Estimate of the Optimum Cutoff Frequency for the Butterworth Low-Pass Digital Filter

1999 ◽  
Vol 15 (3) ◽  
pp. 318-329 ◽  
Author(s):  
Bing Yu ◽  
David Gabriel ◽  
Larry Noble ◽  
Kai-Nan An
Keyword(s):  
Digital Filter ◽  
Cutoff Frequency ◽  
Sampling Frequency ◽  
Residual Analysis ◽  
Data Set ◽  
Raw Data ◽  
Standard Data ◽  
Cutoff Frequencies ◽  
Flexion Extension ◽  
Low Pass

The purposes of this study were (a) to develop a procedure for objectively determining the optimum cutoff frequency for the Butterworth low-pass digital filler, and (b) to evaluate the cutoff frequencies derived from the residual analysis. A set of knee flexion-extension angle data in normal gait was used as the standard data set. The standard data were sampled at different sampling frequencies. Random errors with different magnitudes were added to the standard data to create different sets of raw data with a given sampling frequency. Each raw data set was filtered through a Butterworth low-pass digital filter at different cutoff frequencies. The cutoff frequency corresponding to the minimum error in the second time derivatives for a given set of raw data was considered as the optimum for that set of raw data. A procedure for estimating the optimum cutoff frequency from the sampling frequency and estimated relative mean error in the raw data set was developed. The estimated optimum cutoff frequency significantly correlated to the true optimum cutoff frequency with a correlation determinant value of 0.96. This procedure was applied to estimate the optimum cutoff frequency for another set of kinematic data. The calculated accelerations of the filtered data essentially matched the measured acceleration curve. There is no correlation between the cutoff frequency derived from the residual analysis and the true optimum cutoff frequency. The cutoff frequencies derived from the residual analysis were significantly lower than the optimum, especially when the sampling frequency is high.

Hilbert low-pass filter of non-stationary time sequence using analytical mode decomposition

2015 ◽  
Vol 23 (15) ◽  
pp. 2444-2469 ◽  
Author(s):  
Zuo-Cai Wang ◽  
Yu Xin ◽  
Jin-feng Xing ◽  
Wei-Xin Ren
Keyword(s):  
Cutoff Frequency ◽  
Low Frequency ◽  
Frequency Component ◽  
Sampling Frequency ◽  
Pass Filter ◽  
Low Pass Filter ◽  
Mode Decomposition ◽  
Low Pass ◽  
One Step ◽  
Low Pass Filters

In this paper, the recently developed analytical mode decomposition with a constant or time-varying cutoff frequency is extended into the decomposition of a non-stationary discrete time sequence. The discretization of the signal and the selection of the cutoff frequency may cause the failure of low frequency component extraction. In this study, to eliminate the effects of the signal discretization, the one-step, two-step, and four-step low-pass filters with cutoff frequencies are proposed. Based on the theoretical derivation, the previous one-step low-pass filter is effective only when the cutoff frequency is not greater than a quarter of the sampling frequency and the maximum frequency of the signal not greater than a half of the sampling frequency. In this study, if the cutoff frequency is less than or equal to a quarter of the sampling frequency, a two-step low-pass filter is proposed to extract the low frequency component. If the cutoff frequency is greater than a quarter of the sampling frequency, a four-step low-pass filter with frequency shifting process is proposed. When the time-varying cutoff frequency is not always larger than or less than a quarter of the sampling frequency, a sufficient condition, which is the sampling frequency is greater than four times of the maximum frequency of the signal component, is provided in this study. Two numerical examples are used to validate the effectiveness of the proposed low-pass filters. Both the theoretic derivation and numerical simulations show that the proposed filters can analytical extract the discrete low frequency component with an appropriate cutoff frequency.

scholarly journals 1.0 V-0.18 µm CMOS Tunable Low Pass Filters with 73 dB DR for On-Chip Sensing Acquisition Systems

Electronics ◽  
2021 ◽  
Vol 10 (5) ◽  
pp. 563
Author(s):  
Jorge Pérez-Bailón ◽  
Belén Calvo ◽  
Nicolás Medrano
Keyword(s):  
Power Consumption ◽  
Dynamic Range ◽  
Low Voltage ◽  
Cutoff Frequency ◽  
Cmos Technology ◽  
Active Area ◽  
Current Steering ◽  
Low Pass ◽  
On Chip ◽  
Low Pass Filters

