Improved FFT Algorithm with Hybrid Radix Decomposition and Memory Optimization for Embedded Audio Processing

In order to solve the contradiction between real-time spectrum analysis and resource limitation in embedded audio processing, this paper proposes an efficient FFT algorithm based on mixed cardinality decomposition and memory optimization. By introducing the 2^p×3^q×5^r prime-factor mixed base factorization framework, the number of complex multiplications of the traditional base 2 algorithm was reduced by 43% (taking N=360 as an example, the computation cost was reduced from 2592 to 984). Combined with the 32×32 cache chunking strategy and bit inversion precomputing technology, the L1 cache hit rate was increased to 92% (58% compared with the baseline). The Q15 fixed-point arithmetic hardware adaptation layer was developed to reduce the floating-point arithmetic call by 76%, and the quantization error was controlled within 0.3 dB. The verification results on the STM32F407 platform show that the processing time of the 512-point FFT is only 1.82 ms (32% faster than that of CMSIS-DSP), the memory occupation is 12.3 KB (45% shorter), and the PESQ score of speech enhancement is 3.21 (2.89, p<0.01). Experiments further demonstrate that the algorithm improves speech intelligibility (STI index) from 0.55 to 0.71 and power consumption as low as 83.7 mW in an 80 dB noise environment, which meets the real-time requirements of smart wearable devices (20 ms voice frames), providing a scalable spectrum analysis solution for low-power embedded systems.