New methods for design and implementation of multidimensional digital filters

The aim of proposed research Project is to develop and implement several new techniques for design of multidimensional (M-D) FIR digital filters based on the McClellan transform. At first, we are going to obtain a new 3-D transform function that can describe cone filter characteristic of a 3-D designed filter. A double cone filter oriented in 3-direction will be considered. Our task will be to get closed-form relations for the coefficients of mapping function as a function of the angle of inclination of the cone Te(0,/2). Next, we intend to check the designed 3-D function for all frequencies 1, 2, 3e[-, ] to guarantee that the scale conditions are satisfied. Otherwise, a suitable scaling method for 3-D case should be find out and applied. Second main task of the proposed Project is to apply McClellan transform for design of 2-D filters having a concrete type of characteristic, namely, filters with wideband circularly symmetric frequency response, with bandpass magnitude response, and with tunable cutoff frequency. Our intention is to use the advantages of high- order transform: by increasing the order and adding new terms in the function, we would like to better approximate the circular contours of 2-D filters. Further, a new design method for general shaped bandpass filter with important application in geophysics will be under investigation. Starting with one choice of the generalized transform function and applying a set of properly chosen constraints, we are going to obtain expressions for transform coefficients of this type of filter. A mean-squared error criterion will be used by analogy with other transform methods for fan filters. Also, the design of tunable 2-D filters having variable range of cutoff frequency will be concerned. Next important goal of the Project is to simulate and verify all obtained approaches using MATLAB. A comparison between the designed 2-D/3-D filters and these ones obtained with other well-known techniques (transform and direct methods) is to be realized. Implementation aspects of the structures will be also discussed, e.g. computational organization, complexity, coefficient sensitivity, computational noise, etc. As an essential final step of the work, we are planning to apply the designed filters for seismic depth migration. This will require some adjustment of the approaches taking into account the special constraints imposed by the seismic application. All the work will be supported by various examples (including real and synthetic data sets for the case of depth migration). We expect the results from simulations to give some valuable conclusions about applicability and accuracy of the proposed methods.