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A correction to impulse invariance
Open accessAbstract
The classic equations for discrete time filter design by impulse invariance are not correct, in general. In particular, if the impulse response of the causal continuous-time filter is discontinuous at t=0, then the initial sample h[0] of the discrete-time impulse response should equal one-half the value of the discontinuity, not the full value as classically given. Otherwise, the resulting frequency response does not equal the sum of shifted versions of the original response as expected. This effect will typically be seen only in low order filters such as first order lowpass filters or second order bandpass filters.
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Research works printed but not linked: 8
- mitra, 1998, Digital Signal Processing A Computer-Based Approach, 425
- proakis, 1996, Digital Signal Processing Principles Algorithms and Applications, 671
- 10.1109/TASSP.1977.1162919 · DOI
- papoulis, 1962, The Fourier Integrals and Its Applications
- 10.1016/S0165-1684(00)00113-4 · DOI
- gabel, 1987, Signals and Linear Systems, 408
- oppenheim, 1989, Discrete-Time Signal Processing, 407
- 10.1007/978-1-4757-2458-5 · DOI
Cited by
$H^{\infty}$-Optimal Fractional Delay Filters
Nagahara, M., & Yamamoto, Y. (2013) · IEEE Transactions on Signal Processing · doi:10.1109/tsp.2013.2265678 · Cited by 15
“The weighting function in (4) or (5) is chosen as the impulse-invariant discretization [48] of .”
Background
Metadata
- Authors
- Jackson, L. B.
- Affiliations
- University of Rhode Island (US)
- Corresponding author
- Jackson, L.B.
- Venue
- IEEE Signal Processing Letters
- Published
- 2000-10
- Volume
- 7
- Issue
- 10
- Pages
- 273-275
- ISSN
- 1070-9908 (ISSN-L)
- 1558-2361
- OpenAlex
- W2170601912
- Cited by
- 36
- References
- 0
- Citations by year
- 2026: 1 · 2024: 1 · 2023: 3 · 2022: 1 · 2021: 1 · 2020: 3 · 2019: 1 · 2018: 2 · 2017: 3 · 2016: 3 · 2015: 1 · 2014: 1 · 2013: 2 · 2012: 1
- Type
- journal article
- Language
- en
- Open access
- Locations
- IEEE Signal Processing Letters (publishedVersion)
- Journal of Media Literacy Education (submittedVersion, cc-by)
- Topics
- Physical Sciences › Computer Science › Signal Processing › Digital Filter Design and Implementation
- Physical Sciences › Engineering › Electrical and Electronic Engineering › Analog and Mixed-Signal Circuit Design
- Physical Sciences › Computer Science › Signal Processing › Advanced Adaptive Filtering Techniques
- Keywords
- impulse response, frequency response, low-pass filter, bandpass filter
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- Jackson, L. B. (2000). A correction to impulse invariance. IEEE Signal Processing Letters. https://doi.org/10.1109/97.870677
