Summary

This blog article derives the stereophonic amplitude-panning "Tangent Law", showing how left/right amplitude ratios map to perceived source angle. It explains the mathematical steps, assumptions, and practical implications for designing stereo panning controls and spatial-audio processing.

Key Takeaways

• Derive the tangent-law relationship linking amplitude ratio to perceived stereo angle
• Compute left/right gain values for a desired panned angle using the derived formulas
• Identify the assumptions and limitations (listener position, interaural cues, and loudness effects) that affect panning accuracy
• Implement and validate the panning law in a DSP workflow or MATLAB/Simulink prototype

Who Should Read This

Intermediate audio engineers, DSP practitioners, and researchers who design stereo panning, spatial-audio tools, or mixing controls and want a clear mathematical derivation and practical guidance.

TimelessIntermediate

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