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Assignment I

# Assignment I - EE3008 Assignment I Consider the following...

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EE3008 Assignment I Consider the following bipolar signal s ( t ) using rectangular pulses with amplitudes ± 0.5 volts and transmitting rate 10 kb/sec. (a) Determine the value of T above and answer the follows. 1) Find and plot the energy spectrum of the first pulse in Fig.1. 2) Find the expression of | S ( f )| 2 , the energy spectrum of s ( t ). (No need to plot.) 3) Fine the power spectrum of s ( t ) (Hint: It is | S ( f )| 2 divided by 6 T ). 4) Now assume that K pulses are transmitted and the signs of these pulses are randomly selected from +1 and -1. Find the power spectrum of s ( t ) for K →∞ and plot it. (Hint: Read Tutorial 2.) A matched filter receiver diagram is shown in the figure below. The frequency domain response of the filter is 4 4 4 10 ( ) 10 sinc( 10 ) j f H f f e π π × × = × × × × volts/Hz. ( ) m t ( ) r t (b) Determine the impulse response h ( t ) of the filter. (c) Consider the noise-free case, i.e., r ( t )= s ( t ). 1) Determine and plot the filter output m ( t ) for s ( t ) in Fig.1. (Hint: ( ) ( ) ( ) ( ) t t T m t r t h t r u du = = ) 2) Plot the power of m
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