Sep 15, 2005CS477: Analog and Digital Communications1 Modulation and Sampling Analog and Digital Communications Autumn 2005-2006.

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Presentation transcript:

Sep 15, 2005CS477: Analog and Digital Communications1 Modulation and Sampling Analog and Digital Communications Autumn

Sep 15, 2005CS477: Analog and Digital Communications2 The Dirac Delta Function A generalized function

Sep 15, 2005CS477: Analog and Digital Communications3 FT of 1 and exponentials Fourier transform of RF Pulse:

Sep 15, 2005CS477: Analog and Digital Communications4 Modulation Revisited Multiplication in time domain is the same as convolution in the frequency domain

Sep 15, 2005CS477: Analog and Digital Communications5 Other Functions Signum Function: Unit step Function:

Sep 15, 2005CS477: Analog and Digital Communications6 FT of Periodic Signals

Sep 15, 2005CS477: Analog and Digital Communications7 FT of Periodic Signals

Sep 15, 2005CS477: Analog and Digital Communications8 Sampling First consider modulation Product with Cosine in time domain Convolution with two impulses in frequency domain Next consider sampling Product with a train of impulses in time domain Convolution with a train of impulses in the frequency domain Nyquist sampling theorem A bandlimited signal [-B, +B] can be characterized by its samples taken every 1/(2B) seconds. i.e., 2B samples per second Undersampling leads to aliasing