# Fourier transform in this question assume that all

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2.5: Fourier TransformIn this question, assume that all the required Fourier transforms exist.a) Suppose that the Fourier transform off(t) isF(w), then show that the Fourier transform ofdfdtisjwF(w). Thus differentiation in the time domain corresponds to multiplication by
b) Suppose thatg(t) =tf(t), then prove that the Fourier transform ofg(t) isidFdw.
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ECE 205 - Winter 2017Assignment 7 SolutionsDue 26-03-2017c) Find the Fourier transform off(t) =te-t2in two different ways.
In this question,f(t) is a real valuedoddsquare integrable function.a) What does it mean forf(t) to be odd?
b) Prove that the Fourier transform off(t) is a purely imaginary function and may be obtainedby either of the following:F(w)=2i2πImnR0f(t)eiwtdto,F(w)=2i2πRf(t) sin(wt)dt.
c) Prove thatF(w) is odd, and thatf(t) =-2i
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ECE 205 - Winter 2017Assignment 7 Solutions