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3) (a) Four different transforms have been introduced thus far: I. Continuous-time Fourier series Discrete-time Fourier
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3) (a) Four different transforms have been introduced thus far: I. Continuous-time Fourier series Discrete-time Fourier series II. III. Continuous-time Fourier transform IV. Discrete-time Fourier transform In the following table, fill in the blanks with I, II, III, or IV depending on which transform(s) can be used to represent the signal described on the left. Finite duration means that the signal is guaranteed to be nonzero over only a finite interval. Signal Description Transform Continuous time Infinite duration Periodic Continuous time Infinite duration Aperiodic Continuous time Finite duration Aperiodic Discrete time Infinite duration Periodic Discrete time Infinite duration Aperiodic Discrete time Finite duration Aperiodic (b) Which of the transforms in the preceding table possess the duality property (e) Which of the transforms are always periodic?