Summary

This blog resolves a long-standing confusion about how to obtain and interpret the z-domain transfer function of the coupled-form 2nd-order IIR resonator. Readers will learn the mathematical derivation, how the coupled-form differs from the standard 2nd-order resonator, and the practical implications for implementation and stability.

Key Takeaways

• Derive the z-domain transfer function for the coupled-form 2nd-order IIR resonator step-by-step
• Interpret how coupled-form coefficients map to pole locations and resonator behavior
• Compare the coupled-form and standard 2nd-order resonators to identify implementation advantages and pitfalls
• Assess stability and coefficient-sensitivity issues relevant to fixed-point and real-world implementations

Who Should Read This

DSP engineers, researchers, and advanced students with some background in digital filter design who need a clear, practical explanation of coupled-form resonator transfer functions for audio, communications, or radar applications.

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