Search

Digital notch filters are useful for removing sinusoidal signals with a single frequency or multi-frequencies. For some applications, the sinusoidal signals being processed may change frequencies, and thus the notch filter must also have a variable notch frequency. Such a digital filter with a variable notch-frequency (VNF) is called variable notch-frequency (VNF) digital filter. Generally speaking, a VNF filter has the ability to change its notch frequency continuously, and can remove sinusoidal signals with variable frequencies. To design a recursive VNF filter, guaranteeing its stability is the top-priority issue. In this paper, a recursive VNF filter is designed by utilizing the least Lp-norm criterion, and the stability is guaranteed through adopting the stability-guarantee methodology based on parameter transformations. To perform the parameter transformations, a function that meets a special condition is required, and such a function is called unity-bounded function. In this paper, various unity-bounded functions are developed for the parameter-transformation-based stability guarantee. The unity-bounded functions play a crucial role in the stability guarantee. This paper details how to design a stable VNF filter by incorporating the parameter transformations employing the unity-bounded functions into the Lp-norm minimization of the magnitude response. Theoretically, the stability of the recursive VNF filter resulting from the design is definitely guaranteed. Moreover, since the coefficients of the designed VNF are variable, changing the filter coefficients enables the user to get a VNF filter with updated notch frequency. [ABSTRACT FROM AUTHOR]

An interpolation kernel is required in a wide variety of signal processing applications such as image interpolation and timing adjustment in digital communications. This article presents a general-form interpolation kernel called 3-3-3 interpolation kernel and derives its frequency response in a closed-form by using a simple derivation method. This closed-form formula is preliminary to designing various 3-3-3 interpolation kernels subject to a set of design constraints. The 3-3-3 interpolation kernel is formed through utilising the third-degree piecewise polynomials, and it is an even-symmetric function. Thus, it will suffice to consider only its right-hand side when deriving its frequency response. Since the right-hand side of the interpolation kernel contains three piecewise polynomials of the third degree, i.e. the degrees of the three piecewise polynomials are (3,3,3), we call it the 3-3-3 interpolation kernel. Once the general-form frequency-response formula is derived, we can systematically formulate the design of various 3-3-3 interpolation kernels subject to a set of design constraints, which are targeted for different interpolation applications. Therefore, the closed-form frequency-response expression is preliminary to the optimal design of various 3-3-3 interpolation kernels. We will use an example to show the optimal design of a 3-3-3 interpolation kernel based on the closed-form frequency-response expression. [ABSTRACT FROM PUBLISHER]