Discrete-Time Wireless Signal Intuition — CFO, Sampling & Phase Accumulation — Python Experiments
By Solo Ghost · Developer / Programmer
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Category: Code Snippets & Scripts
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A hands-on Python-based engineering package for building intuition around discrete-time wireless signals, Carrier Frequency Offset (CFO), sampling, phase accumulation, and complex-plane rotation. The product develops intuition step by step: Physical phenomenon → mental model → mathematical equation → discrete-time representation → Python implementation → experimental observation What you will learn • Why sampling creates a discrete-time representation • Why t=nT s matters • Why e jϕ represents complex-plane rotation • How CFO produces deterministic phase rotation • How phase accumulates sample by sample • How CFO affects a QPSK constellation • How packet length and sampling frequency affect CFO phase Six experiments 1A — Constant Symbol + CFO: CFO phase evolution. 1B — Random QPSK + CFO: CFO on changing QPSK data. 1C — CFO Isolation: Separates CFO rotation from transmitted data. 2 — CFO Sweep: CFO versus phase increment per sample. 3 — Packet Length Sweep: Accumulated phase versus packet length. 4 — Sampling-Frequency Sweep: Phase increment versus sampling frequency. What you receive • Complete Python source code • Six reproducible experiments • 11 result plots • Discrete-Time Wireless Signal Intuition technical guide • README and reproducibility instructions • Complete project structure Scope This is a discrete-time/CFO foundation, not a complete wireless synchronization receiver. It deliberately excludes OFDM subcarriers, cyclic prefix, ICI, timing offset, frequency-selective channels, AWGN, estimator noise, and complete synchronization algorithms. These belong to later receiver-design stages. Intended audience Wireless engineers, DSP engineers, students, researchers, and practitioners seeking an experiment-driven understanding of CFO and sampled complex signals. Requirements: Python 3.x, NumPy, and Matplotlib.