# Intersymbol Interference with Raised Cosine Pulses

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Intersymbol interference (ISI) occurs in digital communication systems when the symbols or bits of a digital signal spread or overlap with adjacent symbols in time, distorting the received signal. ISI increases the system bit error rate. ISI can be mitigated using pulse shaping. Ideal pulse shaping consists in having a time domain zero-crossing of the received pulse at the symbol boundaries. This Demonstration illustrates ISI and the zero-crossing property of raised cosine pulse shaping, highlighting the relationship among ISI, the symbol rate and Nyquist bandwidth.

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Contributed by: Victor S. Frost (October 12)

(University of Kansas)

Open content licensed under CC BY-NC-SA

## Details

Adjusting the end-to-end system to have an approximate raised cosine impulse response is a common method to control ISI. The frequency response and the time domain shape of a raised cosine pulse, that is, impulse response of a raised cosine filter, are given by [1]:

and

where is the Nyquist bandwidth and is the roll-off factor.

References

[1] S. Haykin and M. Moher, *Introduction to Analog and Digital Communications*, 2nd ed., Hoboken, NJ: Wiley, 2007.

[2] V. S. Frost. "Introduction to Communication Systems: An Interactive Approach Using the Wolfram Language." University of Kansas Libraries. (Jun 8, 2023) kuscholarworks.ku.edu/bitstream/handle/1808/31779/Introduction-to-Communication-Systems-Deployed-V3.cdf?sequence=5&isAllowed=y.

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