Stability and error bounds for discrete time frequency weighted balanced truncation

2002 ◽  
Author(s):  
K. Zhou ◽  
Y. Zheng ◽  
T. Lu
Keyword(s):  
Discrete Time ◽  
Error Bounds ◽  
Balanced Truncation ◽  
Time Frequency

scholarly journals Balanced truncation of linear time-invariant systems over finite-frequency ranges

2020 ◽  
Vol 46 (6) ◽  
Author(s):  
Peter Benner ◽  
Xin Du ◽  
Guanghong Yang ◽  
Dan Ye
Keyword(s):  
Error Bounds ◽  
Linear Time ◽  
Upper And Lower Bounds ◽  
Single Frequency ◽  
Frequency Interval ◽  
Balanced Truncation ◽  
Frequency Dependent ◽  
Linear Time Invariant ◽  
Type Frequency ◽  
Time Invariant

AbstractThis paper discusses model order reduction of linear time-invariant (LTI) systems over limited frequency intervals within the framework of balanced truncation. Two new frequency-dependent balanced truncation methods are developed, one is single-frequency (SF)-type frequency-dependent balanced truncation to cope with the cases that only a single dominating point of the operating frequency interval is pre-known, and the other is interval-type frequency-dependent balanced truncation to deal with the case that both the upper and lower bounds of the relevant frequency interval are known a priori. Error bounds for both approaches are derived to estimate the approximation error over a pre-specified frequency interval. In contrast to other error bounds for frequency-weighted or frequency-limited balanced truncation, these bounds are given specifically for the interval under consideration and are thus often sharper than the global bounds for previous methods. We show that the new methods generally lead to good in-band approximation performance, and at the same time provide accurate error bounds under certain conditions. Examples are included for illustration.

CWT × DWT × DTWT × SDTWT: Clarifying terminologies and roles of different types of wavelet transforms

2020 ◽  
Vol 18 (06) ◽  
pp. 2030001 ◽  
Author(s):  
Rodrigo Capobianco Guido ◽  
Fernando Pedroso ◽  
André Furlan ◽  
Rodrigo Colnago Contreras ◽  
Luiz Gustavo Caobianco ◽  
...  
Keyword(s):  
Wavelet Transform ◽  
Discrete Time ◽  
Wavelet Transforms ◽  
Signal Analysis ◽  
Applied Mathematics ◽  
Discrete Wavelet ◽  
Frequency Signal ◽  
Time Frequency ◽  
Subsequent Investigation ◽  
Different Types

Wavelets have been placed at the forefront of scientific researches involving signal processing, applied mathematics, pattern recognition and related fields. Nevertheless, as we have observed, students and young researchers still make mistakes when referring to one of the most relevant tools for time–frequency signal analysis. Thus, this correspondence clarifies the terminologies and specific roles of four types of wavelet transforms: the continuous wavelet transform (CWT), the discrete wavelet transform (DWT), the discrete-time wavelet transform (DTWT) and the stationary discrete-time wavelet transform (SDTWT). We believe that, after reading this correspondence, readers will be able to correctly refer to, and identify, the most appropriate type of wavelet transform for a certain application, selecting relevant and accurate material for subsequent investigation.

A subspace algorithm for the identification of discrete time frequency domain power spectra

Automatica ◽  
1997 ◽  
Vol 33 (12) ◽  
pp. 2147-2157 ◽  
Author(s):  
Peter Van Overschee ◽  
Bart De Moor ◽  
Wouter Dehandschutter ◽  
Jan Swevers
Keyword(s):  
Frequency Domain ◽  
Discrete Time ◽  
Power Spectra ◽  
Time Frequency ◽  
Subspace Algorithm
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