EL611 Sampling_2011

# EL611 Sampling_2011 - below for sampling and reconstruction...

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EL6113 Sampling Practice 1. A set of samples, ) ( nT f , is given below. All samples that are not shown are zero. Find the unique function, ) ( t f , whose bandwidth satisfies T / π σ that passes through all of these samples. Your answer may contain the parameter T . 2. A signal, ) ( t f , has the spectrum shown below a) What is the minimum rate (Nyquist rate) at which we can sample ) ( t f if we want to reconstruct it exactly from its samples ) ( nT f ? b) Sketch ) ( ω F if ) ( t f is sampled exactly at the Nyquist rate. c) Sketch ) ( F if ) ( t f is sampled at three fourths of the Nyquist rate, i.e 4 3 = T . ) ( nT f t T T 2 1 2 ) ( F A

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3. Recall that the ideal reconstruction filter has the transfer function shown below. Let the signal ) ( t f be the same as in problem 2, and consider the two schemes shown
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Unformatted text preview: below for sampling and reconstruction. If the sampling rate is such that σ π 4 3 = T , which will be a better reconstruction of ) ( t f- ) ( 1 t f or ) ( 2 t f ? Note that in the upper scheme we just sample ) ( t f directly, and in the lower scheme we first filter out all frequencies above T / . ) ( ω R H T T − 1 ) ( t f ) ( nT f Impulse generator ) ( R H ∑ ∞ −∞ = − = n s nT t nT f T t f ) ( ) ( ) ( δ ) ( ˆ 1 t f Sample T ) ( t f ) ( nT f c Impulse generator ) ( R H ∑ ∞ −∞ = − = n c cs nT t nT f T t f ) ( ) ( ) ( ) ( ˆ 2 t f Sample T ) ( t f c ) ( R H...
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EL611 Sampling_2011 - below for sampling and reconstruction...

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