EE210_F11_HW1

EE210_F11_HW1 - EE210-2, Fall 2011 Prof. Essam Marouf...

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Unformatted text preview: EE210-2, Fall 2011 Prof. Essam Marouf Linear Systems Theory (Transform Theory & Applications) ---------------------------------------------------------------------------------------------------------- Homework #1 To be Completed by Monday September 12, 2011 ------------------------------------------------------------ Most Problems are adapted from Bracewell (Chs. 2, 4, and 5) 1- Starting from the definition of the Fourier transform, show that the spectrum X ( f ) of the signal x ( t ) = 1 2 a exp[ − | t / a |] is X ( f ) = 1 1 + (2 π af ) 2 ; a is a constant. Show that in the limit a → 0, x ( t ) → δ ( t ) , and X ( f ) → 1 . Thus, δ ( t ) ↔ 1 defines a Fourier transform pair “in-the- limit.” Note that x ( t ) = δ ( t ) violates conditions for the existence of a normal transform.--------------------------------------------------------------------------------------------------------------- 2- a) The Fourier transform in-the-limit of x ( t ) = u ( t ) is X ( f ) = 1 j 2...
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This note was uploaded on 11/28/2011 for the course EE 210 taught by Professor Moriarty,e during the Fall '08 term at San Jose State.

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