Eye Diagrams for Raised-Cosine Pulses

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An eye diagram (or eye pattern) is an experiential tool to graphically represent the quality of a digital signal. It provides information on the characteristics of a digital communications system, including the timing error, amount of inter-symbol interference and noise margin.


The eye diagram is created by superimposing multiple signal waveforms taken at the receiver over time, with the vertical axis representing the amplitude of the signal and the horizontal axis representing time. The resulting plot forms the shape of an "eye," with the size and shape of the eye indicating the quality of the signal. A wide, well-formed eye with clear edges indicates a high-quality signal, and a narrow, distorted eye with fuzzy edges indicates a poor-quality signal. Eye diagrams are easily created in the laboratory or as part of a system simulation. The impact of the pulse shape, timing errors (clock jitter), and noise can be observed from eye diagrams. This Demonstration shows the synchronized superposition of seven raised cosine pulses. You can adjust the Nyquist bandwidth, roll-off factor, percentage of clock jitter and energy per bit to noise power spectral density ratio in dB) and see the resulting impact on the eye diagram.


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



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

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