Assignment 5

# Assignment 5 - 1 ECSE304 Signals and Systems 2 Winter...

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Problem Set 5 1 ECSE304 Signals and Systems 2 Winter Semester 20 11 McGill University Department of Electrical and Computer Engineering Problem Set 5 Distributed: Tuesday , March 1, 20 11 Due : Thursday, March 10 , 20 11 Assignments can be worked in Groups of 2. A cover sheet, which is found at the bottom of the Assignments page in the ECSE304 webCT site, should be handed in with each assignment. MatLab Exercises In all MatLab Exercises, you are to show all your work and hand in both your MatLab code and the plots that you generate. An Introduction to Amplitude Modulation and Demodulation : Amplitude modulation is often used to transmit a signal with low-frequency content using a high frequency transmission channel. A common example is AM radio. In AM radio a relatively low frequency signal such as a speech signal (which has frequencies between 50 Hz and 4 kHz) is transmitted by radio waves at frequencies around 1 MHz. Amplitude modulation is performed by multiplying a high frequency signal (called the carrier ) by a the low-frequency message signal m ( t ): () (1 () )cos (2 ) xt mt ft c π φ =+ + (1) where the carrier signal corresponds to the cos(2 ) c + term. Although the message signal m ( t ) may be very complicated, a good understanding of AM can be obtained by analyzing AM signals of the form: cos2 ) x tA f t f t mc ππ (2) i.e., the message signal is a cosine, () co s2 A f t m = . A straightforward expansion of (2) shows that: ( ) cos(2 ) cos 2 ( ) cos 2 ( ) 22 AA x tf t f f t f f t cm c + + (3) In communications terminology, the signal components at f ff = ± are called the sidebands and the signal component with a frequency of f c is called the carrier. When f f >> the spectrum of the AM signal looks like that shown in the following figure:

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Problem Set 5 2
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Assignment 5 - 1 ECSE304 Signals and Systems 2 Winter...

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