its fundamental period and its fundamental frequency. (iii) Discuss why negative frequencies are in the spectrum. Figure 1: Two-sided spectrum of x ( t ) 4. Consider the signal x ( t ) = 6 . 5 + 8 . 4 cos(2 520 t ) + 6 . 1 cos(2 728 t ) (i) Determine the fundamental frequency and period of x ( t ). (ii) Using the finite Fourier synthesis formula N k =- N a k e j (2 /T ) kt determine N and all of the a k needed to describe x ( t ). (You should not need to evaluate any)....
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