1.1 A unit-amplitude rectangular pulse, p(t), having pulse duration Tpulse [sec] and centred on t = 0 is shown in Figure

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1 1 A Unit Amplitude Rectangular Pulse P T Having Pulse Duration Tpulse Sec And Centred On T 0 Is Shown In Figure 1 (138.25 KiB) Viewed 53 times

1.1 A unit-amplitude rectangular pulse, p(t), having pulse duration Tpulse [sec] and centred on t = 0 is shown in Figure 1 below. Tpulse 1 o t [sec] Figure 1: Pulse to be considered in question 1.1. = The Fourier transform of p(t) is: p(t) **P(f) = Tpulse sinc(fTpulse) where sinc (2) 4 sin(ma), and Tpulse = { ms. The bandwidth of this pulse is theoretically infinite, however most of its signal energy is concentrated in a region about f =0: (a) Propose a more practical measure of bandwidth. (b) Accordingly evaluate this bandwidth measure for p(t). (c) If the pulse width were to change to Tpulse = 1 sec, what would the impact on the bandwidth be? (d) What general phenomenon does the above result illustrate? (e) How does this phenomenon relate to the following Fourier Transform property: 2(at) << ** (1) 1 X al [30%] 1.2 For the pulse, r(t), shown in Figure 1, with Tpulse = { ms, write an expression (in integral form) for the energy lying in the frequency band from 6 to 9 kHz. No need to evaluate the integral but numerical values for all constants in the formula should be given (e.g. the answer should not contain "Tpulse"). [20%]