Abstract
This chapter covers two major coupled topics: matched filter and Nyquist pulse. The former maximizes SNR at the sampling time, and the latter is intersymbol interference (ISI) free end-to-end pulse. Both considerations will guide how to design, transmit, and receive filters (shaping pulses). We cover two practical filter design cases: analog and digital hybrid and purely digital ones.
List of sections in Chap. 3:
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3.1
Matched Filters
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3.2
Nyquist Criterion: ISI-Free Pulse
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3.3
Shaping Pulse (Filter) Design
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3.4
Performance Degradation Due to ISI
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3.5
Extension to Linear Channel and Nonwhite Noise
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3.6
References
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Change history
22 May 2019
Spine- Michael Yang corrected to Yang
Notes
- 1.
In practice, D/A is not a unit impulse but a rectangular pulse. This can be compensated readily; thus here we consider it a unit impulse.
- 2.
We assume gX(t) to be real. When it is complex the matched filter is in general\( {g}_X^{\ast}\left(-t\right) \). In other words, time reversal and conjugation of gX(t) will be a matched filter. Unless otherwise stated, we consider only a real impulse response. When h(t) is real, \( h\left(-t\right)={h}^{\ast}\left(-t\right) \).
- 3.
This is generally true whether h(t)is real or complex. Thus matched filter is also called conjugation filter.
- 4.
T is used for temperature as well as for symbol time but no confusion with the context.
3.6 References
Haykin, Simon,“Communication Systems” 4th ed., John-Wiley & Sons, Inc., New York, 2001, Chapter 4. Baseband Pulse Transmission
Carson, A. Bruce, Crilly, Paul B. and Rutledge, Janet C., “Communication Systems – An Introduction to Signals and Noise in Electrical Communication” 4th ed., McGraw Hill, Boston, 2002, Chapter 11. Baseband Digital Transmission
North, D.O., “An Analysis of the Factors Which Determine Signal/Noise Determination in Pulse-Carrier Systems,” RCA Tech. Report No. 6 PTR-6C, 1943
Turin, George, “An Introduction to Matched Filters”, IRE Transaction on Information Theory, 1960, pp 311-329
Nyquist, H., “Certain Factors Affecting Telegraph Speed,” Bell Systems Technical Journal, vol.3, 1924, p.324
IEEE, “Supplement to Standard for Telecommunications and Information Exchange Between Systems – LAN/MAN Specific Requirements – Part II: Wireless MAC and PHY Specifications: High Speed Physical Layer in the 5_GHz Band’ P802.11a/D7.0, July 1999
Yang, Sung-Moon (Michael), “A New Filter Method of CP and Windowing in OFDM Signals” Military Communications Conference 2010 DOI: https://doi.org/10.1109/milcom.2010.5680210
Lapidoth, Amos “A Foundation in Digital Communication” Cambridge University Press, 2009, pp.197 equation (11.31), which unfortunately has errors. See Wikipedia ‘root raised cosine filter’ for correct one.
Harris, Frederic J. “Multirate Signal Processing for Communication Systems “Prentice Hall, 2004, pp.90 equation (4.18)
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Michael Yang, SM. (2019). Matched Filter and Nyquist Pulse. In: Modern Digital Radio Communication Signals and Systems . Springer, Cham. https://doi.org/10.1007/978-3-319-71568-1_3
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DOI: https://doi.org/10.1007/978-3-319-71568-1_3
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