Sequency-based mapped real transform: properties and applications

Abstract

Transforms are tools that decompose a signal into alternate representation. Fourier transform is very popular for frequency domain analysis, and the computations are performed in the complex domain. Mapped real transform (MRT), whose basis functions are rectangular in nature, was evolved by modification of discrete Fourier transform and involves real additions only. But it is expansive and redundant. Unique MRT was developed to remove the redundancies present in MRT. Visual representation of unique MRT coefficients was explored to establish a transform, according to sequency, entitled sequency-based MRT (SMRT). It is a sequency ordered, addition oriented, integer-to-integer transform, whose basis functions are orthogonal. This paper gives an insight into the visual representation, transform kernel and placement of the \(N^2\) unique MRT coefficients corresponding to an \(N \times N\) data, for N a power of 2. Different properties of SMRT, computation of statistical parameters from transform coefficients are also included. Scope of the proposed transform in pattern generation is also investigated in addition to the established applications.

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