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20115ee102_1_project - 1 EE102 Fall Quarter 2011 Systems...

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1 EE102 Systems and Signals Fall Quarter 2011 Jin Hyung Lee Course Project Amplitude Modulation (AM) is a technique widely used in communication area. One exam- ple you can see in your everyday life is the AM radio. The basic principle of the AM technique is modulating a high frequency sinusoidal carrier signal’s amplitude by a low frequency signal (e.g. your voice or music). (See figure 1 ) Figure. 1 This modulation process can be expressed mathematically by: x ( t ) = a ( t ) cos ( ω 0 t ) where the frequency of ω 0 is in the range of MHz/Ghz (The AM spectrum in the US goes from 520 kHz to 1610 kHz, with channels separated by 10 kHz. ), however, the bandwidth of A(t) is usually less than 10kHz. (e.g. Human voice band ranges from approximately 300 Hz to 3400 Hz ). According to the Fourier Transform properties we learned in the lecture, AM signal is the convolution of A ( ) and π [ δ ( ω - ω 0 ) + δ ( ω + ω 0 )] in the frequency domain. Where A ( ) and π [ δ ( ω - ω 0 ) + δ ( ω + ω 0 )] are Fourier Transform of a ( t ) and cos ( ω 0 t ) . Thus in this process the low frequency signal is modulated to a high frequency (See figure 2 ) A(jw) π[δ(w-w 0 )+δ(w-w 0 )] A(jw)*π[δ(w-w 0 )+δ(w-w 0 )] Figure. 2
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2 To demodulate this signal, ideally you can multiply e - 0 t with x ( t ) . This is very easy to program on softwares like Matlab which supports complex number calculations. However, in
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