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 = …

Fundamental concepts for understanding and processing signals. Signal Types Continuous-Time vs Discrete-Time Continuous-Time Signal: $x(t)$, defined for all $t \in \mathbb{R}$ Discrete-Time Signal: $x[n]$, defined only at integer values $n \in \mathbb{Z}$ Analog vs Digital Analog: Continuous in both time and amplitude …

Fundamental concepts and mathematical tools for signal processing, including Fourier analysis, convolutions, and correlations.