Maximally flat and least-square co-design of variable fractional delay filters for wideband software-defined radio

This paper describes improvements in a Farrow-structured variable fractional delay (FD) Lagrange filter for all-pass FD interpolation. The main idea is to integrate the truncated sinc into the Farrow structure of a Lagrange filter, in order that a superior FD approximation in the least-square sense can be achieved. Its primary advantages are the lower level of mean-square-error (MSE) over the whole FD range and the reduced implementation cost. Extra design parameters are introduced for making the trade-off between MSE and maximal flatness under different design requirements. Design examples are included, illustrating an MSE reduction of 50% compared to a classical Farrow-structured Lagrange interpolator while the implementation cost is reduced. This improved variable FD interpolation system is suitable for many applications, such as sample rate conversion, digital beamforming and timing synchronization in wideband software-defined radio (SDR) communications

Improved IIR Low-Pass Smoothers and Differentiators with Tunable Delay

Regression analysis using orthogonal polynomials in the time domain is used to derive closed-form expressions for causal and non-causal filters with an infinite impulse response (IIR) and a maximally-flat magnitude and delay response. The phase response of the resulting low-order smoothers and differentiators, with low-pass characteristics, may be tuned to yield the desired delay in the pass band or for zero gain at the Nyquist frequency. The filter response is improved when the shape of the exponential weighting function is modified and discrete associated Laguerre polynomials are used in the analysis. As an illustrative example, the derivative filters are used to generate an optical-flow field and to detect moving ground targets, in real video data collected from an airborne platform with an electro-optic sensor.Comment: To appear in Proc. International Conference on Digital Image Computing: Techniques and Applications (DICTA), Adelaide, 23rd-25th Nov. 201

H^∞-Optimal Fractional Delay Filters

Fractional delay filters are digital filters to delay discrete-time signals by a fraction of the sampling period. Since the delay is fractional, the intersample behavior of the original analog signal becomes crucial. In contrast to the conventional designs based on the Shannon sampling theorem with the band-limiting hypothesis, the present paper proposes a new approach based on the modern sampled-data $H^{infty}$ optimization that aims at restoring the intersample behavior beyond the Nyquist frequency. By using the lifting transform or continuous-time blocking the design problem is equivalently reduced to a discrete-time $H^{infty}$ optimization, which can be effectively solved by numerical computation softwares. Moreover, a closed-form solution is obtained under an assumption on the original analog signals. Design examples are given to illustrate the advantage of the proposed method

FIR Filter Design Using Distributed Maximal Flatness Method

In the paper a novel method for filter design based on the distributed maximal flatness method is presented. The proposed approach is based on the method used to design the most common FIR fractional delay filter – the maximally flat filter. The MF filter demonstrates excellent performance but only in a relatively narrow frequency range around zero frequency but its magnitude response is no greater than one. This ,,passiveness” is the reason why despite of its narrow band of accurate approximation, the maximally flat filter is widely used in applications in which the adjustable delay is required in feedback loop. In the proposed method the maximal flatness conditions forced in standard approach at zero frequency are spread over the desired band of interest. In the result FIR filters are designed with width of the approximation band adjusted according to needs of the designer. Moreover a weighting function can be applied to the error function allowing for designs differing in error characteristics. Apart from the design of fractional delay filters the method is presented on the example of differentiator, raised cosine and square root raised cosine FIR filters. Additionally, the proposed method can be readily adapted for variable fractional delay filter design regardless of the filter type.

Variable Fractional Digital Delay Filter on Reconfigurable Hardware

This thesis describes a design for a variable fractional delay (VFD) finite impulse reponse (FIR) filter implemented on reconfigurable hardware. Fractionally delayed signals are required for several audio-based applications, including echo cancellation and musical signal analysis. Traditionally, VFD FIR filters have been implemented using a fixed structure in software based upon the order of the filter. This fixed structure restricts the range of valid fractional delay values permitted by the filter. This proposed design implements an order-scalable FIR filter, permitting fractionally delayed signals of widely varying integer sizes. Furthermore, the proposed design of this thesis builds upon the traditional Lagrange interpolator FIR filter using either asoftware-based coefficient computational unit or hardware-based coefficient computational unit in reconfigurable hardware for updating the FIR coefficients in real-time. Traditional Lagrange interpolator FIR filters have only permitted fixed fractional delay. However, by leveraging todays (2012) low-cost high performance reconfigurable hardware, an FIR-based fractional delay filter was created to permit varying fractional delay. A software/hardware hybrid VFD filter was prototyped using the Xilinx System Generator toolkit. The resulting real-time VFD FIR filter was tested usingSystem Generator, as well as Xilinx ISE and ModelSim.M.S., Computer Engineering -- Drexel University, 201

Design of FIR Fractional Delay Filter Based on Maximum Signal-to-Noise Ratio Criterion

Abstract-In this paper, a new approach to the design of digital FIR fractional delay filter with consideration of noise attenuation is presented. The design is based on the maximization of signal-to-noise ratio (SNR) at the output of the fractional delay filter under the constraint that actual frequency response and ideal response have several same derivatives at the prescribed frequency point. The optimal filter coefficients are obtained from the generalized eigenvector associate with maximum eigenvalue of a pair of matrices. Numerical examples are demonstrated to show the proposed method provides higher SNR than the conventional FIR fractional delay filter design methods without considering the noise attenuation

Digital Filters

The new technology advances provide that a great number of system signals can be easily measured with a low cost. The main problem is that usually only a fraction of the signal is useful for different purposes, for example maintenance, DVD-recorders, computers, electric/electronic circuits, econometric, optimization, etc. Digital filters are the most versatile, practical and effective methods for extracting the information necessary from the signal. They can be dynamic, so they can be automatically or manually adjusted to the external and internal conditions. Presented in this book are the most advanced digital filters including different case studies and the most relevant literature