Digital Filter Design and Implementation

An algorithm for efficient and accurate computation of the fractional Fourier transform is given. For signals with time-bandwidth product N, the presented algorithm computes the fractional transform in O(NlogN) time. A definition for the discrete fractional Fourier transform that emerges from our analysis is also disc…

We propose and consolidate a definition of the discrete fractional Fourier transform that generalizes the discrete Fourier transform (DFT) in the same sense that the continuous fractional Fourier transform generalizes the continuous ordinary Fourier transform. This definition is based on a particular set of eigenvecto…

A brief introduction to the fractional Fourier transform and its properties is given. Its relation to phase-space representations (time- or space-frequency representations) and the concept of fractional Fourier domains are discussed. An overview of applications which have so far received interest are given and some po…

A concise introduction to the concept of fractional Fourier transforms is followed by a discussion of their relation to chirp and wavelet transforms. The notion of fractional Fourier domains is developed in conjunction with the Wigner distribution of a signal. Convolution, filtering, and multiplexing of signals in fra…

• BİLLUR BARSHAN ÖZAKTAŞ

For time-invariant degradation models and stationary signals and noise, the classical Fourier domain Wiener filter, which can be implemented in O(N log N) time, gives the minimum mean-square-error estimate of the original undistorted signal. For time-varying degradations and nonstationary processes, however, the optim…

We deal with the problem of efficient and accurate digital computation of the samples of the linear canonical transform (LCT) of a function, from the samples of the original function. Two approaches are presented and compared. The first is based on decomposition of the LCT into chirp multiplication, Fourier transforma…

• AYKUT KOÇ

A novel systematic approach to the design of directivity patterns of higher order differential microphones is proposed. The directivity patterns are obtained by optimizing a cost function which is a convex combination of a front-back energy ratio and uniformity within a frontal sector of interest. Most of the standard…

• HÜSEYİN HACIHABİBOĞLU

Subband decomposition techniques have been extensively used for data coding and analysis. In most filter banks, the goal is to obtain subsampled signals corresponding to different spectral regions of the original data. However, this approach leads to various artifacts in images having spatially varying characteristics…

• ÖMER NEZİH GEREK

The fast Fourier transform (FFT) algorithm has been used in a variety of applications in signal and image processing. In this article, a simple procedure for designing finite-extent impulse response (FIR) discrete-time filters using the FFT algorithm is described. The zero-phase (or linear phase) FIR filter design pro…

• ÖMER NEZİH GEREK

A novel algorithm for designing low-power and hardware-efficient linear-phase finite-impulse response (FIR) filters is presented. The algorithm finds filter coefficients with reduced number of signed-power-of-two (SPT) terms given the filter frequency response characteristics. The algorithm is a branch-and-bound-based…

• GÜNHAN DÜNDAR

A novel algorithm for designing low-power and hardware-efficient linear-phase finite-impulse response (FIR) filters is presented. The algorithm finds filter coefficients with reduced number of signed-power-of-two (SPT) terms given the filter frequency response characteristics. The algorithm is a branch-and-bound-based…

• ARDA YURDAKUL

Filtering in a single time domain or in a single frequency domain has been generalized to filtering in a single fractional Fourier domain. We generalize this to repeated filtering in consecutive fractional Fourier domains and discuss its applications to signal restoration through an illustrative example.