White Noise Amplification Research Articles

Minimum norm design of two-dimensional weighted Chebyshev FIR filters

The weighted Chebyshev design of two-dimensional FIR filters is in general not unique since the Haar condition is not generally satisfied. However, for a design on a discrete frequency domain, the Haar condition might be fulfilled. The question of uniqueness is, however, rather extensive to investigate. It is therefore desirable to define some simple additional constraints to the Chebyshev design in order to obtain a unique solution. The weighted Chebyshev solution of minimum Euclidean filter weight norm is always unique, and represents a sensible additional constraint since it implies minimum white noise amplification. This unique Chebyshev solution can always be obtained by using an efficient quadratic programming formulation with a strictly convex objective function and linear constraints. An example where a conventional Chebyshev solution is nonunique is discussed.

OPTIMUM DIGITAL FILTERING AND INVERSE FILTERING IN THE FREQUENCY DOMAIN*

AbstractTwo distinct filters are developed in the frequency domain which represent an attempt to increase the resolution of fine structure contained in the signal whilst keeping the expected filtered noise energy within reasonable bounds. A parameter termed the White Noise Amplification is defined and used together with a measure of the deconvolved pulse width in order to provide a more complete characterisation of the filters. Each of the two main types of frequency domain filters discussed varies in properties with respect to a single adjustable parameter. This may be contrasted with a time domain Wiener filter which in general has three variables: length, delay and an adjustable noise parameter or weight. The direct frequency domain analogue of the Wiener filter is termed a gamma‐Fourier filter, and is shown to have properties which span the range from those of a spiking filter with zero least square error at one extreme, to those of a matched filter at the other extreme of its variable parameter's range. The second type of filter considered—termed the modulated Gaussian filter—is similarly shown to be a perfect spiking filter at one extreme of its parameter range, but adopts the properties of an output energy filter at the other extreme.