Question

What is the expression for low pass signal component uc(t) that can be expressed in terms of samples of the bandpass signal?

(a) \(\sum_{n=-∞}^∞ (-1)^{n+r+1} x(2nT^{‘}-T^{‘}) \frac{sin⁡(π/(2T^{‘})) (t-2nT^{‘}+T^{‘})}{(π/(2T^{‘}))(t-2nT^{‘}+T^{‘})}\)

(b) \(\sum_{n=-∞}^∞ (-1)^n x(2nT^{‘}) \frac{sin⁡(π/(2T^{‘})) (t-2nT^{‘})}{(π/(2T^{‘}))(t-2nT^{‘})}\)

(c) All of the mentioned

(d) None of the mentioned

This question was posed to me during an online exam.

This key question is from Sampling of Band Pass Signals in chapter Sampling and Reconstruction of Signals of Digital Signal Processing

Answer 1

Right answer is (b) \(\sum_{n=-∞}^∞ (-1)^n x(2nT^{‘}) \frac{sin⁡(π/(2T^{‘})) (t-2nT^{‘})}{(π/(2T^{‘}))(t-2nT^{‘})}\)

Explanation: The low pass signal components uc(t) can be expressed in terms of samples of the

band pass signal as follows:

\(u_c (t) = \sum_{n=-∞}^∞ (-1)^n x(2nT^{‘}) \frac{sin⁡(π/(2T^{‘})) (t-2nT^{‘})}{(π/(2T^{‘}))(t-2nT^{‘})}\).