Fractional Delayer Utilizing Hermite Interpolation with Caratheodory Representation

Fractional delay is indispensable for many sorts of circuits and signal processing applications. Fractional delay filter (FDF) utilizing Hermite interpolation with an analog differentiator is a straightforward way to delay discrete signals. This method has a low time-domain error, but a complicated sampling module than the Shannon sampling scheme. A simplified scheme, which is based on Shannon sampling and utilizing Hermite interpolation with a digital differentiator, will lead a much higher time-domain error when the signal frequency approaches the Nyquist rate. In this letter, we propose a novel fractional delayer utilizing Hermite interpolation with Caratheodory representation. The samples of differential signal are obtained by Caratheodory representation from the samples of the original signal only. So, only one sampler is needed and the sampling module is simple. Simulation results for four types of signals demonstrate that the proposed method has significantly higher interpolation accuracy than Hermite interpolation with digital differentiator

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

Design of Wideband Fractional Delay Filters Using Derivative Sampling Method

[[abstract]]In this paper, the design of wideband fractional delay filter is investigated. First, the reconstruction formula of derivative sampling method is applied to design wideband fractional delay filter by using index substitution and window method. The filter coefficients are easily computed because closed-form design is obtained. Then, the weighted least squares method is used to design fixed and variable wideband fractional delay filters. Finally, numerical examples are demonstrated to show that the proposed method has smaller design error than the conventional fractional delay filter without sampling the derivative of signal