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Impulse Response and Transfer Function of a Raised Cosine Filter

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Intersymbol interference (ISI) occurs in digital communication systems when the symbols or bits of a digital signal overlap with adjacent symbols in time, distorting the received signal. ISI leads to an increase in the bit error rate of the system.

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One way to mitigate ISI is through pulse shaping. Pulse shaping involves designing a filter that modifies the transmitted signal in such a way that the time domain zero-crossing of the received pulse aligns with the symbol boundaries.

The focus of this Demonstration is a specific pulse-shaping technique that results in a raised cosine pulse in the receiver. By adjusting the roll-off factor of the raised cosine pulse, you can observe its characteristics in both the time and frequency domains.

This Demonstration showcases the zero-crossing property of the raised cosine pulse, which remains invariant for all values of the roll-off factor. This property ensures that the pulse aligns with the symbol boundaries, reducing ISI.

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Contributed by: Victor S. Frost (August 25)
(University of Kansas)
Open content licensed under CC BY-NC-SA

Details

ISI can be mitigated using pulse shaping. 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

.

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

In this Demonstration, the Nyquist bandwidth .

References

[1] S. Haykin and M. Moher, Introduction to Analog and Digital Communications, 2nd ed., Hoboken, NJ: Wiley, 2012.

[2] L. W. Couch, Digital and Analog Communications Systems, 7th ed., Upper Saddle River, NJ: Pearson/Prentice Hall, 2007.

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

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