Summary

This article presents a practical, not-widely-known rule for allocating half-band filtering in multistage decimation and interpolation by integer powers of two. Readers will learn how to trade filter specs across stages to minimize overall filter order and implementation cost while meeting aliasing and passband requirements.

Key Takeaways

• Apply a stage-wise half-band allocation rule when decimating/interpolating by powers of two to minimize total filter order.
• Reduce implementation complexity by relaxing stopband specs on intermediate stages without compromising overall aliasing performance.
• Exploit half-band FIR properties (e.g., many zero-valued coefficients) and polyphase structure to lower arithmetic and memory costs.
• Allocate transition-band widths and passband ripple strategically across stages to meet end-to-end spectral requirements.
• Estimate computational savings and quantify trade-offs between filter order, aliasing suppression, and noise/quantization effects.

Who Should Read This

Intermediate-to-advanced DSP engineers and system designers working on multirate decimation/interpolation for audio, communications, or radar who need to reduce filter cost while preserving spectral fidelity.

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