Digital Sound Synthesis has been an exciting field of research over the last two to three decades. The idea is mainly to generate sound artificially using a system. A lot of work has been done in the past for synthesis of musical tones of stringed instruments. In this work, attempt is made for synthesizing Harmonium music using the techniques of Physical Modeling based on Digital Waveguides. In...

− A new method of three-dimensional profile measurement of four-step reference specimens is presented. Instead of measuring only the height difference between central points of the two neighbouring surfaces of the specimen, overall profile of the whole specimen can be measured by using the fringe scanning Fourier transform method. The method to determine step height from its surface profile is ...

Recently several generalizations to higher dimension of the classical Fourier transform (FT) using Clifford geometric algebra have been introduced, including the two-dimensional (2D) Clifford Fourier transform (CFT). Based on the 2D CFT, we establish the two-dimensional Clifford windowed Fourier transform (CWFT). Using the spectral representation of the CFT, we derive several important properti...

a School of Mathematical Sciences, Universiti Sains Malaysia, 11800 Penang, Malaysia e-mail: [email protected] 1 Department of Mathematics, Hasanuddin University, KM 10 Tamalanrea Makassar, Indonesia b Department of Applied Physics, University of Fukui, 910-8507 Fukui, Japan e-mail: [email protected] c Division of Mathematical Sciences, Osaka Kyoiku University, Osaka 582-8582, Japa...

We characterize the Schwartz space of rapidly decaying test functions by the decay of the short-time Fourier transform or cross-Wigner distribution. Then we prove a version of Hardy’s theorem for the short-time Fourier transform and for the Wigner distribution.

The Fourier transform has been used as a reliable tool in signal analysis for many years. Invented in the early 1800s by its namesake, Jean Baptiste Joseph Fourier, the Fourier transform has become a cornerstone of modern signal analysis. The Fourier transform has proven incredibly versatile in applications ranging from patten recognition to image processing. Nevertheless, it suuers from certai...

Fractional Fourier Transform is a generalization of the classical Fourier Transform. The Fractional Fourier span in general depends on the amplitude and phase functions of the signal and varies with the transform order. However, with the development of the Fractional Fourier filter banks, it is advantageous in some cases to have different transform orders for different filter banks to achieve b...

Time-frequency representation of seismic signals provides a source of information that is usually hidden in the Fourier spectrum. The short-time Fourier transform and the wavelet transform are the principal approaches to simultaneously decompose a signal into time and frequency components. Known limitations, such as trade-offs between time and frequency resolution, may be overcome by alternativ...

Given a fixed p 6= 2 we prove a simple and effective characterization of all radial multipliers of FL(R) provided that the dimension d is sufficiently large. The method also yields new L space-time regularity results for solutions of the wave equation in high dimensions.