ps4 - MIT OpenCourseWare http://ocw.mit.edu 2.161 Signal...

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Unformatted text preview: MIT OpenCourseWare http://ocw.mit.edu 2.161 Signal Processing: Continuous and Discrete Fall 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms . -1.5-1-0.5 0.5 1 1.5 f am (t) t MASSACHUSETTS INSTITUTE OF TECHNOLOGY DEPARTMENT OF MECHANICAL ENGINEERING 2.161 Signal Processing- Continuous and Discrete Fall Term 2008 Problem Set 4 Assigned: Oct. 2, 2008 Due: Oct. 9, 2008 Problem 1: An AM (amplitude-modulated) radio signal f AM ( t ) is described by f AM ( t ) = (1 + af audio ( t )) sin( c t ) where f audio ( t ) is the audio signal, sin ( c t ) is known as radio-frequency carrier signal ( f c = 500 1600 kHz- the AM band), and a is a positive constant that determines the modulation depth . (Note that we require af audio ( t ) < 1 otherwise we have over-modulation.) the | | following figure shows an AM signal with an audio waveform that is a simple low frequency sinusoid. You can see how the audio signal modulates the amplitude of the rf signal. (a) Sketch the magnitude of the Fourier transform of f AM ( t ) when f audio ( t ) = 0. (b) Let a = 0 . 5, and sketch the magnitude of the Fourier transform of f AM ( t ) when f audio ( t ) = 0 . 5 cos(2 1000 t ) + 0 . 25cos(2 2000 t ) ( Hint: There is no need to actually compute the FT. Consider expanding f AM ( t ), or simply use properties of the FT.) (c) Use your result from (b) to generalize, and sketch the...
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This note was uploaded on 02/27/2012 for the course MECHANICAL 2.161 taught by Professor Derekrowell during the Fall '08 term at MIT.

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ps4 - MIT OpenCourseWare http://ocw.mit.edu 2.161 Signal...

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