Summary

This paper derives a closed-form formula that directly generates digital IIR filter coefficients from an analog prototype using the bilinear transformation, removing the need for manual algebraic manipulation. It demonstrates the method, addresses frequency prewarping and implementation considerations, and highlights suitability for embedded real-time systems that must produce coefficients dynamically for difference-equation implementations.

Key Takeaways

• Apply a single closed-form formula to compute digital IIR coefficients directly from an analog prototype using the bilinear transform.
• Avoid manual algebraic re-derivation of analog prototypes by feeding specifications into the formula and obtaining coefficients ready for difference equations.
• Incorporate frequency prewarping and pole-zero mapping guidance to preserve frequency response when converting from s-domain to z-domain.
• Implement the method in embedded or real-time DSP environments to dynamically generate coefficients for on-the-fly filter creation.
• Account for practical issues such as coefficient scaling and fixed-point quantization for stable runtime implementations.

Who Should Read This

DSP engineers and embedded systems developers with experience in filter design who need a practical, implementable method to convert analog prototypes to digital IIR coefficients for real-time applications.

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