The conventional sampling theorem states a signal x(t) must be sampled at a rate greater than its bandwidth (a rate greater than twice its highest frequency). This implies that if x(t) has a spectrum as indicated in Figure 2, x(t) must be sampled at a rate greater than 2w2. Given the signal has most of its energy concentrated in a narrow band, it seems reasonable to expect that a sampling rate lower than twice the highest frequency could be used. This technique is referred to as bandpass sampling. Consider the system shown in Figure 3. Assuming wi > (w2 – wi), 1. Plot the spectrum of xp(t). Determine the aliasing conditions for conventional sampling and band-pass sampling. Combine the results for the general aliasing condition. 2. Find the maximum value of T and the values of the constants Wa and wh such that ar (t) = x(t). X(w) 1. -w2 Figure 2: Problem 4, band-pass signal r(t)

The conventional sampling theorem states a signal x(t) must be sampled at a rate greater than its bandwidth (a rate greater than twice its highest frequency). This implies that if x(t) has a spectrum as indicated in Figure 2, x(t) must be sampled at a rate greater than 2w2. Given the signal has most of its energy concentrated in a narrow band, it seems reasonable to expect that a sampling rate lower than twice the highest frequency could be used. This technique is referred to as bandpass sampling. Consider the system shown in Figure 3. Assuming wi > (w2 – wi), 1. Plot the spectrum of xp(t). Determine the aliasing conditions for conventional sampling and band-pass sampling. Combine the results for the general aliasing condition. 2. Find the maximum value of T and the values of the constants Wa and wh such that ar (t) = x(t). X(w) 1. -w2 Figure 2: Problem 4, band-pass signal r(t)

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...

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