This paper studies multidimensional linear periodically shift-variant digital filters (LPSV filters). The notion of a generalized multidimensional transfer function is presented for LPSV filters. The frequency characteristic of the filters is discussed in terms of this transfer function. Since LPSV filters can decompose the spectrum of an input signal into some spectral partitions and rearrange the spectrum, LPSV filters can serve as a frequency scrambler. To show the effect of multidimensional frequency scramble, 2-D LPSV filters are designed based on the 1-D Parks-McClellan algorithm. The resultant LPSV filters divide the input spectrum into some components that are permuted and possibly inverted with keeping the symmetric of the spectrum. Experimental results are presented to illustrate the effectiveness of frequency scramble for real images.

The design of N-dimensional (N-D) FIR filters requires in general an enormous computational effort. One of the most successful methods for design and implementation is the McClellan transformation. In this paper a numerically simple technique for determining the coefficients of the transformation is suggested. This appears to be the simplest available method for the design of N-D hyperspherically symmetric FIR filters with excellent symmetry.