Summary

This blog presents the single-pole low-pass filter (one-pole IIR), deriving the discrete coefficient from an analog time constant and sampling rate, and explaining its time- and frequency-domain behavior. It shows efficient implementations, discusses numerical and initialization issues, and gives practical usage examples for audio and real-time DSP.

Key Takeaways

• Compute the filter coefficient (alpha) from cutoff frequency or time constant and sampling rate to match analog behavior.
• Implement the single-pole IIR efficiently in code (floating- and fixed-point) for low-latency real-time use.
• Analyze the filter's frequency response and time-domain step response to choose appropriate cutoff and time-constant tradeoffs.
• Identify numerical issues (initial conditions, stability, quantization) and apply pragmatic fixes for embedded and audio systems.

Who Should Read This

Intermediate DSP engineers, embedded audio or real-time systems developers, and signal-processing hobbyists who want a concise, practical reference for implementing and tuning a single-pole low-pass filter.

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