19

Discrete Fourier Transform

Discrete Fourier transform (DFT) is a powerful tool for frequency analysis of discrete time signals. It transforms discrete-time signal of finite length into discrete-frequency sequence of finite length. As we shall observe, the DFT can also be used to calculate Fourier coefficients.

19.1 APPROXIMATION OF FOURIER COEFFICIENTS OF A PERIODIC FUNCTION

Let f be a real-valued periodic function with period T over the interval [0, T]. We divide [0, T] into N subintervals In of equal length T/N. Thus

 

image

 

The linear interpolation ln(t) of f (t) is given by

 

 

Thus the graph (Figure 19.1) of ln(t) consists of the line segment ...

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