By David T. Westwick, Robert E. Kearney

Major advances were made within the box because the earlier vintage texts have been written. this article brings the to be had wisdom as much as date.* permits the reader to take advantage of a wide selection of nonlinear procedure identity techniques.* deals a radical remedy of the underlying theory.* presents a MATLAB toolbox containing implementation of the newest identity equipment including an intensive set of difficulties utilizing real looking facts units.

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**Additional info for Identification of Nonlinear Physiological Systems (IEEE Press Series on Biomedical Engineering)**

**Sample text**

Left Column: Power series polynomials over the arbitrarily chosen domain [−10 10]. Middle Column: Hermite polynomials over the domain [−3 3] corresponding to most of the range of the unitvariance, normal random variable. Right Column: Tchebyshev polynomials over their full domain [−1 1]. 3 Hermite Polynomials The Hermite polynomials H(q) (u) result when the orthogonalization is done for inputs with a zero-mean, unit-variance, Gaussian distribution. 3), the Hermite polynomials can be shown to be n/2 H(n) (u) = n!

Add this to the square wave, and plot the result as a function of time. Compute and plot the autocorrelation function of the noisy square wave. Filter the noise record with a fourth-order low-pass ﬁlter with a 20 Hz cutoff. Add the low-pass ﬁltered noise to the square wave. Plot the resulting signal, and compute and plot its autocorrelation. 5. Generate an NLDAT object containing 10,000 samples of zero-mean, unit variance, white Gaussian noise, and compute and plot its autocorrelation. Next, compute and plot the second-order autocorrelation function for this signal.

Square the Gaussian noise signal, and shift and rescale the result so that it has zero mean and unit variance. Compute and plot its ﬁrst- and second-order autocorrelation functions. Repeat this procedure with the cube of the Gaussian noise signal. What, if anything, does the second-order autocorrelation tell you about the nonlinearity? Does it generalize to higher exponents? 6. Use POLYNOM to create an empty polynomial object. Set the type to “power,” and set the coefﬁcients so that it represents y = 1 + 3u − 2u2 Generate an object containing 1000 samples of white Gaussian noise, with mean 1 and variance 2.