A Variational Approach for Designing Infinite Impulse Response Filters With Time-Varying Parameters

Filter design with short transient state is a problem encountered in many fields of circuits, systems, and signal processing. In this paper, a novel low-pass filter design technique with time-varying parameters is introduced in order to minimize the rise-time parameter. Through the use of calculus o...

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Bibliographic Details
Published in:IEEE transactions on circuits and systems. I, Regular papers Regular papers, 2018-04, Vol.65 (4), p.1303-1313
Main Authors: Toledo de la Garza, Karel, Torres Gomez, Jorge, de Lamare, Rodrigo C., Fernandez-Getino Garcia, Maria Julia
Format: Article
Language:English
Subjects:
Band-pass filters
Bandwidth
Bandwidths
Calculus of variations
Closed-form solutions
Design parameters
Filter design
Filter design (mathematics)
IIR filters
Impulse response
Low pass filters
Order parameters
rise-time
Signal processing
Time-frequency analysis
time-varying parameters
Transfer functions
Transient analysis
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Summary:Filter design with short transient state is a problem encountered in many fields of circuits, systems, and signal processing. In this paper, a novel low-pass filter design technique with time-varying parameters is introduced in order to minimize the rise-time parameter. Through the use of calculus of variations a method is developed to obtain the optimal closed-form expression for adjusting the parameters. In this context, two cases are addressed: the ideal case in which infinite bandwidth is required and a solution of finite bandwidth. The latter is obtained by means of a proper constraint formulation in the frequency domain. The proposed filter achieves the shortest rise time and allows better preservation of the edge shape in comparison with other existing filtering methods. The analysis, synthesis, and performance of the proposed system are discussed and illustrated with the aid of simulations.
ISSN:1549-8328
1558-0806
DOI:10.1109/TCSI.2017.2746747