Given a signal and its Fourier transform, we derive formulas for its polyphase decomposition in the frequency domain and for the reconstruction from the polyphase representation back to the Fourier representation. We present two frequency-domain implementations of the shift-invariant periodic discrete wavelet transform (SI-DWT) and its inverse: one that is based on frequency-domain polyphase de...

A method of registering images at subpixel accuracy has been proposed, which does not resort to interpolation. The method is based on the phase correlation method and is remarkably robust to correlated noise and uniform variations of luminance. We have shown that the cross power spectrum of two images, containing subpixel shifts, is a polyphase decomposition of a Dirac delta function. By estima...

The problem of the design of effective 2-D and 3-D multirate systems with prescribed properties is considered using tools from commutative algebra. Results for factoring 2-channel polyphase matrices are presented. After such a factorization, the number of computations may be reduced. For a 3-channel multirate system, an algorithmic version of Suslin’s stability theorem may be useful for factori...

A novel approach for constructing symmetric compactly supported biorthogonal multiwavelets with short sequences is proposed in this paper. For some symmetric types of biorthogonal multiwavelet systems, starting from the symmetric properties of scaling and wavelet functions, parameterized symmetric forms of polyphase matrices can be derived. Furthermore, according to the matrix equations of the ...

This paper presents an efficient method for the design of two-channel quadrature mirror filter (QMF) bank by polyphase representation of low-pass prototype filter and power optimization method for minimization of an objective function. The objective function is formulated as linear combination of pass-band error and stop-band residual energy of the low-pass analysis filter of the filter bank. O...

A read-forward polyphase merge algorithm is described which performs the polyphase merge starting from an arbitrary string distribution. This algorithm minimizes the volume of information moved. Since this volume is easily computed, it is possible to construct dispersion algorithms which anticipate the merge algorithm. Two such dispersion techniques are described. The first algorithm requires t...

In this paper, we devise a computational approach for designing polyphase sequences with two key properties; (i) a phase argument which is piecewise linear, and (ii) an impulse-like autocorrelation. The proposed approach relies on fast Fourier transform (FFT) operations and thus can be used efficiently to design sequences with a large length or alphabet size. Moreover, using the suggested metho...