Simplifying Single-Bin Discrete Fourier Transform Computations [Tips & Tricks]

A digital signal processing (DSP) architecture is presented to compute single bins of the discrete Fourier transform (DFT) with low complexity. This architecture consists of a cascade of simple accumulators working at the input sampling rate and a polyphase finite impulse response (FIR) filter with complex coefficients working at a lower rate. The advantage of this structure is that, for several cases, it is possible to have a system with only one accumulator operating in the high-rate section and a low-order FIR filter working in the low-rate section. However, this depends on the index of the frequency bin to be computed (k) and the number of DFT points (N). Advantages and limitations of this approach are presented, and the implementation scheme is elaborated.