L3-Sampling

L3-Sampling - A typical digital communication system...

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1 Channel h(t) Analog source ADC Source encoder Digital source Channel encoder Modulator Output amplifier Digital user DAC Source decoder Analog user Channel decoder Demodulator Low noise amplifier LPF Sampler Quantiser Encoder LPF PCM signal Regenerative repeater Regenerative repeater × + Multiplicative disturbance e.g., fading Additive noise & interference Channel A typical digital communication system Note: (1) Source encoder reduces the redundancy in the PCM signal, thus converting it into a shorter digital signal. (2) Channel coder deliberately added redundancy into the digital signal to enable error detection and correction at the receiver. (3) Modulator is either baseband or passband Baseband – formats digital sequences into suitable pulse for transmission (line coding) Passband – injects with a high frequency carrier.
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2 Sampling of Analog Signals The process of sampling has been introduced to convert an analog signal to a discrete time form for further signal processing. The sampling process may be illustrated by switching an analog input signal ) ( t v a using a gating signal ) ( t v g to produce the output sampled signal ) ( t v s as shown below: Questions: Can we uniquely recover the original analog signal ) ( t v a from the sampled signal ) ( t v s ? If so, what should be the sampling rate g f ? Analog input v a (t ) Sampled Signal v s ( t ) Sampling switch Gating signal v g ( t ) t T = 1/f g v a ( t ) v g ( t ) v s ( t )
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3 The operation of sampling at a single time instant 1 t t = can be defined by the “shifting theorem” involving the impulse function ) ( t δ , such that ). ( ) ( ) ( 1 1 = t f dt t t t f Now, assume that the analog waveform is sampled periodically with a period T by means of a sampling or gating impulse train ) ( t g expressed as −∞ = = k kT t t g ) ( ) ( . Then the sampled waveform is given by −∞ = = k a s kT t t v t v ) ( ) ( ) ( . The Fourier series of the sampling impulse train ) ( t g is = = −∞ = −∞ = T nt j kT t t g n n k π 2 exp ) ( ) ( where n. all for 1 2 exp ) ( 1 2 / 2 / T dt T nt j t T T T n = = In this case, the sampled waveform ) ( t v s can be expressed as .
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L3-Sampling - A typical digital communication system...

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