An interactive Streamlit web application for performing Continuous Wavelet Transform (CWT) analysis and Fast Fourier Transform (FFT) on signal data, with a focus on Phonocardiogram (PCG) signal analysis.

• Upload Custom Data: Load 2-column .txt files (time and signal values)
• Generate Synthetic Signals: Create sine waves with customizable parameters:
  • Two independent sine wave components
  • Adjustable frequency, amplitude, and noise levels
  • Configurable sampling frequency and duration

• Signal Slicing: Select specific time ranges for focused analysis
• FFT-Based Bandpass Filtering: 20-330 Hz frequency range filtering
• Decimation: Automatic downsampling to ~2000 Hz if needed
• Smoothing: Moving average noise reduction

1. Time-Domain Analysis

   • Normalized signal visualization
   • Shannon Energy envelope computation with peak detection
   • Interactive plots with zoom capabilities
   • Configurable peak detection parameters:
     • Shannon peak threshold
     • Minimum peak distance

2. Shannon Energy Timing Analysis

   • Systole & Diastole Calculation: Automatic interval classification based on Shannon Energy peaks
   • Component Intervals Table: Displays S1-S2 and S2-S1 intervals in seconds and milliseconds
   • Heart Rate Estimation: Calculated from systole and diastole intervals
   • Peak Visualization: Black markers on detected energy peaks

3. Frequency-Domain Analysis (FFT)

   • Fast Fourier Transform using Radix-2 algorithm (implemented from scratch)
   • Frequency spectrum visualization
   • Magnitude analysis up to Nyquist frequency

4. Time-Frequency Analysis (CWT)

   • Continuous Wavelet Transform using Morlet wavelet
   • Fast CWT Mode: Vectorized computation (significantly faster)
   • Interactive scalogram visualization (contour plot)
   • 3D surface plot of CWT coefficients
   • Configurable CWT parameters:
     • Morlet ω₀ parameter
     • Scale parameters (start, step, count)
     • Number of time translations

• Automated Feature Detection: Identify heart sound components (S1, S2, M1, T1, A2, P2)
• Binary Thresholding: Adjustable amplitude threshold for region detection
• Center of Gravity (CoG): Weight-based calculation for time, frequency, and amplitude of each detected component
• Sub-segmentation: Split merged components using 1D time profile analysis
• Adaptive Labeling: Frequency-based discrimination (S1: <60 Hz, S2: >60 Hz)
• Manual Override: Force cycle type classification (S1 or S2)
• Component Intervals: Calculate time differences between consecutive PCG components
• Systole/Diastole Detection: Automatic S1-S2 and S2-S1 interval calculation
• Component Visualization: Labels and markers displayed on scalogram

• Python 3.7 or higher
• pip package manager

Install the required packages:

pip install streamlit numpy pandas scipy plotly

Or use the requirements file if available:

pip install -r requirements.txt

1. Navigate to the project directory:

cd CWT-From-Scratch

2. Launch the Streamlit app:

streamlit run cwt.py

3. The application will open in your default web browser (typically at http://localhost:8501)

1. Select "Upload File" in the sidebar
2. Upload a .txt file with two columns: time and signal values
3. The sampling frequency will be automatically calculated from the time data
4. Adjust CWT parameters as needed

1. Select "Generate Sine Wave" in the sidebar
2. Configure signal parameters:
   • Sampling frequency (Hz)
   • Duration (seconds)
   • Frequency and amplitude for two sine components
   • Noise level
3. The signal will be generated automatically

1. Adjust CWT parameters in the sidebar:

   • ω₀: Morlet wavelet parameter (default: 2π × 0.849)
   • Start Scale (a): Initial scale value
   • Scale Step (da): Increment for scale values
   • Number of Scales: Resolution in frequency dimension
   • Number of Time-Shifts: Resolution in time dimension
   • Use Fast CWT: Enable vectorized computation for faster processing

2. Optional: Signal Slicing

   • Enable signal slicing to analyze specific time ranges
   • Use the time range slider to select the region of interest

3. Optional: Preprocessing

   • Apply preprocessing for PCG signals:
     • FFT-based bandpass filter (20-330 Hz)
     • Decimation to ~2000 Hz
     • Moving average smoothing

4. Click "Compute CWT" to perform the analysis

5. View results:

   • CWT scalogram (contour plot)
   • Binary mask with threshold adjustment
   • Detected PCG components with time, frequency, and amplitude
   • Optional 3D surface plot
   • Scale-to-frequency and translation-to-time mappings

