There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

A fast-Fourier-transform method of topography and interferometry is proposed. By computer processing of a noncontour type of fringe pattern, automatic discrimination is achieved between elevation and depression of the object or wave-front form, which has not been possible by the fringe-contour-generation techniques. The method has advantages over moire topography and conventional fringe-contour interferometry in both accuracy and sensitivity. Unlike fringe-scanning techniques, the method is easy to apply because it uses no moving components.

Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry

Economic Control of Quality of Manufactured Product.

The Theory of Matrices. By F R. Gantmacher. Two volumes, pp. 374 and 276. 1959. (Translated from the Russian by K. A. Hirsch; Chelsea Publishing Company, New York)

Most of the signal processing that we will study in this course involves local operations on a signal, namely transforming the signal by applying linear combinations of values in the neighborhood of each sample point. You are familiar with such operations from Calculus, namely, taking derivatives and you are also familiar with this from optics namely blurring a signal. We will be looking at sampled signals only. Let's start with a few basic examples. Local difference Suppose we have a 1D image and we take the local difference of intensities, DI(x) = 1 2 (I(x + 1) − I(x − 1)) which give a discrete approximation to a partial derivative. (We compute this for each x in the image.) What is the effect of such a transformation? One key idea is that such a derivative would be useful for marking positions where the intensity changes. Such a change is called an edge. It is important to detect edges in images because they often mark locations at which object properties change. These can include changes in illumination along a surface due to a shadow boundary, or a material (pigment) change, or a change in depth as when one object ends and another begins. The computational problem of finding intensity edges in images is called edge detection. We could look for positions at which DI(x) has a large negative or positive value. Large positive values indicate an edge that goes from low to high intensity, and large negative values indicate an edge that goes from high to low intensity. Example Suppose the image consists of a single (slightly sloped) edge:

http://ieeexplore.ieee.org/iel5/5/31307/01456462.pdf

Linear systems

Recently, a new non-iterative frequency-domain parameter estimation method was proposed. It is based on a (weighted) least-squares approach and uses multiple-input-multiple-output frequency response functions as primary data. This so-called "PolyMAX" or polyreference least-squares complex frequency-domain method can be implemented in a very similar way as the industry standard polyreference (time-domain) least-squares complex exponential method: in a first step a stabilisation diagram is constructed containing frequency, damping and participation information. Next, the mode shapes are found in a second least- squares step, based on the user selection of stable poles. One of the specific advantages of the technique lies in the very stable identification of the system poles and participation factors as a function of the specified system order, leading to easy-to-interpret stabilisation diagrams. This implies a potential for automating the method and to apply it to "difficult" estimation cases such as high-order and/or highly damped systems with large modal overlap. Some real-life automotive and aerospace case studies are discussed. PolyMAX is compared with classical methods concerning stability, accuracy of the estimated modal parameters and quality of the frequency response function synthesis.

/pdf/the-polymax-frequency-domain-method-a-new-standard-for-modal-3yams394c6.pdf

The PolyMAX Frequency-Domain Method: A New Standard for Modal Parameter Estimation?

This paper gives a survey of frequency domain identification methods for rational transfer functions in the Laplace (s) or z-domain. The interrelations between the different approaches are highlighted through a study of the (equivalent) cost functions. The properties of the various estimators are discussed and illustrated by several examples. >

Parametric identification of transfer functions in the frequency domain-a survey

Low crest-factor of excitation and response signals is desirable in transfer function measurements, since this allows the maximization of the signal-to-noise ratios (SNRs) for given allowable amplitude ranges of the signals. The authors present a new crest-factor minimization algorithm for periodic signals with prescribed power spectrum. The algorithm is based on approximation of the nondifferentiable Chebyshev (minimax) norm by l/sub p/-norms with increasing values of p, and the calculations are accelerated by using FFTs. Several signals related by linear systems can also be compressed simultaneously. The resulting crest-factors are significantly better than those provided by earlier methods. It is shown that the peak value of a signal can be further decreased by allowing some extra energy at additional frequencies. >

/pdf/crest-factor-minimization-using-nonlinear-chebyshev-529o28ptab.pdf

Patrick Guillaume

Papers

The PolyMAX Frequency-Domain Method: A New Standard for Modal Parameter Estimation?

Parametric identification of transfer functions in the frequency domain-a survey

Crest-factor minimization using nonlinear Chebyshev approximation methods

Identification of modal parameters from transmissibility measurements

Sensitivity-based operational mode shape normalisation