Sy-Been Jaw

Computation of discrete Hilbert transform through fast Hartley transform

A fast algorithm is proposed to compute the discrete Hilbert transform via the fast Hartley transform (FHT). Instead of the conventional fast Fourier transform (FFT) approach, the processing is carried out entirely in the real domain. Also, since many efficient FHT algorithms exist, the computation complexity can be greatly reduced from two complex FFTs into two real FHTs. >

Efficient design of 2-D multiplierless FIR filters by transformation

This paper deals with the design of 2-D multiplierless FIR digital filters. First, a special class of multiplierless 1-D FIR filters is designed with coefficients which are a sum or difference of power of two. This is then mapped into 2-D multiplierless FIR filters by the McClellan transform. This technique has the advantage that it is very fast, because only a 1-D filter must be designed. Also, the hardware implementation for these 2-D FIR filters is very attractive and efficient.

Two-dimensional general fan-type FIR digital filter design

Abstract Conventional transform methods can only design ordinary and quadrant fan-type filters with 90° pass-angle. In this paper, three efficient approaches are proposed for designing general arbitrary pass-angle fan-type filters. They include the analytic closed form, the rotated, and the frequency sampling design methods. Each approach has its features and is very suitable for directional filtering and image processing applications.

The analytic signal in the Hartley transform domain

An analytic signal in the Hartley transform domain is presented. It operates entirely in the real domain, and has many properties similar to the Fourier analytic signal; also, many efficient existing fast Hartley algorithms can be used to reduce computation complexity. The discrete Hartley analytic signals and the Hartley spectra associated with two real signals are presented. The results correspond exactly with the derived theory. >

Efficient design of 2D multiplierless FIR filters by transformation

This paper deals with the design of 2D multiplierless FIR digital filters, first a special class of multiplierless 1D FIR filters are designed with coefficients which are a sum or difference of power-of-two, and then map it into 2D multiplierless FIR filters by McClellan transform; This technique has the advantage that it is very fast, because only a 1-D filter must be designed, also the hardware implementation for these 2D FIR filters is very attractive and efficient.

In-place in-order mixed radix fast Hartley transforms

This paper presents two Fortran programs that calculate the mixed radix discrete Hartley transform (DHT) using a general odd length p-point DHT module and several short length Winograd DHT (WDHT) modules. Each program has its own advantages such as simplicity for implementation or minimum arithmetic complexity. New efficient radix-3, odd radix-p FHT algorithms and short WDHT modules have been developed to be incorporated into a general FHT algorithm. It allows a much wider selection of transform sizes, and calculates the DHT in order.

Modifications to the Liang, McClellan and Parks computer program for designing optimal recursive multirate digital filters

A class of recursive digital filters of the form H(z)=A(z)/B(z/sup D/) for sampling rate conversion is designed with an iterative Remez exchange algorithm. Simple modifications are made to the Liang, McClellan, and Parks computer program for designing these multirate digital filters. The resulting filters can greatly reduce the multiplication rate and the coefficients memory storage. Some design examples are presented to show the effectiveness of this approach. >

A novel 2-D window for spectral estimation

A novel 2-D window can be easily generated by the McClellan transform of Tsengs 1-D window. The transformed window has nearly circularly symmetric frequency response and preserves the features and flexibility of Tsengs 1-D prototype window. It can independently control the pattern falloff rate, the sidelobe level, and the depth of a steerable wide dip. Examples of detecting multiple 2-D closely spaced sinusoids have demonstrated the superiority of this novel 2-D window.

A class of efficient recursive quadrature mirror filters for subband coding

A class of recursive quadrature mirror filters (QMFs) of the form H(Z)=N(Z)/D(Z/sup 2/) is proposed for subband coding. These filters can be efficiently designed with the iterative Remez exchange algorithm. Simple modifications are made to the Pei (see IEEE Trans. Circuits Syst., vol.CAS-36, no.2, p.311, 1989), Liang, McClellan, and Parks computer program for designing these recursive QMF filters efficiently. The resulting filters totally eliminate the aliasing terms and can achieve almost perfect magnitude reconstruction, with -131.5-dB distortion. A design example is presented to show the effectiveness of this approach. >