A state-space approach for adaptive second-order IIR notch digital filters is explored. A simplified iterative algorithm is derived from the gradient-descent method to minimize the mean-squared output of an adaptive notch digital filter. The stability and parameter-estimation bias are then analyzed by employing a first-order linear dynamical system. As a consequence, it is clarified that the resulting parameter estimate is unbiased. Finally, a numerical example is presented to demonstrate the validity and effectiveness of the adaptive state-space notch digital filter and bias analysis of parameter estimation.

In a field of biomedical engineering, not only low-pass filters for high frequency elimination but also notch filters for suppressing powerline interference are necessary to process low-frequency biosignals. For integration of low-frequency filters, chip implementation of large capacitances is major difficulty. As methods to enhance capacitances with small chip area, use of capacitance multipliers is effective. This letter describes design consideration of integrated low-frequency low-pass notch filter employing capacitance multipliers. Two main points are presented. Firstly, a new floating capacitance multiplier is proposed. Secondly, a technique to reduce the number of capacitance multipliers is proposed. By this technique, power consumption is reduced. The proposed techniques are applied a 3rd order low-pass notch filter. Simulation results show the effectiveness of the proposed techniques.

This paper deals with a state-space approach for adaptive second-order IIR notch digital filters with constrained poles and zeros. A simplified iterative algorithm is derived from the gradient-descent method to minimize the mean-squared output of an adaptive notch digital filter. Then, stability and parameter-estimation bias are analyzed for the simplified iterative algorithm. A numerical example is presented to demonstrate the validity and effectiveness of the proposed adaptive state-space notch digital filter and parameter-estimation bias analysis.

This paper investigates an adaptive notch digital filter that employs normal state-space realization of a single-frequency second-order IIR notch digital filter. An adaptive algorithm is developed to minimize the mean-squared output error of the filter iteratively. This algorithm is based on a simplified form of the gradient-decent method. Stability and frequency estimation bias are analyzed for the adaptive iterative algorithm. Finally, a numerical example is presented to demonstrate the validity and effectiveness of the proposed adaptive notch digital filter and the frequency-estimation bias analyzed for the adaptive iterative algorithm.

A narrowband active noise control (NANC) system is very effective for controlling low-frequency periodic noise. A frequency mismatch (FM) with the reference signal will degrade the performance or even cause the system to diverge. To deal with an FM and obtain an accurate reference signal, NANC systems often employ a frequency estimator. Combining an autoregressive predictive filter with a variable step size (VSS) all-pass-based lattice adaptive notch filter (ANF), a new frequency estimation method is proposed that does not require prior information of the primary signal, and the convergence characteristics are much improved. Simulation results show that the designed frequency estimator has a higher accuracy than the conventional algorithm. Finally, hardware experiments are carried out to verify the noise reduction effect.

This paper proposes a noise reduction technology for a specific frequency band that uses the pulse coding controlled method to automatically set the notch frequency in DC-DC switching converters of communication equipment. For reducing the power levels at the frequency and its harmonics in the switching converter, we often use a frequency-modulated clock. This paper investigates a technology that prevents modulated clock frequency noise from spreading into protected frequency bands; this proposed noise reduction technology does not distribute the switching noise into some specified frequency bands. The notch in the spectrum of the switching pulses is created by the Pulse Width Coding (PWC) method. In communication devices, the noise in the receiving signal band must be as small as possible. The notch frequency is automatically set to the frequency of the received signal by adjusting the clock frequency using the equation Fn = (P+0.5)Fck. Here Fn is the notch frequency, Fck is the clock frequency, and P is a positive integer that determines the noise spectrum location. Therefore, simply be setting the notch frequency to the received signal frequency can suppress the noise present. We confirm with simulations that the proposed technique is effective for noise reduction and notch generation. Also we implement a method of automatic switching between two receiving channels. The conversion voltage ratio in the pulse width coding method switching converter is analyzed and full automatic notch frequency generation is realized. Experiments on a prototype circuit confirm notch frequency generation.

Hum noise such as power line interference is one of the critical problems in the biomedical signal acquisition. Various techniques have been proposed to suppress power line interference. However, some of the techniques require more components and power consumption. The notch depth in the conventional N-path notch filter circuits needs a higher number of paths and switches off-resistance. It makes the conventional N-path notch filter less of efficiency to suppress hum noise. This work proposed the new N-path notch filter to hum noise suppression in biomedical signal acquisition. The new N-path notch filter achieved notch depth above 40dB with sampling frequency 50Hz and 60Hz. Although the proposed circuits use less number of path and switches off-resistance. The proposed circuit has been verified using artificial ECG signal contaminated by hum noise at frequency 50Hz and 60Hz. The output of N-path notch filter achieved a noise-free signal even if the sampling frequency changes.

