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1D Signal Filtering Examples

This directory contains interactive demonstrations of various 1D filtering techniques commonly used in signal processing.

mean_filter.py

Moving Average Filter Demonstration

This script demonstrates how a moving average filter (box filter) works on a 1D signal.

Explanation: - Signal Creation: Generates a step signal with random Gaussian noise. - Filter Implementation: Uses a uniform kernel (all coefficients equal) normalized to sum to 1. - Visualization: Shows the filtering process step by step with animation: - Top plot: Shows the noisy signal with the sliding kernel/window. - Bottom plot: Shows the filtered output being built as the kernel moves through the signal. - How it Works: As the kernel slides across the input signal, each output point is calculated as the average of signal values within the window. - Effect: Moving average smooths the signal by reducing high-frequency noise, but also blurs edges.

Mathematical Process: The output at each position is the weighted sum of neighboring input values, with all weights equal to 1/window_size.

gaussian_filter.py

Gaussian Filter Demonstration

This script demonstrates how a Gaussian filter works on a 1D signal.

Explanation: - Signal Creation: Same step signal with noise as in the mean filter. - Filter Implementation: Uses a Gaussian kernel where weights follow a Gaussian (normal) distribution. - Visualization: Similar animation to the mean filter: - Top plot: Shows the noisy signal with the bell-shaped Gaussian kernel sliding across. - Bottom plot: Shows the filtered output. - How it Works: Similar to moving average, but input values closer to the center are weighted more heavily. - Effect: Smooths noise while better preserving edges compared to the moving average filter.

Mathematical Process: The Gaussian filter applies weights according to a Gaussian distribution, giving more importance to pixels near the center of the kernel.

edge_detection.py

Edge Detection Filter Demonstration

This script demonstrates how edge detection works using a simple edge detection kernel.

Explanation: - Signal Creation: Same step signal with noise as previous examples. - Filter Implementation: Uses a kernel with negative values on one side and positive values on the other side. - Visualization: - Top plot: Shows the noisy signal with the bipolar edge kernel sliding across. - Bottom plot: Shows the edge detection output. - How it Works: The kernel responds strongly at points where the signal changes rapidly (edges). - Positive peaks: Rising edges - Negative peaks: Falling edges - Near-zero values: Flat regions - Effect: Highlights areas of rapid change in the signal.

Mathematical Process: The edge detection works by calculating the difference between signal regions on either side of the current position, emphasizing discontinuities.

Key Differences Between Filters

  1. Moving Average Filter: Simple averaging with equal weights; good noise reduction but blurs edges.
  2. Gaussian Filter: Weighted averaging with bell curve distribution; better edge preservation than box filter.
  3. Edge Detection: Highlights changes in the signal; amplifies edges rather than smoothing them.

All three examples use the convolution operation, which is fundamental to signal and image processing.