A Unified Theory for NAR Noise Power Estimation with Application to Adaptive Detection
Xiangkun Chen, Thomas W. Parks, Bruce R. Musicus, Allan M. Kabel · 1986
The design of FIR digital filters with a complex-valued de- sired frequency response using the Chebychev error is investigated. The complex approximation problem is converted into a real approximation problem which is nearly equivalent to the complex problem. A standard linear programming algorithm for the Chebychev solution of overdeter- mined equations is used to solve the real approximation problem. Ad- ditional constraints are introduced which allow weighting of the phase and/or group delay of the approximation. Digital filters are designed which have nearly constant group delay in the passbands. The desired constant group delay which gives the minimum Chebychev error is found to be smaller than that of a linear phase filter of the same length. These filters, in addition to having a smaller, approximately constant group delay, have better magnitude characteristics than exactly linear phase filters with the same length. The @ten have nearly equiripple magnitude and group delay. Abstract-We describe a new maximum entropy pole-zero spectrum estimation method. The model is designed to achieve the maximum pos- sible entropy subject to constraints on the first few correlation and cep- stral values. The solution, which is in the form of an ARMA model, is based on solving a generalized, symmetric, almost-Toeplitz eigenvalue problem. We characterize the existence, uniqueness, stability, and min- imum phase properties of the solution, and categorize all possible oc- currences of cancelling pole-zero pairs. A search procedure based on a fast Levinson-like algorithm is given for estimating the model, and examples are presented to illustrate its performance. A special case of the method gives a model estimate similar to that of Pisarenko's har- monic retrieval problem.