In this paper, an optimal method is proposed to design sparse-coefficient notch filters with principal basic vectors in the column space of a matrix constituted with frequency samples. The proposed scheme can perform in two stages. At the first stage, the principal vectors can be determined in the least-squares sense. At the second stage, with some components of the principal vectors, the notch filter design is formulated as a linear optimization problem according to the desired specifications. Optimal results can form sparse coefficients of the notch filter by solving the linear optimization problem. The simulation results show that the proposed scheme can achieve better performance in designing a sparse-coefficient notch filter of small order compared with other methods such as the equiripple method, the orthogonal matching pursuit based scheme and the L1-norm based method.

In the field of adaptive notch filtering, Monotonically Increasing Gradient (MIG) algorithm has recently been proposed by Sugiura and Shimamura [1], where it is claimed that the MIG algorithm shows monotonically increasing gradient characteristics. However, our analysis has found that the underlying theory in [1] includes crucial errors. This letter shows that the formulation of the gradient characteristics in [1] is incorrect, and reveals that the MIG algorithm fails to realize monotonically increasing gradient characteristics when the input signal includes white noise.

Power line noise is one of critical problems in bio-sensing. Various approaches utilizing both analog and digital techniques has been proposed. However, these approaches need active circuits with a wide dynamic range. N-path notch filters which implementable using passive components can be a promising solution to this problem. However, the notch depth of a conventional N-path notch filter is limited by the number of path. A new N-path notch filter with additional S/H circuit is proposed. Simulation results show that the proposed topology improves the notch depth by 43dB.

Multiple notch filters are used to suppress narrow-band or sinusoidal interferences in digital signals. In this paper, we propose a novel optimization design technique of an infinite impulse response (IIR) multiple notch filter. It is based on the Nelder-Mead simplex method. Firstly, the system function of the desired notch filter is constructed to form the objective function of the optimization technique. Secondly, the design parameters of the desired notch filter are optimized by Nelder-Mead simplex method. A weight function is also introduced to improve amplitude response of the notch filter. Thirdly, the convergence and amplitude response of the proposed technique are compared with other Nelder-Mead based design methods and the cascade-based design method. Finally, the practicability of the proposed notch filter design technique is demonstrated by some practical applications.

In this paper, we propose Affine Combination Lattice Algorithm (ACLA) as a new lattice-based adaptive notch filtering algorithm. The ACLA makes use of the affine combination of Regalia's Simplified Lattice Algorithm (SLA) and Lattice Gradient Algorithm (LGA). It is proved that the ACLA has faster convergence speed than the conventional lattice-based algorithms. We conduct this proof by means of theoretical analysis of the mean update term. Specifically, we show that the mean update term of the ACLA is always larger than that of the conventional algorithms. Simulation examples demonstrate the validity of this analytical result and the utility of the ACLA. In addition, we also derive the step-size bound for the ACLA. Furthermore, we show that this step-size bound is characterized by the gradient of the mean update term.

Conventional adaptive notch filter based on an infinite impulse response (IIR) filter is well known. However, this kind of adaptive notch filter has a problem of stability due to its adaptive IIR filter. In addition, tap coefficients of this notch filter converge to solutions with bias error. In order to solve these problems, an adaptive notch filter using Fourier sine series (ANFF) is proposed. The ANFF is stable because an adaptive IIR filter is not used as an all-pass filter. Further, the proposed adaptive notch filter is robust enough to overcome effects of a disturbance signal, due to a structure of the notch filter based on an exponential filter and line symmetry of auto correlation.

This paper proposes a new adaptive comb filter which automatically designs its characteristics. The comb filter is used to eliminate a periodic noise from an observed signal. To design the comb filter, there exists three important factors which are so-called notch frequency, notch gain, and notch bandwidth. The notch frequency is the null frequency which is aligned at equally spaced frequencies. The notch gain controls an elimination quantity of the observed signal at notch frequencies. The notch bandwidth controls an elimination bandwidth of the observed signal at notch frequencies. We have previously proposed a comb filter which can adjust the notch gain adaptively to eliminate the periodic noise. In this paper, to eliminate the periodic noise when its frequencies fluctuate, we propose the comb filter which achieves the adaptive notch gain and the adaptive notch bandwidth, simultaneously. Simulation results show the effectiveness of the proposed adaptive comb filter.

