Let Sp(n,R) be the symplectic group, and K∗ n its maximal compact subgroup. Then G = Sp(n,R)/K∗ n can be realized as the Siegel domain of type one. The square-integrable representation of G gives the admissible wavelets AW and wavelet transform. The characterization of admissibility condition in terms of the Fourier transform is given. The Bergman kernel follows from the viewpoint of coherent s...

35 ABSTRACT This paper presents a new approach for power signal time series data mining using S-transform based K-means clustering technique and fuzzy decision tree. Initially the power signal time series disturbance data are pre-processed through an advanced signal processing tool such as S-transform and various statistical features are extracted, which are used as inputs to the K-means algori...

Chirps are signals (or sums of signals) that may be characterized by a local (i.e. time-dependent) amplitude and a local frequency. Time-frequency representations such as wavelet representations are well adapted to the characterization problem of such chirps. Ridges in the modulus of the transform determine regions in the transform domain with a high concentration of energy, and are regarded as...

Consider the Vandermonde-like matrix P := (Pk(cos jπ N ))j,k=0, where the polynomials Pk satisfy a three-term recurrence relation. If Pk are the Chebyshev polynomials Tk , then P coincides with CN+1 := (cos jkπ N )j,k=0. This paper presents a new fast algorithm for the computation of the matrixvector product Pa in O(N logN) arithmetical operations. The algorithm divides into a fast transform wh...

It is now nearly a decade since the theories of perverse sheaves and of the /adic Fourier transform came into being and gave fundamental new insights into the behavior of additive character sums over finite fields. Most of these insights were spellings out of the basic fact that the Fourier transform of a perverse sheaf is itself a perverse sheaf, a statement that amounts to a succession of van...

In the process of image acquisition and transmission, noise is always contained inevitably. So it is necessary to image denoising processing to improve the quality of image. Generally speaking, each algorithm has some filtering and threshold parameters. Taking variety kinds of images into account, it is a key problem of how to set these parameters in de-noising algorithms under different condit...

We consider the problem of quickly estimating the best k-term Fourier representation for a given frequency-sparse band-limited signal (i.e., function) f : [0,2π] → C. In essence, this requires the identification of k of the largest magnitude frequencies of f̂ ∈CN , and the estimation their Fourier coefficients. Randomized sublinear-time Monte Carlo algorithms, which have a small probability of f...

Notations For a real discrete-time filter whose impulse response is h[n], h̄[n] = h[−n], n ∈ Z is its timereversed version. The hat ˆ notation will be used for the Fourier transform of square-integrable signals. For a filter h, its z-transform is written H(z). The convolution product of two signals in l2(Z) will be written ∗. For the octave band wavelet representation, analysis (respectively, sy...