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What is the Fourier transform of the unit step function U(ω)?(a) πδ(ω)-0.5-j0.5cot(ω/2)(b) πδ(ω)-0.5+j0.5cot(ω/2)(c) πδ(ω)+0.5+j0.5cot(ω/2)(d) πδ(ω)+0.5-j0.5cot(ω/2)I got this question in examination.This interesting question is from General Considerations for Design of Digital Filters topic in section Digital Filters Design of Digital Signal Processing

Answer»

Correct CHOICE is (d) πδ(ω)+0.5-j0.5cot(ω/2)

The best I can EXPLAIN: Since the UNIT step function is not ABSOLUTELY summable, it has a Fourier TRANSFORM which is given by the equation

U(ω)= πδ(ω)+0.5-j0.5cot(ω/2).



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