1/22/08

signal reconstruction

process of reconstruction a signal from its samples is known as interpolation
to exactly reconstruct a signal from its samples, we must pass the sampled signal through an ideal low pass filter of bandwidth B and gain T
filter must have transfer function of 

time domain rep of ideal low pass filter is h(t) = 2BTsinc(2pi*Bt)
PROBLEM: non-causal, must have an infinite delay to use it properly
if we sample at the nyquist rate, then we have sinc(2pi*Bt)
original signal van be found by (Fig1)
example (Fig2)
end up delaying output of filter by half a sample (required for a causal filter)
effect of time delay on frequency response - 
can create a first-order hold by using a time pulse with a linear variation such as (Fig3)
since we cannot make an ideal low pass filter, we can sample faster than the nyquist rate
we can not create any filter that has a finite bandwidth, because filters can't be both band limited and time limited
can't recover the exact original signal in a practical system, because that would require ideal filters and the system would have to be running forever or have an infinite delay

aliasing - the effect (distortion) of unavoidable overlap of the original spectrum and copies
can be reduced by antialiasing filters
goal is to reduce the magnitude of the freq components that will be affected by aliasing prior to sampling