Bessel filter

About: Bessel filter is a research topic. Over the lifetime, 656 publications have been published within this topic receiving 16808 citations.

A recursive digital filter with maximally flat linear phase at an arbitrary specified frequency

Abstract: An available recursive digital low-pass filter with constant group delay cannot be spectral transformed to give, for example, a bandpass filter which also has constant group delay. This correspondence describes a technique, using Gauss-Jordan elimination, to design a recursive digital filter with maximally flat linear phase at an arbitrary specified frequency.

Special Relativity via Modified Bessel Functions

Abstract: The recursive formulas of modified Bessel functions give the relativistic expressions for energy and momentum. Modified Bessel functions are solutions to a continuous time, one-dimensional discrete jump process. The jump process is analyzed from two inertial frames with a relative constant velocity; the average distance of a particle along the chain corresponds to the distance between two observers in the two inertial frames. The recursion relations of modified Bessel functions are compared to the ‘ calculus’ which uses the radial Doppler effect to derive relativistic kinematics. The Doppler effect predicts that the frequency is a decreasing function of the velocity, and the Planck frequency, which increases with velocity, does not transform like the frequency of a clock. The Lorentz transformation can be interpreted as energy and momentum conservation relations through the addition formula for hyperbolic cosine and sine, respectively. The addition formula for the hyperbolic tangent gives the well-known relativistic formula for the addition of velocities. In the non-relativistic and ultra-relativistic limits the distributions of the particle’s position are Gaussian and Poisson, respectively.

Spectral delay filters with feedback and time-varying coefficients

Abstract: Arecentlyintroducedstructuretoimplementacontinuouslysmooth spectral delay, based on a cascade of first-order allpass filters and an equalizing filter, is described and the properties of this spectral delay filter are reviewed. A new amplitude envelope equalizing filter for the spectral delay filter is proposed and the properties of structures utilizing feedback and/or time-varying filter coefficients are discussed. In addition, the stability conditions for the feedback and the time-varying structures are derived. A spectral delay filter can be used for synthesizing chirp-like sounds or for modifying the timbre of arbitrary audio signals. Sound examples on the use of the spectral delay filters utilizing the structures discussed in this paper can be found at http://www.acoustics.hut. fi/publications/papers/dafx09-sdf/.