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Bioen303_25January2010

# Bioen303_25January2010 - Odd-Even Symmetry If x(n is real...

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1/25/2010 1 Odd-Even Symmetry If x(n) is real and even , that is: x(n)=x*(n) and x(-n)=x(n), then: • X(m) is real and even X(m) is and . If x(n) is real and odd , that is: x(n)=x*(n) and x(-n)=-x(n), then X(m) is imaginary and odd . Discrete Fourier Transform There are three possible phenomena that result in errors between the computed and the desired transform. These three phenomena are – (a) aliasing (Lyons 2.1) – (b) leakage (Lyons 3.8) – (c) scalloping loss (Lyons 3.10) http://www.cage.curtin.edu.au/mechanical/info/vibrations/tut4.htm Leakage and the Discrete Fourier Transform The DFT gives exact frequency results for sinusoidal signals if the N-samples sequence contains an integer number of complete cycles of the sampled continuous signal x(t). If it does not, the DFT produces a spread spectrum whose values are not exactly correct. We will discuss frequency leakage in detail later. DFT Leakage DFT Leakage Discrete Fourier Transform • (b) Leakage . This problem arises because we must limit observation of the signal to a finite interval. The process of terminating the signal after a finite number of terms is equivalent to multiplying the number of terms is equivalent to multiplying the signal by a window function . The net effect is a distortion of the spectrum. There is a spreading or leakage of the spectral components away from the correct frequency, resulting in an undesirable modification of the total spectrum. http://www.cage.curtin.edu.au/mechanical/info/vibrations/tut4.htm

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