Bit-precision and performance analysis of dynamic kernel function fast fourier transform

The proposed dynamic kernel function uses an efficient fixed-point numerical representation of the twiddle factor (i.e., complex roots of unity) and replaces the cumbersome multipliers in FFT with simple shift-and-add operations to enhance the data throughput rate for high-speed wideband signal detection. Numerical representation in hardware plays a role in determining the dynamic range and bit precision of FFT processors. The proposed variable truncation scheme dynamically scales the computation data and maximizes the use of fixed-input and inter-stage wordlength in a fixed-point FFT. The dynamic data scaling algorithm enhances the dynamic range of fixed-point fixed-precision FFT designs and emulates the precision benefits of floating-point representation without complicated design additions. The development of dynamic kernel function FFT performance models using different variations of inter-stage bit precision shows a relative trade-off between precision bits to FFT SFDR.