Filter Types Type Passband Stopband Transition Butterworth Flat Monotonic Moderate Chebyshev I Ripple Monotonic Sharp Chebyshev II Flat Ripple Sharp Elliptic Ripple Ripple Sharpest Design Workflow Specify requirements: Passband, stopband, ripple, attenuation Choose filter type: FIR vs IIR, Butterworth vs Chebyshev, …

Practical guides and mathematical principles behind digital filters, including Kalman, FIR, and IIR filters.

Finite Impulse Response filters - always stable, linear phase possible. Definition $$ y[n] = \sum_{k=0}^{M-1} b_k x[n-k] $$ Design Methods Window Method 1from scipy import signal 2import numpy as np 3 4# Design lowpass FIR filter 5numtaps = 51 # Filter order + 1 6cutoff = 0.3 # Normalized frequency (0 to 1) 7 8# Using …

Infinite Impulse Response filters - efficient but can be unstable. Definition $$ y[n] = \sum_{k=0}^{M} b_k x[n-k] - \sum_{k=1}^{N} a_k y[n-k] $$ Design Methods Butterworth (Maximally Flat) 1from scipy import signal 2 3# Design 4th-order Butterworth lowpass 4order = 4 5cutoff = 0.3 # Normalized frequency 6b, a = …

Blur & Sharpen Blur 1# Gaussian blur 2convert input.jpg -blur 0x8 output.jpg 3 4# Motion blur 5convert input.jpg -motion-blur 0x20+45 output.jpg 6 7# Radial blur 8convert input.jpg -radial-blur 10 output.jpg Sharpen 1# Sharpen 2convert input.jpg -sharpen 0x1 output.jpg 3 4# Unsharp mask (best for photos) 5convert …

Visual guide to the Kalman Filter - optimal recursive estimator for linear systems with Gaussian noise. Intuition The Kalman Filter combines two sources of information: Prediction from a model (physics/dynamics) Measurement from sensors (noisy observations) It finds the optimal balance between trusting the model vs …

Comprehensive guide to the Madgwick filter - an efficient gradient descent algorithm for IMU orientation estimation. Overview The Madgwick filter is an orientation estimation algorithm that fuses: Gyroscope (angular velocity) Accelerometer (gravity direction) Magnetometer (magnetic north) - optional Key Innovation: …

Comprehensive guide to the Mahony filter - a complementary filter with PI feedback for IMU orientation estimation. Overview The Mahony filter is an orientation estimation algorithm that uses a complementary filter approach with PI (Proportional-Integral) feedback to fuse: Gyroscope (angular velocity) Accelerometer …

Non-linear filter excellent for removing salt-and-pepper noise while preserving edges. Definition Replace each sample with the median of its neighborhood: $$ y[n] = \text{median}{x[n-k], \ldots, x[n], \ldots, x[n+k]} $$ Implementation 1from scipy import signal, ndimage 2import numpy as np 3 4# 1D median filter …

Comprehensive guide to sensor fusion using Kalman filters for combining data from multiple sensors. What is Sensor Fusion? Sensor Fusion: Combining data from multiple sensors to produce more accurate, reliable, and complete information than any single sensor alone. Why Fuse Sensors? Individual Sensor Limitations Sensor …