📊 Power Spectral Density Analysis — MATLAB

MATLAB implementations of Power Spectral Density (PSD) analysis, line coding schemes, pulse shaping techniques, and eye diagram generation for baseband digital communication systems.

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✨ Features

• 📊 PSD Analysis — Welch's method and Wiener-Khinchin theorem implementations
• 📡 Line Coding — Polar NRZ, Bipolar AMI, On-Off Keying (OOK) comparison
• 🔄 Pulse Shaping — Rectangular (RZ/NRZ), raised cosine, and half-sine pulses
• 👁️ Eye Diagrams — Visual assessment of inter-symbol interference (ISI)
• 📈 FFT Analysis — Spectral decomposition of multi-frequency signals

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📁 Project Structure

signal-processing-psd-matlab/
├── main/
│   ├── psd_line_coding.m          # PSD of Polar, AMI, and OOK line codes
│   ├── pam_pulse_shaping.m        # PAM2 waveforms with 4 pulse shapes
│   ├── psd_autocorrelation.m      # PSD via autocorrelation (Wiener-Khinchin)
│   └── fft_piecewise_signal.m     # FFT spectral analysis of composite signals
│
└── utils/
    ├── eyeplot.m                  # Eye diagram plotting utility
    ├── pnrz.m                     # Polar Non-Return-to-Zero pulse generator
    ├── prcos.m                    # Raised cosine pulse generator
    ├── prz.m                      # Polar Return-to-Zero pulse generator
    └── psine.m                    # Half-sine pulse generator

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🚀 Getting Started

Prerequisites

• MATLAB R2020a or later
• Signal Processing Toolbox

How to Run

1. Clone this repository:

   git clone https://github.com/q-ms8/signal-processing-psd-matlab.git

2. Open MATLAB and navigate to the project folder
3. Add the utils/ folder to your MATLAB path:

   >> addpath('utils')

4. Run any script from main/:

   >> run('main/psd_line_coding.m')

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📈 Main Scripts

Script	Description	Key Concepts
psd_line_coding.m	Compares PSD of three line coding schemes: Polar, Bipolar AMI, and OOK	pwelch(), line codes, spectral analysis
pam_pulse_shaping.m	Generates PAM2 waveforms with RZ, NRZ, half-sine, and raised cosine pulses	Pulse shaping, upsample(), conv()
psd_autocorrelation.m	Computes PSD via autocorrelation function and FFT (Wiener-Khinchin theorem)	xcorr(), fft(), fftshift()
fft_piecewise_signal.m	FFT analysis of a piecewise signal with 50, 100, and 150 Hz components	fft(), single/double-sided spectrum

🛠️ Utility Functions

Function	Signature	Description
eyeplot.m	eyeplot(signal, T)	Overlays symbol-period segments to create an eye diagram
pnrz.m	pnrz(T)	Generates a Polar NRZ rectangular pulse of width T
prz.m	prz(T)	Generates a Polar RZ pulse (width T/2, centered in T)
prcos.m	prcos(rolloff, T, rate)	Generates a raised cosine pulse with configurable rolloff
psine.m	psine(T)	Generates a half-sine pulse of width T

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🧮 Mathematical Background

Power Spectral Density

The PSD describes how power is distributed across frequency:

Welch's Method: Divide signal into overlapping segments, window each, compute periodogram, and average.

Wiener-Khinchin Theorem: PSD is the Fourier transform of the autocorrelation function:

S(f) = F{R(τ)} where R(τ) = E[x(t) · x(t+τ)]

Line Coding Schemes

Scheme	Binary 1	Binary 0	DC Component
Polar NRZ	+V	−V	None
Bipolar AMI	±V (alternating)	0	None
On-Off Keying	+V	0	Present

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📊 Sample Outputs

• 📉 PSD plots comparing spectral characteristics of different line codes
• 👁️ Eye diagrams showing ISI-free and ISI-affected signals
• 📈 Single-sided and double-sided FFT spectrum plots
• 🔄 Pulse shape waveforms (RZ, NRZ, raised cosine, half-sine)

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📝 License

This project is licensed under the MIT License — see the LICENSE file for details.