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A general approach based on polyphase splines, with analysis in the frequency domain, is developed for studying wavelet frames of periodic functions of one or higher dimensions. Characterizations of frames for shift-invariant subspaces of periodic functions and results on the structure of these subspaces are obtained. Starting from any multiresolutionâ€¦ (More)

- Say Song Goh
- 2007

A unitary extension principle for constructing normalized tight wavelet frames of periodic functions of one or higher dimensions is established. While the wavelets are nonstationary, the method much simplifies their construction by reducing it to a matrix extension problem that involves finite rows of complex numbers. Further flexibility is achieved byâ€¦ (More)

- Say Song Goh, Tim N. T. Goodman, Fuchun Shang
- IEEE Transactions on Signal Processing
- 2010

The standard approach for joint estimation of time delay and Doppler shift of a signal is to estimate the point at which the cross ambiguity function of the original and modified signals attains its maximum modulus. Since band-limited signals can be expressed exactly by their Shannon series, we here consider approximated signals gained by truncating theirâ€¦ (More)

- Kah-Chye Tan, Say Song Goh, Eng-Chye Tan
- IEEE Trans. Signal Processing
- 1996

We first extend a theorem on linear independence of steering vectors proposed by Godara and Cantoni to include more array-sensor scenarios. We then show that an array can have pairwise linearly independent steering vectors even when all its intersensor spacings are more than X / 2 where X is the wavelength of the signals. We next propose a theorem forâ€¦ (More)

- Say Song Goh, Chee Heng Yeo
- Adv. Comput. Math.
- 2000

This paper is on the angle-frequency localization of periodic scaling functions and wavelets. It is shown that the uncertainty products of uniformly local, uniformly regular and uniformly stable scaling functions and wavelets are uniformly bounded from above by a constant. Results for the construction of such scaling functions and wavelets are alsoâ€¦ (More)

- P. M. D. S. Pallawala, Wynne Hsu, Mong-Li Lee, Say Song Goh
- 2005 Seventh IEEE Workshops on Applications ofâ€¦
- 2005

Diabetic retinopathy is a major cause of blindness and microaneurysms are the first clinically observable manifestations of diabetic retinopathy. Regular screening and timely intervention can halt or reverse the progression of this disease. This paper describes an approach that is based on the generalized eigenvectors of affinity matrix to extractâ€¦ (More)

- Say Song Goh, Bin Han, Zuowei Shen, SONG GOH
- 2010

A systematic study on tight periodic wavelet frames and their approximation orders is conducted. We identify a necessary and sufficient condition, in terms of refinement masks, for applying the unitary extension principle for periodic functions to construct tight wavelet frames. Then a theory on the approximation orders of truncated tight frame series isâ€¦ (More)

- Ole Christensen, Say Song Goh
- Adv. Comput. Math.
- 2010

We construct non-tight frames in finite-dimensional spaces consisting of periodic functions. In order for these frames to be useful in practice one needs to calculate a dual frame; while the canonical dual frame might be cumbersome to work with, the setup presented here enables us to obtain explicit constructions of some particularly convenient obliqueâ€¦ (More)

- Say Song Goh, Tim N. T. Goodman, S. L. Lee
- Adv. Comput. Math.
- 2007

Abstract. We show that the scale-space operators defined by a class of refinable kernels satisfy a version of the causality property, and a sequence of such operators converges to the corresponding operator with the Gaussian kernel, if the sequence of refinable kernels converges to the Gaussian function. In addition, we consider discrete analogs of theseâ€¦ (More)

- Ole Christensen, Say Song Goh
- Journal of Approximation Theory
- 2015

We consider a class of functions, defined on a locally compact abelian group by letting a class of modulation operators act on a countable collection of functions. We derive sufficient conditions for such a class of functions to form a Bessel sequence or a frame and for two such systems to be dual frames. Explicit constructions are obtained via variousâ€¦ (More)