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From: drick@hplvle.UUCP (drick)
Newsgroups: net.math
Subject: Interview question
Message-ID: <7700002@hplvle.UUCP>
Date: Wed, 13-Feb-85 22:58:00 EST
Article-I.D.: hplvle.7700002
Posted: Wed Feb 13 22:58:00 1985
Date-Received: Thu, 21-Feb-85 02:50:00 EST
Organization: Hewlett-Packard - Loveland, CO
Lines: 33
Nf-ID: #N:hplvle:7700002:000:1110
Nf-From: hplvle!drick    Feb 13 19:58:00 1985

[generalized bug trap]

Recently, I interviewed someone who claimed to have a lot of 
coursework in communication theory.  The recent discussion of
Dirac's delta function (function used advisedly) reminded me
of a problem I gave this interviewee, to wit:

The Fourier Transform is defined as:

F{f(t)} = F(w) = Integral[-inf,inf]: f(t)e^(-jwt)dt.
[ j is the square root of -1, w is usually omega ]

a.  Prove that F{ d(f(t))/dt } = jwF(w).
    (What assumptions are necessary?)

b.  If f(t) is the function sketched below [here I substitute the
    definition because graphics work poorly on the net], find F(w).
    (Hint: use the result of part a.)

    f(t) =  -1/T,   -5T/2 < t < -T
             2/T,      -T < t <  T
            -1/T,       T < t < 5T/2
               0,       else.

c.  What happens to F(w) in the limit as T approaches zero?  What does
    this suggest about f(t)? 

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If I express any opinions in this note, they are my own.
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David L. Rick
...!hplabs!hplvla!hplvle!drick