scholarly journals Generalized sub band analysis and signal synthesis

2020 ◽  
Vol 9 (3) ◽  
pp. 964-972 ◽  
Author(s):  
Evgeny G. Zhilyakov ◽  
Sergei P. Belov ◽  
Ivan I. Oleinik ◽  
Sergei L. Babarinov ◽  
Diana I. Trubitsyna
Keyword(s):  
Orthonormal Basis ◽  
Finite Impulse Response ◽  
Main Tool ◽  
Fir Filters ◽  
Optimal Selection ◽  
Mathematical Apparatus ◽  
New Class ◽  
Signal Synthesis ◽  
Selection For ◽  
Class Of Matrices

Currently, one of the main approaches used in analyzing properties and synthesis of signals in various classes is the subband methodology, which is carried out from the position of Fourier transform of signal samples (frequency representations) into subbands of the transform definition domain  (transformants). In this case, the main tool, which is widely used for subband analysis (including wavelet analysis), is usage of bandpass filters (mainly those with finite impulse response or FIR filters). The present paper  introduces the basics of building a theory forsubband analysis / signal  synthesis for various classes, and using transformations based on any  orthonormal basis with weight. This proposed approach is based on the  concept of Euclidean signal norm square fraction in a given subband of the transformant definition domain. It is shown that the basis for mathematical apparatus of subband analysis is a new class of matrices, called subband ones. Some eigenvalue properties of these matrices are established, and the problem of optimal selection for additive signal components is formulated and solved

scholarly journals Design of Cut off-Frequency Fixing Filters by Error Compensation of MAXFLAT FIR Filters

Electronics ◽  
2021 ◽  
Vol 10 (5) ◽  
pp. 553
Author(s):  
Daewon Chung ◽  
Woon Cho ◽  
Inyeob Jeong ◽  
Joonhyeon Jeon
Keyword(s):  
Closed Form ◽  
Error Compensation ◽  
Finite Impulse Response ◽  
Cutoff Frequency ◽  
Closed Form Solution ◽  
Form Solution ◽  
Fir Filters ◽  
Frequency Error ◽  
Computationally Efficient ◽  
Filter Type

Maximally-flat (MAXFLAT) finite impulse response (FIR) filters often face a problem of the cutoff-frequency error due to approximation of the desired frequency response by some closed-form solution. So far, there have been plenty of efforts to design such a filter with an arbitrarily specified cut off-frequency, but this filter type requires extensive computation and is not MAXFLAT anymore. Thus, a computationally efficient and effective design is needed for highly accurate filters with desired frequency characteristics. This paper describes a new method for designing cutoff-frequency-fixing FIR filters through the cutoff-frequency error compensation of MAXFLAT FIR filters. The proposed method provides a closed-form Chebyshev polynomial containing a cutoff-error compensation function, which can characterize the “cutoff-error-free” filters in terms of the degree of flatness for a given order of filter and cut off-frequency. This method also allows a computationally efficient and accurate formula to directly determine the degree of flatness, so that this filter type has a flat magnitude characteristic both in the passband and the stopband. The remarkable effectiveness of the proposed method in design efficiency and accuracy is clearly demonstrated through various examples, indicating that the cutoff-fixing filters exhibit amplitude distortion error of less than 10−14 and no cut off-frequency error. This new approach is shown to provide significant advantages over the previous works in design flexibility and accuracy.

scholarly journals Constant-coefficient FIR filters based on residue number system arithmetic

2012 ◽  
Vol 9 (3) ◽  
pp. 325-342 ◽  
Author(s):  
Negovan Stamenkovic ◽  
Vladica Stojanovic
Keyword(s):  
Power Dissipation ◽  
High Speed ◽  
Finite Impulse Response ◽  
Number System ◽  
Residue Number System ◽  
Fir Filter ◽  
Fir Filters ◽  
Residue Number ◽  
Low Power Dissipation ◽  
Residue Arithmetic

In this paper, the design of a Finite Impulse Response (FIR) filter based on the residue number system (RNS) is presented. We chose to implement it in the (RNS), because the RNS offers high speed and low power dissipation. This architecture is based on the single RNS multiplier-accumulator (MAC) unit. The three moduli set {2n+1,2n,2n-1}, which avoids 2n+1 modulus, is used to design FIR filter. A numerical example illustrates the principles of residue encoding, residue arithmetic, and residue decoding for FIR filters.

