Designing Digital Filters: IIR and FIR Filter Foundations

Digital signal processing relies heavily on the ability to shape signals and remove unwanted noise. Understanding how to design stable, efficient Infinite Impulse Response (IIR) and Finite Impulse Response (FIR) filters is a crucial skill for any aspiring engineer or developer working with audio, sensor data, or communications. This written course guides you through the core mathematical concepts and practical design workflows of digital filters. You will transition from understanding basic signal theory to confidently selecting, designing, and analyzing both filter types for real-world applications. What you'll learn: Understand the fundamental differences, advantages, and trade-offs between IIR and FIR filters; Analyze filter characteristics using transfer functions, poles, zeros, and frequency response; Design FIR filters using windowing methods and frequency sampling techniques; Calculate IIR filter coefficients using bilinear transformation and impulse invariance; Apply modern Python-based computational libraries to automate filter design and simulation; Evaluate finite word-length effects, quantization noise, and filter stability in practical implementations. The course begins with essential terminology, signal representation, and the mathematical foundations of Z-transforms. You will then progress step-by-step through manual numerical calculations and modern algorithmic design approaches for both filter types. This course is designed for engineering students, software developers, and technology enthusiasts who want a solid, beginner-friendly introduction to digital filter design without needing advanced prior signal processing experience. Start reading today to build a strong foundation in digital signal processing and filter design.