Interactive Eye Diagram & ISI Simulator: Visualizing Signal Integrity

Interactive Eye Diagram & Noise Margin

Filter Roll-off (α) α = 0.4

Noise Level

Bitstream (TX)

Stage 1: Components (Click Legend to Hide/Show)

Stage 2: Composite Signal

Stage 3: The Eye (Annotated Analysis)

Simulation Workflow

1. Pulse Mapping: Each bit a[k] is mapped to a pulse shape p(t). We use the Raised Cosine filter, which is the standard for bandwidth-limited communication. Clicking the legend above removes a specific bit's contribution to show how it affects the neighbors.

2. Linear Superposition: The total signal x(t) is the sum of all individual pulses shifted by the symbol period T. This "Combined Waveform" shows how pulses "bleed" into each other, creating Intersymbol Interference (ISI).

3. Signal Folding (The Eye): We "fold" the long composite waveform into segments of 2-symbol durations and stack them. The Yellow Sampling Stick is placed at the exact center of the symbol where the "Eye" is widest.

Mathematical Framework

The core of this simulation is the Nyquist First Criterion. The mathematical expression for the combined signal at any time t is:

r(t) = Σ a[k] p(t - kT) + n(t)

Where a[k] are the bits, p(t) is the Raised Cosine pulse, and n(t) is the Additive White Gaussian Noise (AWGN). The pulse p(t) is defined by the Roll-off factor α:

p(t) = sinc(t/T) * [ cos(παt/T) / (1 - (2αt/T)^2) ]

When the α is small, the pulse tails are longer, causing the "Eye" to close horizontally and vertically, making the system more sensitive to timing jitter and noise.