Comparison of Infinite Impulse Response (IIR) and Finite Impulse Response (FIR) Filters in Cardiac Optical Mapping Records

2021 ◽  
pp. 207-224
Author(s):  
David Rivas-Lalaleo ◽  
Sergio Muñoz-Romero ◽  
Monica Huerta ◽  
Víctor Bautista-Naranjo ◽  
Jorge García-Quintanilla ◽  
...  
Keyword(s):  
Impulse Response ◽  
Optical Mapping ◽  
Finite Impulse Response ◽  
Infinite Impulse Response ◽  
Fir Filters

scholarly journals State Fusion of Decentralized Optimal Unbiased FIR Filters

2018 ◽  
Vol 2018 ◽  
pp. 1-11
Author(s):  
Xuefeng Fan ◽  
Fei Liu
Keyword(s):  
Finite Impulse Response ◽  
Discrete Systems ◽  
Measurement Noise ◽  
Fir Filters ◽  
Fusion Strategy ◽  
Optimal Weights ◽  
Modeling Uncertainties ◽  
Cross Covariance ◽  
Local Filters ◽  
State Fusion

The paper presents a decentralized fusion strategy based on the optimal unbiased finite impulse response (OUFIR) filter for discrete systems with correlated process and measurement noise. We extend OUFIR filter to apply in the model with control inputs. Taking it as local filters, cross covariance between any two is calculated; then it is expressed to the fast iterative form. Finally based on cross covariance, optimal weights are utilized to fuse local estimates and the overall outcome is obtained. The numerical examples show that the proposed filter exhibits better robustness against temporary modeling uncertainties than the fusion Kalman filter used commonly.

scholarly journals A note on generalised linear complementarity problems

1978 ◽  
Vol 18 (2) ◽  
pp. 161-168 ◽  
Author(s):  
J. Parida ◽  
B. Sahoo
Keyword(s):  
Linear Complementarity Problems ◽  
Linear Complementarity ◽  
Closed Convex Cone ◽  
Arbitrary Vector ◽  
Existence Of A Solution ◽  
Polar Cone ◽  
New Class ◽  
Class A ◽  
Class Of Matrices ◽  
Image Position

Given an n × n matrix A, an n-dimensional vector q, and a closed, convex cone S of Rn, the generalized linear complementarity problem considered here is the following: find a z ∈ Rn such thatwhere s* is the polar cone of S. The existence of a solution to this problem for arbitrary vector q has been established both analytically and constructively for several classes of matrices A. In this note, a new class of matrices, denoted by J, is introduced. A is a J-matrix ifThe new class can be seen to be broader than previously studied classes. We analytically show that for any A in this class, a solution to the above problem exists for arbitrary vector q. This is achieved by using a result on variational inequalities.

A WAVELET-BASED SPEAKER VERIFICATION ALGORITHM

2010 ◽  
Vol 08 (06) ◽  
pp. 905-912 ◽  
Author(s):  
MICHEL ALVES LACERDA ◽  
RODRIGO CAPOBIANCO GUIDO ◽  
LEONARDO MENDES DE SOUZA ◽  
PAULO RICARDO FRANCHI ZULATO ◽  
JUSSARA RIBEIRO ◽  
...  
Keyword(s):  
Neural Network ◽  
Wavelet Transforms ◽  
Finite Impulse Response ◽  
Speaker Verification ◽  
Fir Filters ◽  
Discrete Wavelet ◽  
Discrete Wavelet Transforms ◽  
Verification Algorithm ◽  
Support Size ◽  
Artificial Neural Network Ann

This paper presents a study on wavelets and their characteristics for the specific purpose of serving as a feature extraction tool for speaker verification (SV), considering a Radial Basis Function (RBF) classifier, which is a particular type of Artificial Neural Network (ANN). Examining characteristics such as support-size, frequency and phase responses, amongst others, we show how Discrete Wavelet Transforms (DWTs), particularly the ones which derive from Finite Impulse Response (FIR) filters, can be used to extract important features from a speech signal which are useful for SV. Lastly, an SV algorithm based on the concepts presented is described.

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