Variable Fractional Delay Filter Design Using a Symmetric Window

Abstract

In this paper a numerically efficient method for designing a nearly optimal variable fractional delay (VFD) filter based on a simple and well-known window method is presented. In the proposed method a single window extracted from the optimal filter with fixed fractional delay (FD) is divided into even and odd part. Subsequently, the odd part is discarded and symmetric even part of the extracted window is used to design a family of nearly optimal filters with varying FD. In addition to window extraction, the proposed approach requires filter gain correction which is dependent on the desired FD. Optimum values of the gain correction factor as well as the extracted window can be computed beforehand, which allows us to design a nearly optimal FD filter with arbitrary FD at low numerical costs during runtime. On the basis of the proposed filter design method, the universal structure of VFD filter allowing for change of filter type and length has been proposed. In the paper, three FD filter optimality criteria are considered, which are maximal flatness, Chebyshev (minimax), and least squares.

Adaptive Wideband Beamforming Based on Digital Delay Filter

“…Clearly, for a non-integer D , () hn is infinite as well as non-causal and a filter with such an impulse response is thus non-realizable [22]. So we approximate the ideal filter by window method.…”

“…Taking into consideration advantages and disadvantages of available window methods [22], we have chosen Chebyshev window characterized by a minimum main-lobe width for a given side-lobe attenuation [23]. Chebyshev Window has the unique property that all its side-lobes are equal and the side-lobe height is the same at all frequencies [25].…”

Optimal design of symmetric fractional delay filter using firefly algorithm

“…Tseng et al designed FD FIR filter using interpolation methods such as discrete Hilbert transform, discrete cosine term, and discrete sine term 18 . Blok et al presented an efficient method for designing the variable FD filter based on symmetric window 19 . Although these techniques were able to design a FD filter, they were unable to reach nearer to ideal FD filter response.…”

Optimal design of fractional delay FIR filter using cuckoo search algorithm

“…[17][18][19][20][21][22] Farrow presents an FIR filter that implements the adjustable delay. 30 The main concern in FD filter design problem is the nondifferentiability and a multimodal error function. 17 Liu and Wei used nonlinear interpolation 18 and Lagrange interpolation 19 techniques to implement the fractional sample delay.…”

“…29 Blok and Sac presented an efficient method based on symmetric window for the design of variable FD filter. 30 The main concern in FD filter design problem is the nondifferentiability and a multimodal error function. The design methods reported in literature are not sufficient to optimize the nonlinear and multimodal error function as they get struck at local minima because of high sensitive to initial coefficients.…”