Signal processing system for performing a fast fourier transform with adaptive bit shifting, and methods for adaptive bit shifting

A signal processing system for performing a Fast Fourier Transformation (FFT), the system comprising:

• a first stage of the FFT which has a first radix kernel arranged to receive a first input comprising signed binary integers, the signed binary integers of the first input each representing a component of a complex number associated with a time domain signal and having a bit width;
• apply a fixed left shift to the signed binary integers of the first input;
• performing a first radix kernel operation on the shifted first input at a bit resolution higher than the bit width;
• apply a fixed right shift to signed binary integers of an output of a butterfly of the first radix kernel operation which is mapped to the bit width to provide a first output of the first stage of the FFT;
• and determine a leading bit count of signed binary integers in the first output;
• a second stage of the FFT which has a second radix kernel arranged to receive the first output which is a second input to the second radix kernel;
• apply an adaptive left shift to signed binary integers of the second input based on the leading bit count;
• perform a second radix kernel operation on the shifted second input at the bit resolution higher than the bit width;
• and apply an adaptive right shift based on the leading bit count to signed binary integers of an output of a butterfly of the second radix kernel operation which is mapped to the bit width to provide a second output of the second stage of the FFT;
• wherein the adaptive left shift and adaptive right shift determines a resolution of the FFT.