Recursive filter

In signal processing, a recursive filter (also called an infinite impulse response filter) is a type of filter which reuses one or more of its outputs as an input. They allow a system to respond over a long period of time to a brief input signal, without needing to perform complex calculations on every past input.[1] This feedback typically results in an unending impulse response, characterized by either exponentially growing, decaying, or sinusoidal signal output components.

However, a recursive filter does not always have an infinite impulse response. Some implementations of moving average filter are recursive filters but with a finite impulse response.

Non-recursive Filter Example: y[n] = 0.5x[n − 1] + 0.5x[n].

Recursive Filter Example: y[n] = 0.5y[n − 1] + 0.5x[n].

Examples of recursive filters

References

  1. ^ Smith, Steven W. (1999). "Chapter 19: Recursive Filters". The Scientist and Engineer’s Guide to Digital Signal Processing (PDF). Analog Devices / California Technical Publishing. Retrieved 2026-02-28.
Stub icon

This signal processing–related article is a stub. You can help Wikipedia by adding missing information.

Content Disclaimer

Informasi ini disarikan dari Wikipedia dan disajikan kembali untuk tujuan edukasi. Konten tersedia di bawah lisensi CC BY-SA 3.0. Kami tidak bertanggung jawab atas ketidakakuratan data yang bersumber dari kontribusi publik tersebut.

  1. The information displayed on this website is sourced in part or in whole from Wikipedia and has been adapted for the purpose of restating it. We strive to provide accurate and relevant information, however:
  2. There is no guarantee of absolute accuracy. Wikipedia is an open, collaborative project that can be edited by anyone, so information is subject to change.
  3. It is not intended to constitute professional advice. The content displayed is for informational and educational purposes only. For important decisions (e.g., medical, legal, or financial), please consult a professional.
  4. Content copyright. Wikipedia is licensed under the Creative Commons Attribution-ShareAlike License (CC BY-SA). This means that content may be reused with appropriate attribution and shared under a similar license.
  5. Responsible use. Any risk arising from the use of information from this website is entirely the responsibility of the user.