This paper presents a new approach based on the use of a Current Steering (CS) technique for the design of fully integrated Gm–C Low Pass Filters (LPF) with sub-Hz to kHz tunable cut-off frequencies and an enhanced power-area-dynamic range trade-off. The proposed approach has been experimentally validated by two different first-order single-ended LPFs designed in a 0.18 µm CMOS technology powered by a 1.0 V single supply: a folded-OTA based LPF and a mirrored-OTA based LPF. The first one exhibits a constant power consumption of 180 nW at 100 nA bias current with an active area of 0.00135 mm2 and a tunable cutoff frequency that spans over 4 orders of magnitude (~100 mHz–152 Hz @ CL = 50 pF) preserving dynamic figures greater than 78 dB. The second one exhibits a power consumption of 1.75 µW at 500 nA with an active area of 0.0137 mm2 and a tunable cutoff frequency that spans over 5 orders of magnitude (~80 mHz–~1.2 kHz @ CL = 50 pF) preserving a dynamic range greater than 73 dB. Compared with previously reported filters, this proposal is a competitive solution while satisfying the low-voltage low-power on-chip constraints, becoming a preferable choice for general-purpose reconfigurable front-end sensor interfaces.

scholarly journals The Study of Multiple Classes Boosting Classification Method Based on Local Similarity

Algorithms ◽  
2021 ◽  
Vol 14 (2) ◽  
pp. 37
Author(s):  
Shixun Wang ◽  
Qiang Chen
Keyword(s):  
Image Retrieval ◽  
Loss Function ◽  
Single Mode ◽  
Local Similarity ◽  
Text And Image ◽  
Data Set ◽  
Standard Data ◽  
Weak Learner ◽  
Great Progress ◽  
Data Points

Boosting of the ensemble learning model has made great progress, but most of the methods are Boosting the single mode. For this reason, based on the simple multiclass enhancement framework that uses local similarity as a weak learner, it is extended to multimodal multiclass enhancement Boosting. First, based on the local similarity as a weak learner, the loss function is used to find the basic loss, and the logarithmic data points are binarized. Then, we find the optimal local similarity and find the corresponding loss. Compared with the basic loss, the smaller one is the best so far. Second, the local similarity of the two points is calculated, and then the loss is calculated by the local similarity of the two points. Finally, the text and image are retrieved from each other, and the correct rate of text and image retrieval is obtained, respectively. The experimental results show that the multimodal multi-class enhancement framework with local similarity as the weak learner is evaluated on the standard data set and compared with other most advanced methods, showing the experience proficiency of this method.

Design and Simulation of Switched Capacitor Filter for Speed Change Parameter Converter

2013 ◽  
Vol 562-565 ◽  
pp. 1132-1136
Author(s):  
Xiao Wei Liu ◽  
Jian Yang ◽  
Song Chen ◽  
Liang Liu ◽  
Rui Zhang ◽  
...  
Keyword(s):  
Stop Band ◽  
Cutoff Frequency ◽  
Rapid Change ◽  
Pass Band ◽  
Cmos Process ◽  
Switched Capacitor ◽  
Pass Filter ◽  
Low Pass Filter ◽  
Low Pass ◽  
The Time Domain

In this paper, we design a high-order switched capacitor filter for rapid change parameter converter. This design uses a structure which consists of three biquads filter sub-units. The design is a 6th-order SC elliptic low-pass filter, and the sample frequency is 250 kHz. By the MATLAB Simulink simulation, the system can meet the design requirements in the time domain. In this paper, the 6th-order switched capacitor elliptic low-pass filter was implemented under 0.5 um CMOS process and simulated in Cadence. The final simulation results show that the pass-band cutoff frequency is 10 kHz, and the maximum pass-band ripple is about 0.106 dB. The stop-band cutoff frequency is 20 kHz, and the minimum stop-band attenuation is 74.78 dB.

scholarly journals Elemental ratio measurements of organic compounds using aerosol mass spectrometry: characterization, improved calibration, and implications

2015 ◽  
Vol 15 (1) ◽  
pp. 253-272 ◽  
Author(s):  
M. R. Canagaratna ◽  
J. L. Jimenez ◽  
J. H. Kroll ◽  
Q. Chen ◽  
S. H. Kessler ◽  
...  
Keyword(s):  
High Resolution ◽  
Vacuum Ultraviolet ◽  
Laboratory Data ◽  
Detailed Examination ◽  
Relative Difference ◽  
Data Set ◽  
Elemental Ratios ◽  
Standard Data ◽  
Aerosol Mass ◽  
Relative Errors

