PS-3-2009

PS-3-2009 - EE 261 The Fourier Transform and its...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon

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

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: EE 261 The Fourier Transform and its Applications Fall 2009 Problem Set Three Due Wednesday, October 14, 2009 1. (25 points) Piecewise linear approximations and Fourier transforms. (a) The stretched triangle function is defined by a ( t ) = ( t/a ) = braceleftBigg a-| t | a , | t | a , | t | > a Find F a ( s ). (b) Find the Fourier transform of the following signal. 1 2 2 2 . 5 4 6 t Hint: Think s. (c) Consider a signal f ( t ) defined on an interval from 0 to D with f (0) = 0 and f ( D ) = 0. We get a uniform, piecewise linear approximation to f ( t ) by dividing the inter- val into n equal subintervals of length T = D/n , and then joining the values 0 = f (0) , f ( T ) , f (2 T ) , . . . , f ( nT ) = f ( D ) = 0 by consecutive line segments. Let g ( t ) be the linear approximation of a signal f ( t ), obtained in this manner, as illustrated in the following figure where T = 1 and D = 6. 1 1 1 2 2 3 3 4 5 6 t f ( t ) g ( t ) Find F g ( s ) for the general problem ( not for the example given in the figure above) using any necessary information about the signal f ( t ) or its Fourier transform F f ( s ). Think s, again. 2. (15 points) Hubbard-Stratonovich Formula Show that integraldisplay - e- x 2 e- 2 sx dx = e s 2 ....
View Full Document

Page1 / 4

PS-3-2009 - EE 261 The Fourier Transform and its...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online