Question #61219

Derive the Fourier Transform of a rectangular pulse by

a) Differentiating the pulse to form two delta functions

b) Fourier Transforming the derivative

c) Integrating in the frequency domain by dividing by j2πf

Repeat this procedure for the triangle function using a double derivative.

Hence or otherwise, show that if a function has discontinuities in the nth derivative, the sidelobes will fall off as 1/(f^(n+1)).

a) Differentiating the pulse to form two delta functions

b) Fourier Transforming the derivative

c) Integrating in the frequency domain by dividing by j2πf

Repeat this procedure for the triangle function using a double derivative.

Hence or otherwise, show that if a function has discontinuities in the nth derivative, the sidelobes will fall off as 1/(f^(n+1)).

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