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Home/Engineering/Digital Modulation Eye Diagram

Digital Modulation Eye Diagram

NRZ / PAM-4 eye diagram with raised-cosine shaping, ISI, AWGN, timing jitter, and vertical opening estimate.

Digital eye diagram

18 dB
0.25
0.04 UI
0.35

Overlapped 2-UI windows of a pulse-shaped random bitstream after a two-tap ISI channel, AWGN, and sampling jitter. A closed eye means hard decisions become unreliable.

Shortcuts

  • •Raise noise, ISI, or jitter to close the eye; reseed for a new bit pattern.

Measured values

Vertical opening (est.)0.220
Traces overlayed220
Noise σ (rel.)0.069
Samples / UI32

About this model

An eye diagram overlays many symbol-spaced windows of a received baseband waveform. For NRZ or PAM-4 with raised-cosine pulse shaping, intersymbol interference (ISI), additive noise, and timing jitter close the eye opening. A wide open eye at the sampling instant means reliable hard decisions; a closed eye foreshadows bit errors.

Who it's for: Digital communications, signals and systems, and electrical engineering courses covering baseband modulation and link quality.

Key terms

  • Eye diagram
  • NRZ
  • PAM-4
  • ISI
  • Raised cosine
  • Timing jitter
  • SNR

How it works

Build a classic communications eye diagram from NRZ or PAM-4 symbols with raised-cosine pulse shaping. Add ISI, AWGN, and timing jitter to watch the eye close — the visual cue for bit-error risk.

Key equations

TX: pulse-shaped symbols (raised cosine, roll-off α)
RX: y[n] ≈ (1−a)x[n] + a x[n−d] + noise
Eye = overlay of 2-UI windows · pink line = sampling instant

Frequently asked questions

Why does ISI close the eye?
Energy from neighboring symbols leaks into the current decision sample. A two-tap channel is a simple model of that leakage; stronger taps smear transitions and shrink vertical opening.
What does jitter do?
Random sampling-time errors move the decision point away from the eye center, so you sample during transitions more often and the overlaid traces thicken horizontally.