explain the advantages and disadvantages of using higher orders in measuring spe

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Advantages of HOS A random signal x(n) is completely characterized by its ACF only if it originates from a random process with gaussian characteristics. In non–gaussian processes the higher order moments carry information that can not be found in the ACF. Such signals can be found for example in speech, radar, sonar, bio–medicine and seismology. The extra information provided by HOS leads to better estimates of parameters and sheds light on non–linearities in the source of the signal. In detail the advantages are: 1. Cumulants of gaussian random processes are = 0 for orders > 2. 2. May z(n) = x(n) + y(n) with x and y statistically independent random variables. Then the cumulants of z are: 3. May z(n) = s(n) + g(n) with g being noise with symmetric probability density function. Then the noise is suppressed in 3rd and 4th order cumulants: 4. For any independent, identically distributed (IID) process the cumulants are non zero only at the origin: 5. If x(n) is a linear, non–gaussian random variable and the noise u(n) is IID and non–gaussian, and x(n) =summission h(i) u(n -i) with h being the impulse response of the system, then the cumulants are de?ned by the impulse response: The MATLAB–toolbox ’Higher–Order Spectral Analysis’ (HOSA) implements a variety of advanced signal processing algorithms. Two of them will be showed here with short examples, namely the estimation of the bispectrum of signals with quadratic phase coupling, and time delay estimation with the cross–bispectrum.

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