16-Point Reversible Integer Discrete Fourier Transform With 12 Control Bits

This correspondence discusses the reversible integer 16-point discrete Fourier transform (RiDFT) which uses integer operations with control bits. The decomposition of the RiDFT is based on the paired representation, when the Fourier transform is split recursively into a set of short transforms of orders 8, 4, 2, and 1. Control bits allow for inverting the integer approximations of multiplications by twiddle factors. The proposed 16-point RiDFT uses 16 operations of real multiplication and 62 additions. The integer approximation of the transform with eight control bits with additional two lifting schemes, which requires two more multiplications, is also considered.