Time-Bandwidth Product Online Simulator

1. Simulator: Data Pulse (Raised Cosine)

This mimics how a single bit of data is shaped in modern wireless communication.

Roll-off Factor (β) 0.5

(Adjusts how "sharp" the filter is)

Filter Span (Time) 6

(How long the pulse lasts)

Calculated TBP: 1.25 Good Efficiency

2. Simulator: Gaussian Pulse (The Perfect Balance)

The Gaussian pulse is special because it achieves the minimum possible TBP. It is the "smoothest" possible signal.

Pulse Width (Standard Deviation) 1.0

(Widening in time automatically narrows frequency)

Calculated TBP: 0.44 Fundamental Minimum

3. The Math Behind the Simulators

The Time-Bandwidth Product (TBP) is like a "Space-Time" budget for signals. No matter how you design a signal, you cannot make it infinitely small in both time and frequency at once.

• The Formula: TBP = Δt × Δf
• The Limit: For any signal, TBP ≥ 0.5 (approx). You can never go below this limit. This is the Heisenberg Uncertainty Principle applied to signals.
• The Trade-off:
  • If TBP ≈ 0.5 to 1.5: High Spectral Efficiency. Used in 5G, Wi-Fi, and Fiber Optics.
  • If TBP > 10: Spread Spectrum. Used in GPS and Radar to resist interference.