[PDF] discrete fourier transform periodic boundary conditions

  • What are the conditions for the existence of the discrete Fourier transform?

    Condition for Existence of Fourier Transform
    The function x(t) has a finite number of maxima and minima in every finite interval of time.
    The function x(t) has a finite number of discontinuities in every finite interval of time.
    Also, each of these discontinuities must be finite.

  • What is the periodic property of DFT?

    In the time domain, the DFT is periodic by definition.
    While DFT stands for Discrete Fourier Transform, the operation is in fact a discrete fourier series. The signal to be analyzed is assumed to be periodic in the lenght of the signal.
    This periodic signal is decomposed into a series of periodic sequences.

  • What is the periodicity of DTFT?

    Due to discrete-time nature of the original signal, the DTFT is 2?-periodic.
    Hence, ?=2? is the highest frequency component a discrete-time signal can have.
    The DTFT possesses several important properties, which can be exploited both in calculations and in conceptual reasoning about discrete-time signals and systems.

  • What is the periodicity of DTFT?

    The Fourier series can be used to analyse only the periodic signals, while the Fourier transform can be used to analyse both periodic as well as non-periodic functions.

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