1. Adjust Shannon Energy parameters in the sidebar:

   • Shannon Peak Threshold: Minimum prominence for peak detection (0.0-1.0)
   • Min Peak Distance: Minimum time separation between peaks (0.05-0.5s)

2. View Shannon Energy results:

   • Energy envelope overlay on signal plot
   • Detected peaks marked with black crosses
   • Component Intervals table showing S1-S2 and S2-S1 durations
   • Average Systole interval (S1-S2)
   • Average Diastole interval (S2-S1)
   • Estimated heart rate in BPM

1. After computing CWT, adjust the CWT Amplitude Threshold slider
2. Optionally use Force Cycle Type to override automatic S1/S2 classification
3. Enable/disable Sub-segmentation to split merged components
4. View detection results:
   • Binary mask with labeled components
   • Detection Analysis showing frequency, energy, and duration for each group
   • PCG Components table with time, frequency, and weight
   • Component Intervals showing time between consecutive components
   • Systole (S1-S2) and Diastole (S2-S1) intervals
   • Estimated heart rate

The application expects a 2-column space or tab-delimited .txt file:

0.0000    0.1234
0.0010    0.2345
0.0020    0.3456
...

Column 1: Time (seconds)
Column 2: Signal amplitude

• Wavelet: Complex Morlet wavelet
• Method: Direct convolution in time domain (standard mode) or vectorized computation (fast mode)
• Normalization: Energy-preserving normalization
• Output: Magnitude of complex CWT coefficients
• Fast Mode: Vectorized time-domain computation using NumPy broadcasting

• Algorithm: Radix-2 Cooley-Tukey FFT
• Padding: Zero-padding to nearest power of 2
• Scaling: Normalized magnitude spectrum

• Formula: E(t) = -1/N × Σ(x²·log(x² + ε))
• Parameters: Frame length (default: 0.02s) and hop size (frame_len/2) based on sampling rate
• Output: Energy envelope with mean and standard deviation
• Peak Detection: Simple peak finder with configurable prominence and minimum distance

• Method: Adaptive threshold-based interval classification
• Threshold: (min_interval + max_interval) / 2
• Systole: Intervals ≤ threshold (typically S1-S2)
• Diastole: Intervals > threshold (typically S2-S1)
• Heart Rate: 60 / (avg_systole + avg_diastole)

• FFT-Based Bandpass Filter:
  • Frequency range: 20-330 Hz
  • Smooth transitions to avoid ringing (5 Hz transition width)
• Decimation: Downsample to target frequency (~2000 Hz)
• Smoothing: 5-point moving average

• Frequency-Based Discrimination:
  • S1 components: < 60 Hz (M1, T1)
  • S2 components: > 60 Hz (A2, P2)
• Adaptive Grouping: Time-based clustering with dynamic threshold
• Sub-segmentation: 1D time profile peak detection to split merged regions

• Caching: CWT results are cached using Streamlit's caching mechanism
• Progress Tracking: Real-time progress bar during CWT computation
• Interactive Plots: Plotly-based visualizations with zoom and pan
• Fast CWT: Vectorized computation significantly reduces processing time for large datasets
• Adaptive Parameters: Signal slicing and preprocessing reduce computational load

This tool is particularly useful for:

• Cardiac Signal Analysis: PCG (phonocardiogram) heart sound analysis with automated S1/S2 detection
• Clinical Diagnostics: Systole and diastole interval measurement for cardiac assessment
• Signal Processing Education: Understanding time-frequency analysis and wavelet transforms
• Research: Exploring wavelet transform parameters and heart sound characteristics
• Feature Extraction: Identifying signal components in time-frequency domain with weight-based CoG calculation

• CWT Computation: O(N × M × K) where:
  • N = number of scales
  • M = number of translations
  • K = signal length
• FFT Computation: O(N log N) where N is the padded signal length

• Large parameter combinations (high scale/translation counts) may result in long computation times
• Memory usage scales with the product of scales and translations
• CWT is computed in the time domain (not optimized with FFT-based convolution)

This project is open-source and available for educational and research purposes.

Created as part of signal processing and biomedical engineering research.

• Wavelet theory and Morlet wavelet implementation
• PCG signal analysis methodology
• Streamlit framework for interactive web applications