June 2009
Intermediate to advanced
1100 pages
42h 22m
English
Content preview from Engineering Mathematics
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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
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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