Band Pass Sampling

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However when the given signal is a Band Pass signal then a different criterion must be used to sample the signal , the Band Pass signal x(t) whose maximum BW is ‘ $2f_{m}/W$ ‘ Hz can be completely represented and recovered from it’s samples if it is sampled at the minimum rate of greater than or equals to twice that of the BW.

then sampling rate $f_{s}\geq 2 X BW$

i.e, $f_{s}\geq 4f_{m} or f_{s}\geq 2W$

Any band pass signal in time-domain can be represented in it’s in-phase $x_{I}(t)$ and quadrature phase $x_{Q}(t)$ components as

$x(t) = x_{I}(t)cos 2\pi f_{c}t \pm x_{Q}(t)sin 2\pi f_{c}t$

after sampling the band pass signal, the signal after reconstruction is

$x(t) = \sum_{n=-\infty }^{\infty }sinc(2f_{m}t-\frac{n}{2})cos(2\pi f_{c}(t-\frac{n}{4f_{m}}))$

$T_{s} = \frac{1}{4f_{m}}$ , where BW of band pass signal is $2f_{m}$ Hz

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Author: Lakshmi Prasanna Ponnala

Completed M.Tech in Digital Electronics and Communication Systems. View all posts by Lakshmi Prasanna Ponnala

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