{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# A#10 - Assignment#10 p.1 ECSE-2410 Signals Systems Fall...

This preview shows pages 1–2. Sign up to view the full content.

Assignment #10 – p.1 ECSE-2410 Signals & Systems - Fall 2006 Due Fri 10/13/06 1(10). Suppose we know the Fourier transform pair 2 2 2 1 2 2 ) ( ) ( ω π ω = = = e X e t x F t , called the Gaussian pulse. Use the duality property developed in class to find the transform of 2 2 ) ( t e t X = . 2(10). Suppose . Find the steady-state response, , to the input ) ( 2 ) ( 2 t u e t h t = ) ( t y ) 2 cos( 2 ) ( t t x + = . Use the steady-state equation derived in class. ( ) H t h ω 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 ) ( ω X and plot ω ω . ) ( vs X for 5 < ω . (b). Let ( ) < = , 0 3 , 1 else H ω ω , and sketch ω ω . ) ( vs H . (c). Sketch ( ) ( ) ( ) ω ω ω ω . vs H X Y = for 5 < ω . (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 (e). Prove the following: If and are real and even, then is real and even.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 3

A#10 - Assignment#10 p.1 ECSE-2410 Signals Systems Fall...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online