Abstract. Elemental compositions of organic aerosol (OA) particles provide useful constraints on OA sources, chemical evolution, and effects. The Aerodyne high-resolution time-of-flight aerosol mass spectrometer (HR-ToF-AMS) is widely used to measure OA elemental composition. This study evaluates AMS measurements of atomic oxygen-to-carbon (O : C), hydrogen-to-carbon (H : C), and organic mass-to-organic carbon (OM : OC) ratios, and of carbon oxidation state (OS C) for a vastly expanded laboratory data set of multifunctional oxidized OA standards. For the expanded standard data set, the method introduced by Aiken et al. (2008), which uses experimentally measured ion intensities at all ions to determine elemental ratios (referred to here as "Aiken-Explicit"), reproduces known O : C and H : C ratio values within 20% (average absolute value of relative errors) and 12%, respectively. The more commonly used method, which uses empirically estimated H2O+ and CO+ ion intensities to avoid gas phase air interferences at these ions (referred to here as "Aiken-Ambient"), reproduces O : C and H : C of multifunctional oxidized species within 28 and 14% of known values. The values from the latter method are systematically biased low, however, with larger biases observed for alcohols and simple diacids. A detailed examination of the H2O+, CO+, and CO2+ fragments in the high-resolution mass spectra of the standard compounds indicates that the Aiken-Ambient method underestimates the CO+ and especially H2O+ produced from many oxidized species. Combined AMS–vacuum ultraviolet (VUV) ionization measurements indicate that these ions are produced by dehydration and decarboxylation on the AMS vaporizer (usually operated at 600 °C). Thermal decomposition is observed to be efficient at vaporizer temperatures down to 200 °C. These results are used together to develop an "Improved-Ambient" elemental analysis method for AMS spectra measured in air. The Improved-Ambient method uses specific ion fragments as markers to correct for molecular functionality-dependent systematic biases and reproduces known O : C (H : C) ratios of individual oxidized standards within 28% (13%) of the known molecular values. The error in Improved-Ambient O : C (H : C) values is smaller for theoretical standard mixtures of the oxidized organic standards, which are more representative of the complex mix of species present in ambient OA. For ambient OA, the Improved-Ambient method produces O : C (H : C) values that are 27% (11%) larger than previously published Aiken-Ambient values; a corresponding increase of 9% is observed for OM : OC values. These results imply that ambient OA has a higher relative oxygen content than previously estimated. The OS C values calculated for ambient OA by the two methods agree well, however (average relative difference of 0.06 OS C units). This indicates that OS C is a more robust metric of oxidation than O : C, likely since OS C is not affected by hydration or dehydration, either in the atmosphere or during analysis.

Investigating Recurrent Neural Networks for OCT A-scan Based Tissue Analysis

2014 ◽  
Vol 53 (04) ◽  
pp. 245-249 ◽  
Author(s):  
S. Otte ◽  
L. Wittig ◽  
G. Hüttmann ◽  
C. Kugler ◽  
D. Drömann ◽  
...  
Keyword(s):  
Short Term Memory ◽  
Pulmonary Nodules ◽  
Patient Specific ◽  
Specific Training ◽  
Reference Distribution ◽  
Human Lung Tissue ◽  
Additional Information ◽  
Cutoff Frequencies ◽  
Low Pass ◽  
Lower Cutoff

Summary Objectives: Optical Coherence Tomography (OCT) has been proposed as a high resolution image modality to guide transbronchial biopsies. In this study we address the question, whether individual A-scans obtained in needle direction can contribute to the identification of pulmonary nodules. Methods: OCT A-scans from freshly resected human lung tissue specimen were recorded through a customized needle with an embedded optical fiber. Bidirectional Long Short Term Memory networks (BLSTMs) were trained on randomly distributed training and test sets of the acquired A-scans. Patient specific training and different pre-processing steps were evaluated. Results: Classification rates from 67.5% up to 76% were archived for different training scenarios. Sensitivity and specificity were highest for a patient specific training with 0.87 and 0.85. Low pass filtering decreased the accuracy from 73.2% on a reference distribution to 62.2% for higher cutoff frequencies and to 56% for lower cutoff frequencies. Conclusion: The results indicate that a grey value based classification is feasible and may provide additional information for diagnosis and navigation. Furthermore, the experiments show patient specific signal properties and indicate that the lower and upper parts of the frequency spectrum contribute to the classification.

Design of Digital Filter Based on Numerical Simulation

2014 ◽  
Vol 539 ◽  
pp. 79-83
Author(s):  
Chuan Ting Wei ◽  
Quan Li Ning ◽  
Dong Chen
Keyword(s):  
Numerical Simulation ◽  
Mathematical Model ◽  
Digital Filter ◽  
Sampling Frequency ◽  
New Wave ◽  
Matlab Software ◽  
Frequency Wave

In MATLAB software, it has FDATool toolbox, which can design digital filter specific according to specific circuit, and analyze the performance of the filter according to the parameters of filter. In this paper we establish simulation mathematical model of digital filter based on the calculation principle of distributed multiplication accumulator. According to the logic algorithm we design delay algorithm of digital filter, and use MATLAB software to do simulation on amplitude frequency and phase frequency of digital filter. After superposition of different sampling frequency wave we get new waveform, and realize the digital filter for the new wave. It proves the availability of mathematical model and the program, and provides the technical reference for the design of digital filter.

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