EE200_Weber_9-14

# EE200_Weber_9-14 - EE 200 Amplitude Modulation In AM the...

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5 EE 200 Amplitude Modulation In AM, the carrier frequency is multiplied by the signal. Let f c = 500Hz, and 100 300 500 -100 -300 -500 4 f (Hz) x ( t ) = v ( t )cos(2 " f c t ) v ( t ) = A 0 + A s cos(2 f s t ) = 4 + 3cos(2 50 t )

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6 EE 200 Amplitude Modulation The shape, or “envelope”, of the modulated carrier is the information in the lower frequency signal. x ( t ) = v ( t )cos(2 " f c t ) = (4 + 3cos(2 50 t ))cos(2 500 t )
7 EE 200 Amplitude Modulation Resulting signal has components around both f c and -f c 100 300 500 -100 -300 -500 2 f (Hz) x ( t ) = (4 + 3cos(2 " 50 t ))cos(2 500 t ) = 4cos(2 500 t ) + 3 2 cos(2 (500 # 50) t ) + 3 2 cos(2 (500 + 50) t ) = 500 t ) + 3 2 cos(2 450 t ) + 3 2 cos(2 550 t )

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8 EE 200 Amplitude Modulation The entire spectrum of the signal is shifted and mirrored around both f c and -f c 100 300 500 -100 -300 -500 A f (Hz) 100 300 500 -100 -300 -500 A f (Hz)
9 EE 200 Fourier Series Jean Baptiste Joseph Fourier proposed that a periodic signal can (usually) be represented as a sum of sinusoids plus a constant term. Fourier was not the first to think of using sums of sinusoids to represent signals. The Babylonians had used trigonometric sums for astronomy.

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EE200_Weber_9-14 - EE 200 Amplitude Modulation In AM the...

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