Intersymbol Interference with Raised Cosine Pulses

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.
Here the symbol rate is normalized to 1 symbol/sec and a symbol is represented by . The input to a raised cosine filter is three symbols, . You can vary the Nyquist bandwidth and roll-off factor. The time domain output of the raised cosine filter is displayed. Given a symbol rate of 1, this Demonstration shows that there is no ISI when the Nyquist bandwidth is an integer multiple of 0.5. The Demonstration also illustrates that the severity of ISI decreases as the roll-off factor is increased from zero to unity [1]. Note that the required system bandwidth increases as the roll-off factor increases.


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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]:
where is the Nyquist bandwidth and is the roll-off factor.
[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)
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