3.2. Variable Streaming FFTs
If you select the fixed-point data representation, the FFT variation uses a radix 22 single delay feedback, which is fully pipelined. If you select the floating point representation, the FFT variation uses a mixed radix-4/2. For a length N transform, log4(N) stages are concatenated together. The radix 22 algorithm has the same multiplicative complexity of a fully pipelined radix-4 FFT, but the butterfly unit retains a radix-2 FFT. The radix-4/2 algorithm combines radix-4 and radix-2 FFTs to achieve the computational advantage of the radix-4 algorithm while supporting FFT computation with a wider range of transform lengths. The butterfly units use the DIF decomposition.
Fixed point representation allows for natural word growth through the pipeline. The maximum growth of each stage is 2 bits. After the complex multiplication the data is rounded down to the expanded data size using convergent rounding. The overall bit growth is less than or equal to log2(N)+1.
The floating point internal data representation is single-precision floating-point (32-bit, IEEE 754 representation). Floating-point operations provide more precise computation results but are costly in hardware resources. To reduce the amount of logic required for floating point operations, the variable streaming FFT uses fused floating point kernels. The reduction in logic occurs by fusing together several floating point operations and reducing the number of normalizations that need to occur.