An ultra-wideband (UWB) system usually occupies a large frequency band, which may overlap with the spectrum of a narrow band system. The latter is referred to as a victim system. To effectively use frequency, a UWB system may create a notch in its spectrum to accommodate the victim signal for interference avoidance. Parameters of the notch such as the depth and the width of a notch need to be decided in accordance to victim systems. In this paper, we investigate the effective UWB avoidance by examining the suitable notch based on experimental evaluation. In the experiments, 3GPP LTE, Mobile WiMAX, as well as an IMT Advanced Test-bed are respectively employed to represent different types of victim systems. The UWB system is set up based on WiMedia specifications and operates at the UWB low band of 3.1–4.8 GHz. A notch is fabricated by nullifying the related subcarriers of the UWB signal. In addition, a filter or a window function is formed and employed to further smooth the notch. Bit error rate (BER) or packet error rate (PER) performances of victim systems are measured and used to evaluate the UWB interference. Our results show that when a notch is properly formed, the interference level introduced by UWB can be below the permitted level by regulations.

This paper presents a multi-band WCDMA receiver consisting of a multi-band low noise amplifier (LNA), a multi-band mixer and an inter-stage tunable notch filter. The notch filter is used to suppress Tx leakage, and 0.8–1.5 GHz (66%) of tuning range is achieved. The receiver achieves 33 and 30 dB conversion gain, 6.4 and 8 dB NF, 50 and 35.5 dBm IIP2, and -6 and -4.7 dBm IIP3 at 0.8 and 1.5 GHz, respectively. The power consumption is 121 mW from a 1.8-V power supply. The receiver is implemented in a 0.18-µm CMOS process.

We have previously proposed a howling canceller which cancels howling by using a cascade notch filter designed from a distance between a loudspeaker and a microphone. This method utilizes a pilot signal to estimate the distance. In this paper, we introduce two methods into the distance-based howling canceller to improve speech quality. The first one is an adaptive cascade notch filter which adaptively adjusts the nulls to eliminate howling and to keep speech components. The second one is a silent pilot signal whose frequencies exist in the ultrasonic band, and it is inaudible while on transmission. We implement the proposed howling canceller on a DSP to evaluate its capability. The experimental results show that the proposed howling canceller improves speech quality in comparison to the conventional one.

This paper analyzes frequency tracking characteristics of a complex-coefficient adaptive infinite impulse response (IIR) notch filter with a simplified gradient-based algorithm. The input signal to the complex notch filter is a complex linear chirp embedded in a complex zero-mean white Gaussian noise. The analysis starts with derivation of a first-order real-coefficient difference equation with respect to steady-state instantaneous frequency tracking error. Closed-form expression for frequency tracking mean square error (MSE) is then derived from the difference equation. Lastly, closed-form expressions for optimum notch bandwidth coefficient and step size constant that minimize the frequency tracking MSE are derived. Computer simulations are presented to validate the analysis.

In this paper, a notch-band implemented UWB bandpass filter was proposed. The filter was realized by integrating a full ultra-wideband bandpass filter using broadside coupling structure with a bandstop filter using in-line open stub. The in-line open stub was installed in the removed area in the broadside coupled microstrip conductors, which demonstrated a narrow notch-band performance. The proposed filters were designed based on the electromagnetic simulation and fabricated using a wet etching system. Parameter study of length dependence of the notch-band was carried out. The first resonant frequency of the in-line stub appears when the length is approximately equal to one quarter of the guided wavelength. Based on this fact, the notch-band can be adjusted to almost any specified band in the UWB passband. A three-section notch-band implemented filter demonstrated good characteristics: its full frequency bandwidth form 2.8 GHz to 10.2 GHz, good insertion loss of 0.6 dB and 1.0 dB at the centers of the first and second bands respectively, and flat and small group delay of less than 0.40 ns over main pass band, and a large attenuation stopband about 55 dB at 5.63 GHz. A lowpass filter was also introduced in order to improve the out-band performance, by which the measured results show an excellent attenuation better than 30 dB from 10.4 GHz to 17.8 GHz.

In this paper, we report the detailed investigation of novel printed disc monopole antennas for ultra-wideband (UWB) applications focusing on miniaturization of the disc radiator. First, the basic property was examined for the case of a circular disc with diameter of 50 mm, and it was found that the VSWR is less than 2 in the UWB band of 3.1-10.6 GHz when the feed gap length is between about -0.1 and 0.2 mm. Next, in order to reduce the size of the disc radiator, various dimensions of elliptical discs were investigated. It is shown that if the dimensions of the elliptical disc are chosen appropriately, a smaller disc size antenna can be achieved. To decrease the antenna size further, a triangular notch and an exponentially curved notch on the ground plane of the antenna were examined. It is observed that the use of the notched ground is very effective and that the diameter of the circular radiator can be reduced to 17 mm. The proposed antenna has an omnidirectional pattern in the x-y plane. The influence of the notch on the radiation pattern is very small. Details of the simulation results using the FDTD method and experimental results for the proposed antenna are presented and analyzed. These features are very attractive for UWB applications.