What is the Fourier transform X(ω) of a finite energy discrete time signal x(n)?(a) \(\sum_{n=-∞}^∞x(n)e^{-jωn}\)(b) \(\sum_{n=0}^∞x(n)e^{-jωn}\)(c) \(\sum_{n=0}^{N-1}x(n)e^{-jωn}\)(d) None of the mentionedThis question was addressed to me in an interview for job.This interesting question is from Frequency Analysis of Discrete Time Signal in portion Frequency Analysis of Signals and Systems of Digital Signal Processing

What is the Fourier transform X(ω) of a finite energy discrete time s

1.	What is the Fourier transform X(ω) of a finite energy discrete time signal x(n)?(a) \(\sum_{n=-∞}^∞x(n)e^{-jωn}\)(b) \(\sum_{n=0}^∞x(n)e^{-jωn}\)(c) \(\sum_{n=0}^{N-1}x(n)e^{-jωn}\)(d) None of the mentionedThis question was addressed to me in an interview for job.This interesting question is from Frequency Analysis of Discrete Time Signal in portion Frequency Analysis of Signals and Systems of Digital Signal Processing
Answer» Correct option is (a) \(\sum_{n=-∞}^∞x(n)e^{-jωn}\) Easy explanation: If we consider a SIGNAL x(n) which is discrete in NATURE and has finite energy, then the Fourier TRANSFORM of that signal is given as X(ω)=\(\sum_{n=-∞}^∞x(n)e^{-jωn}\)

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