Interactive Frequency Domain Analysis
Explore advanced spectral techniques applied to biological systems. This platform demonstrates key concepts from the comprehensive review on Frequency Domain Analysis in Systems Biology.
Learning Objectives
Master spectral decomposition, wavelet analysis, higher-order statistics, and their applications to biological time series, networks, and omics data.
📊 Power Spectral Density & Phase Coherence
The foundation of frequency domain analysis is the Power Spectral Density (PSD), which quantifies how power is distributed across different frequencies. Phase coherence measures the reliability of oscillatory components in stochastic biological systems.
Signal Generation
Analysis Parameters
Time Domain Signal
Power Spectral Density
Phase Coherence Analysis
🌊 Wavelet Analysis for Non-Stationary Signals
Unlike Fourier analysis which assumes stationarity, wavelet transforms can localize spectral features in both time and frequency domains, making them ideal for analyzing transient biological phenomena like damping rhythms or burst events.
Signal Parameters
Analysis Controls
Time Domain Signal
Time-Frequency Spectrogram
Wavelet Analysis Results
🔗 Higher-Order Spectral Analysis (HOSA)
Higher-Order Spectral Analysis goes beyond the Power Spectral Density to detect quadratic phase coupling (QPC) between frequencies. The bispectrum and bicoherence reveal nonlinear interactions that standard Fourier analysis cannot detect.
Coupled Signal Generation
Analysis Method
Time Domain Signals
Frequency Domain (PSD)
Bispectrum Magnitude
Bicoherence
HOSA Analysis Results
🕸️ Spectral Graph Theory in GRNs
Spectral Graph Theory analyzes gene regulatory networks using eigenvalue decomposition of adjacency and Laplacian matrices. This reveals network connectivity patterns, prioritizes critical interactions, and provides robust analysis against molecular noise.
Network Generation
Spectral Analysis
Network Visualization
Eigenvalue Spectrum
Adjacency Matrix
Network Metrics
🧬 Protein Folding Dynamics
Protein folding is a complex process where linear amino acid sequences self-organize into functional 3D structures. Spectral analysis reveals the dynamical landscape of folding pathways, energy barriers, and conformational transitions that govern protein function and misfolding diseases.
Folding Parameters
Energy Landscape
Folding Trajectory
Conformational Dynamics
Spectral Analysis
Folding Dynamics Metrics
⏰ Circadian Rhythm Analysis
Circadian rhythms are biological oscillations with periods of approximately 24 hours. This interactive tool demonstrates spectral analysis of circadian signals, including period detection, phase coherence, and damping rhythm analysis using concepts from specialized tools like Rhythmidia.
Circadian Signal Parameters
Analysis Method
Time Domain Signal
Periodogram Analysis
Phase Distribution
Rhythm Metrics
🧬 DNA Transcription Dynamics
DNA transcription involves the conversion of genetic information from DNA to RNA by RNA polymerase. Spectral analysis reveals the dynamical processes of initiation, elongation, pausing, and termination that regulate gene expression and cellular function.