Abstract
This paper presents a new complex adaptive notch filter to estimate and track the frequency of a complex sinusoidal signal. The gradient-adaptive lattice structure instead of the traditional gradient one is adopted to accelerate the convergence rate. It is proved that the proposed algorithm results in unbiased estimations by using the ordinary differential equation approach. The closed-form expressions for the steady-state mean square error and the upper bound of step size are also derived. Simulations are conducted to validate the theoretical analysis and demonstrate that the proposed method generates considerably better convergence rates and tracking properties than existing methods, particularly in low signal-to-noise ratio environments.
Highlights
The adaptive notch filter (ANF) is an efficient frequency estimation and tracking technique that is utilised in a wide variety of applications, such as communication systems, biomedical engineering and radar systems [1,2,3,4,5,6,7,8,9,10,11,12]
The upper bound of the step size in LMSbased methods must be maintained within a limited range to ensure stability; this range depends on the eigenvalue of the correlation matrix of the input signal
We develop a new complex ANF (CANF) system based on the lattice algorithm [21]
Summary
The adaptive notch filter (ANF) is an efficient frequency estimation and tracking technique that is utilised in a wide variety of applications, such as communication systems, biomedical engineering and radar systems [1,2,3,4,5,6,7,8,9,10,11,12]. Both algorithms are computationally complicated and can result in biased estimations To address this problem, numerous efficient and unbiased least mean square (LMS)-based algorithms have been developed, such as the complex plain gradient (CPG) [15], modified CPG (MCPG) [16], lattice-form CANF (LCANF) [17], and arctangent-based algorithms [18]. Numerous efficient and unbiased least mean square (LMS)-based algorithms have been developed, such as the complex plain gradient (CPG) [15], modified CPG (MCPG) [16], lattice-form CANF (LCANF) [17], and arctangent-based algorithms [18] All these LMS-based algorithms generate a lower convergence rate than the RLS-based algorithms do. Asterisk ∗ denotes a complex conjugate and ⊗ is the convolution operator
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