HW 06

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Problem

Figure out why seems to equal an imaginary odd function of frequency, but there is no j.

Background

This is the incorrect solution derived in class. Cosine is incorrect, because a real odd function of time, ,should map to an imaginary odd function of frequency.

Proof

Euler's identity
Even function integrates out over symmetric limits
Time integrates out
  • The odd function of time has no component (ie. 0) of frequency. Thus it is an even function in frequency.

Functions

  • Even*Even=Even
  • Odd*Odd=Even
  • Odd*Even=Odd

Incorrect Solution derived in class

Correct Solution