ECE405HW8Su2010

# ECE405HW8Su2010 - ECE 405 HOMEWORK#8 SUMMER 2010 ©DR JAMES...

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Unformatted text preview: ECE 405 HOMEWORK #8 SUMMER 2010 ©DR. JAMES S. KANG 1 Suppose that for binary 1, h(t) is transmitted and for binary 0, –h(t) is transmitted. Find the autocorrelation function and the power spectral density when h(t) = e − at u(t), 0 ≤ t ≤ T and h(t) = 0 elsewhere, where 0 < a < 1. 2 Let 2, 0 / 2 ( ) 1, / 2 0, t T h t T t T elsewhere ≤ ≤ ⎧ ⎪ = < ⎨ ⎪ ⎩ ≤ (a) Find and plot the autocorrelation function R H ( τ ) of h(t). (b) Find the Fourier transform H(f) of h(t). (c) Suppose that binary message 1 is transmitted by h(t) and binary 0 is transmitted by –h(t). Let the resulting signal be m(t). Find the autocorrelation function ( ) M R τ of m(t). (d) Find the power spectral density S M (f) of m(t). (e) Let y(t) be the product of m(t) and A c cos( ω c t). Find the autocorrelation function ( ) Y R τ of y(t). (f) Find the power spectral density S Y (f) of y(t). (g) What is the null-to-null bandwidth of y(t)? 3 A computer outputs binary symbols at a 56 kbits/s rate. Find the baseband bandwidths required for transmission for each of the following roll-off factors if sinusoidal roll-off spectral...
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## This note was uploaded on 08/09/2010 for the course ECE ECE 405 taught by Professor Jameskang during the Summer '10 term at Cal Poly Pomona.

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ECE405HW8Su2010 - ECE 405 HOMEWORK#8 SUMMER 2010 ©DR JAMES...

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