10dig | Fp Cat Et

| Transform | Precision (digits) | Cycles/sample (FP) | Cycles/sample (10dig fixed) | |-----------|-------------------|--------------------|-------------------------------| | 256-FFT | 7.2 (float) | 142 | 38 | | 256-FFT | 10.1 (10dig fixed) | — | 41 | | DCT (128) | 9.8 (float) | 98 | 29 |

This post unpacks what these terms mean, why they matter for low-power and real-time systems, and how you can implement 10-digit efficient transforms without floating-point hardware. | Term | Meaning | |------|---------| | FP | Fixed-point arithmetic (integer scaling, no FPU) | | CAT | Category theory — composable, structure-preserving transforms | | ET | Efficient transforms (FFT, DCT, wavelet, etc.) | | 10dig | 10 significant decimal digits of precision (~33–34 bits) | fp cat et 10dig

— after each stage: Error ~ 1e-8 → 8 digits lost. | Transform | Precision (digits) | Cycles/sample (FP)