# SolSec7.3 - Problems and Solutions Section 7.3(7.6-7.9 7.6...

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Problems and Solutions Section 7.3 (7.6-7.9) 7.6 Represent 5 sin 3 t as a digital signal by sampling the signal at π /3, π /6 and π /12 seconds. Compare these three digital representations. Solution: Four plots are shown. The one at the top far right is the exact wave form. The one on the top left is sampled at π /3 seconds. The next plot is sampled at π /6 seconds.

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The next plot is sampled at π /12 seconds. None of the plots give the shape of a sine wave. However if the s3 is connected by lines, the wave shape is close.
7.7 Compute the Fourier coefficient of the signal |1120 sin (120 π t )|. Solution: f ( t ) = |120 sin (120 π t )| (absolute value of the sine wave) To calculate the Fourier series: T = 1/120 sec T ω = 240 π rad/sec at d t o = 240 120 120 0 1 120 sin( ) π 480 = o a a t nt dt n = 240 120 120 240 0 1 120 sin( )cos( ) ππ ) 4 1 ( 480 2 n a n = b t nt dt n = 240 120 120 240 0 1 120 sin( )sin( ) 0 = n b ft n nt n ( ) cos( ) =+ = 240 1 2 14 240 2 1

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7.8 Consider the periodic function x ( t ) = −< < << 50 52 t t π ππ and x ( t ) = ( t + 2 π ). Calculate the Fourier coefficients.
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## This note was uploaded on 02/11/2010 for the course MECHANICAL ms316 taught by Professor Abduljaba during the Spring '09 term at Kalamazoo.

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SolSec7.3 - Problems and Solutions Section 7.3(7.6-7.9 7.6...

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