A#10-1 - ) ( t x ⎪ ⎩ ⎪ ⎨ ⎧ ≤ − = else X ,...

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Assignment #10 ECSE-2410 Signals & Systems - Spring 2007 Due Fri 03/02/07 1.(20 pts) Find the Fourier transform of t π 2 ) ( t x truncated cosine wave 1 1 2.(15 pts) Suppose , where has the Fourier transform shown. Find ) 2 cos( ) ( ) ( t t x t y = ) ( t x ) ( ω Y in terms of ) ( X and sketch ) ( Y . ) ( X 1 1 0 -1 ( ) H t h Assign #10 Spring 2007 p.1 3(25). The input to the system, is the periodic signal shown ) ( t ) ( ) ( t y LTI x 1 2 3 4 0 -1 x ( t ) t 1 (a). Find the equation for ) ( X and plot . ) ( vs X for 5 < . (b). Let () < = , 0 3 , 1 else H , and sketch . ) ( vs H . (c). Sketch () ()() . vs H X Y = for 5 < . (d). Use the plot in (c) to write the equation for . Express exponentials in terms of trigonometric functions (i.e., cosines and/or sines.) ) ( t y

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Assignment #10 ECSE-2410 Signals & Systems - Spring 2007 Due Fri 03/02/07 4(40). Speech scramblers are designed to prevent electronic eavesdropping. The input voice, , is made unintelligible by altering the original spectrum,
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Unformatted text preview: ) ( t x ⎪ ⎩ ⎪ ⎨ ⎧ ≤ − = else X , 1000 , 1000 1 ) ( ω . The garbled output is then transmitted to a receiver at the listening end. The receiver (not shown) sequentially undoes all the frequency spectrum alterations done at the transmitter. ) ( t y Highpass Filter Lowpass Filter H 1 ( ) H 2 ( ) 1 1 x ( t ) a ( t ) b ( t ) c ( t ) y ( t ) -2000 0 2000 -1500 0 1500 cos(2000 t ) cos(3000 t ) For the transmitter filtering operations shown in the block diagram above, sketch (a). Sketch ) ( A . Show all amplitudes and frequencies. Label all axes. (b). Sketch B ( ) and label the axes. (c). Sketch C ( ) and label all important points. (d). Sketch Y ( ) and label all important points. Assign #10 Spring 2007 p.2...
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This note was uploaded on 04/10/2008 for the course ECSE 2410 taught by Professor Wozny during the Spring '07 term at Rensselaer Polytechnic Institute.

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A#10-1 - ) ( t x ⎪ ⎩ ⎪ ⎨ ⎧ ≤ − = else X ,...

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