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Phase Locked Loop Design
Published in Mike Golio, Commercial Wireless Circuits and Components Handbook, 2018
Figure 8.7 shows an example of the closed-loop gain, the open-loop gain and phase margin of a type I, second-order loop. The addition of the filter has added phase shift to the open-loop response, but at 75°, the phase margin is adequate for stability. The loop filter, however, still doesn’t offer much filtering for reference signal spurs. Higher order filters are typically added to the PLL in order to provide the appropriate attenuation, but as can be seen in Fig. 8.7, the additional filtering adds phase shift. The goal here is to maximize the filter’s attenuation while realizing minimum phase shift. An elliptic filter is often used due to the fact that they have higher selectivity (i.e., the passband is closest to the stopband) compared to other filters. The higher selectivity results in a minimization of phase shift.
Switched-Capacitor Circuits
Published in Tertulien Ndjountche, CMOS Analog Integrated Circuits, 2017
The frequency responses of a discrete-time filter, an anti-aliasing filter and the overall system are shown in Figure 8.3. The discrete-time filter has a low-pass characteristic with a cutoff frequency fc and a stopband attenuation As. Note that the spectrum of every discrete-time system is replicated at multiples of the sampling frequency. The transition from the passband to the stopband of the anti-aliasing filter consists of the frequency region located between fs/2 and fs – fc. A lowpass filter prototype is characterized by a cutoff (or passband) frequency, a stopband frequency, a maximum attenuation (or ripple) in the passband, and a minimum attenuation in the stopband. Depending on the type of application, the filter transfer function can be approximated by functions known as the Butterworth, Bessel, Chebyshev, or elliptic response, each of which has its own advantages or disadvantages. The Butterworth filter exhibits the flattest passband and lowest attenuation in the stopband. The Bessel filter has a more gradual roll-off and features a linear phase response, resulting in a constant time delay over a wide range of frequencies through the passband. The Chebyshev filter has a steeper roll-off near the cutoff fre quency and ripples in the passband. The elliptic filter has the steepest roll-off and equal ripples in both passband and stopband.
Partial Responses and Single-Sideband Optical Modulation
Published in Le Nguyen Binh, Advanced Digital, 2017
To achieve the VSB-modulation-formatted signals, OF is implemented. In this chapter, a number of low-pass elliptic filters (LPEF) are chosen because this filter type offers the steepest transition region between the passband and stopband without stability problems. The elliptic filter is a combination of the Chebyshev Type I and Chebyshev Type II, and exhibit some amplitude response ripples in the passband and stopband. The main advantage of the elliptic filter is that the width of the transition band is minimized for a finite ripple limit in the passband and a minimum attenuation in the stopband. Furthermore, these filters can be implemented using planar circuit technology [24]. The spectral response of the optical LPEF of the order N is given by [24]
Classification of Nonlinear Features of Uterine Electromyogram Signal Towards the Prediction of Preterm Birth
Published in IETE Journal of Research, 2022
P. Shaniba Asmi, Kamalraj Subramaniam, Nisheena V. Iqbal
The EHG signal after segmentation using a window size 1200 was considered in three different scenarios: 75% overlap, 50% overlap, and without overlap. These segments were then pre-processed in three methods using the Butterworth filter, elliptic filter, and three-level db4 wavelet transform. Ten different features were extracted from this segment for evaluating the discriminating capacity of each. As the uterus is a complex non-linear dynamic system, nonlinear signal processing techniques will be potentially very useful in analysing the system [2]. Therefore, non-linear features such as sample entropy, energy entropy, Teager energy, and Teager energy entropy were selected. Detrended fluctuation analysis and the Higuchi fractal dimension were the two fractal features considered to analyze the discriminating performance depending on the shape and self-similarity of the signal [16]. Linear features such as the RMS and frequency-related parameters, peak frequency, and median frequency were also added to the feature set. Finally, the bi-spectrum feature was also extracted, which included the phase information of the signal. The section below discusses each of these features.
Assessing the manageable portion of ground-level ozone in the contiguous United States
Published in Journal of the Air & Waste Management Association, 2020
Huiying Luo, Marina Astitha, S. Trivikrama Rao, Christian Hogrefe, Rohit Mathur
It is well recognized that various atmospheric processes operating on different timescales are embedded in ambient ozone time series data (see Rao et al. 1997 and Figure 2 in; Dennis et al. 2010). Different filtering techniques such as the Empirical Mode Decomposition (Huang et al. 1998), Elliptic filter (Poularika 1998), Kolmogorov-Zurbenko (KZ) filter (Rao and Zurbenko 1994), Adaptive Filtering Technique (Zurbenko et al. 1996), and Wavelet (Lau and Weng 1995) can be used to achieve scale separation in time series of meteorological and air quality variables (Hogrefe et al. 2003). Rao et al. (2020) applied a modified version of the Empirical Mode Decomposition (EMD), known as the Improved Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (Colominas, Schlotthauer, and Torres 2014) and the KZ filter to the observed ozone time series in 2010 and found that both methods yielded similar spectral decomposition results for the DM8HR time series data (see Figure 2 in Rao et al. 2020). Therefore, only the results from the KZ filter are presented in this paper to assess the impacts of emissions forcing and the stochastic nature of the atmosphere on the observed 8-hr ozone time series data.
A hybrid approach for speech enhancement using Bionic wavelet transform and Butterworth filter
Published in International Journal of Computers and Applications, 2020
Butterworth filters monotonically have a varying enormity function with ω, not like other filter kinds which hold non-monotonic ripple in pass band and/or else stop band. Matched with a Chebyshev Type I/Type II filter otherwise an elliptic filter, BW filter holds a dawdling roll-off, thus it will also require a greater order for executing stop band description. The Butterworth filter's squared response is provided like the function of the cut-off frequency. Ω implies the frequency response, Ωc is the 3db cut-off frequency. Here, the first 2n−1 derivative of |H(jΩ)|2 at Ω = 0 are equal to zero, so the Butterworth response is flat maximally at Ω = 0.