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Reconstructing a signal using an equilizer "filter" function
A low pass signal g(t) is sampled at a rate of ##f_{s} > 2B## needs to be reconstructed. Sampling interval is ##T_s=\frac{1}{f_s}##
The reconstruction pulse to be used is
$$p(t)=∏(\frac{t}{T_s}-\frac{1}{2})$$
Specify the equalizer filter ##E(f)## to recover ##g(t)##
$$E(f)P(f)=0 / |f|>f_s-B$$
$$E(f)P(f)=T_s / |f|<B$$
$$E(f)=T_s \frac{ \pi f}{sin( \pi f T_p)} ≈ \frac{T_s}{T_p} \ \ |f|≤B$$
There is one example in my text and it is not very clear at all.
I understand my "sampling interval" is ##T_s=\frac{1}{f_s}## What is ##T_p##?
if my sampling frequency is greater then 2B then my last equation posted above does not apply right?
Im confused as where to start..
Thanks in advance for any help
Homework Statement
A low pass signal g(t) is sampled at a rate of ##f_{s} > 2B## needs to be reconstructed. Sampling interval is ##T_s=\frac{1}{f_s}##
The reconstruction pulse to be used is
$$p(t)=∏(\frac{t}{T_s}-\frac{1}{2})$$
Specify the equalizer filter ##E(f)## to recover ##g(t)##
Homework Equations
$$E(f)P(f)=0 / |f|>f_s-B$$
$$E(f)P(f)=T_s / |f|<B$$
$$E(f)=T_s \frac{ \pi f}{sin( \pi f T_p)} ≈ \frac{T_s}{T_p} \ \ |f|≤B$$
The Attempt at a Solution
There is one example in my text and it is not very clear at all.
I understand my "sampling interval" is ##T_s=\frac{1}{f_s}## What is ##T_p##?
if my sampling frequency is greater then 2B then my last equation posted above does not apply right?
Im confused as where to start..
Thanks in advance for any help
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