Introduction to Digital Communications pp 17-22 | Cite as

# Removal of Intersymbol Interference

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## Abstract

To remove the intersymbol interference (2.1) is called Nyquist’s first criterion in the time domain [1] and the corresponding impulse is referred to as Nyquist impulse. An example of a real-valued impulse response satisfying (2.1) is depicted in Fig. 2.1. Obviously, \(h_{e}(t)\) owns equidistant zeros except at \(t=t_{0}\).

*I*(*k*) defined in ( 1.42), we may not impose any constraint on the symbol sequence*a*(*k*), because the system design should hold for any sequence given by the user at the transmitter. Therefore we can only touch upon the impulse response*h*(*k*). Looking at ( 1.38) the system is prepared already with two degrees of freedom, \(g_{I}(t)\) and \(g_{R}(t)\). Hence, for a given impulse response \(g_{C}(t)\) of the physical channel we can design the overall impulse response in such a way that$$\begin{aligned} h(k-m)=h_{e}\left( t_{0}+(k-m)T\right) ={\left\{ \begin{array}{ll} \begin{array}{ccc} 0 &{} ; &{} m\,\epsilon \,\mathbb {Z}\,\,;\,\,m\ne k\\ h(0)=h_{e}(t_{0})\ne 0 &{} ; &{} m=k \end{array}\end{array}\right. } \end{aligned}$$

## References

- 1.H. Nyquist, Certain topics in telegraph transmission theory (reprint from Transactions of the A.I.E.E., Feb 1928),
*Proceedings of the IEEE*(2002)Google Scholar - 2.S. ten Brink, Pulse shaping, webdemo, Technical report, Institute of Telecommunications, University of Stuttgart, Germany (2018), http://webdemo.inue.uni-stuttgart.de

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