Problem Set #1 - Addition Question

Problem Set #1 - Addition Question - f on the interval ( )...

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332:322 Principles of Communications Systems Problem Set #1 - Addition Question emailed on 1/26/2008 (Updated on 1/19/2008) The following Fourier transform pair was shown in class: { } ( ) 0 2 0 j f t F e f f p d = - . a) Calculate the Fourier transform of ( ) 2 a t j ft g t e e - = where a is a positive constant. Notice that this function is bounded for all t owing to the absolute value t inside the exponent. b) Calculate the integral of ( ) G f with respect to
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Unformatted text preview: f on the interval ( ) ,-. Use an integral table, or look it up in your old calc text. HINT: Put everything over a common denominator in ( ) G f-- unless you know how to evaluate the log of a complex number :) . c) Make the argument that as the constant a f , ( ) ( ) G f f d (i.e., that in the limit, ( ) G f satisfies the properties of a delta function)....
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