discrete fourier series properties

The discrete Fourier series (DFS): For infinitely long but periodic signals ⇒ basis for the discrete Fourier transform The discrete Fourier transform (DFT): For general, finite length signals ⇒ Used in practice with signals from experiments

series (DFS), discrete Fourier transform (DFT) and fast Fourier transform (FFT) (ii ) Understanding the characteristics and properties of DFS and DFT (iii) Ability 

It is useful to summarize our observations on the spectral characteristics of different classes of signals i Continuous-time signals have aperiodic spectra ii

Discrete–time Fourier series have properties very similar to the linearity, time shifting, etc properties of the Fourier transform A table of some of the most 

TABLE 4 5 Properties of the Fourier Transform for Discrete-Time Signals Property Notation Linearity Time shifting Time reversal Convolution Correlation

Properties of the Discrete-time Fourier Transform ▻ Periodicity ▻ Time Scaling Property ▻ Multiplication Property Periodic Discrete Duality DFT

Soliman, S S and Srinath, M D Continuous and Discrete Signals and Systems, New York, Prentice-Hall, 1990 22 Tetley, L

rather than the aperiodic convolution of the individual Fourier transforms The modulation property for discrete-time signals and systems is also very useful in the 

3 Fourier coefficients and their properties Definition 3 1 We say that a trigonometric series ∞ ∑ n=−∞ cneinx a) converges pointwise if for each x ∈ [ −π, 

Consider a periodic discrete-time signal with period N: x(n) = x(n + N), Fourier series of discrete-time periodic signal An N-periodic PROPERTIES OF DFT