5 n n its dtft is given below on the left along with

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Unformatted text preview: s a bandwidth of ω p 9 • A highpass discrete-time real signal has a spectrum occupying the frequency range 0 < ω p ≤ ω < π and has a bandwidth of π − ωp • A bandpass discrete-time real signal has a spectrum occupying the frequency range 0 < ωL ≤ ω ≤ ωH < π and has a bandwidth of ωH − ωL 10 Copyright © 2005, S. K. Mitra Copyright © 2005, S. K. Mitra Band-limited Discrete-time BandDiscreteSignals Band-limited Discrete-time BandDiscreteSignals • Example – Consider the sequence x[ n] = (0.5) n µ[n] • It can be shown that 80% of the energy of this lowpass signal is contained in the frequency range 0 ≤ ω ≤ 0.5081π • Hence, we can define the 80% bandwidth to be 0.5081π radians • Its DTFT is given below on the left along with its magnitude spectrum shown below on the right |X(e ω )| j X ( e jω ) = 1 1 − 0.5e − jω Magnitude 2 1.5 1 0.5 11 0 0.2 0.4 0.6 0.8 1 ω/π Copyright © 2005, S. K. Mitra 12 Copyright © 2005, S. K. Mitra 2 Energy Density Spectrum Energy Density Spectrum •...
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This document was uploaded on 11/09/2013.

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