A computationally efficient power-of-two window for spectral analysis

Spectral analysis techniques such as the Fast Fourier Transform (FFT) commonly employ a windowing technique to minimise spectral leakage due to truncation of the time signal. Each data point is multiplied by the corresponding window value prior to computing the spectrum. An extreme case is seen with the moving-FFT, used to study time-varying spectra, where the spectrum of data from within a relatively narrow time window is repeatedly computed as the window is moved along the continuous time signal. A novel method of windowing the time signal using a `power-of-two´ curve is presented, where points of the window are represented as either a negative integer power of two, or as unity minus some negative integer power of two. Multiplication of data and window is accomplished simply by arithmetic binary shifts and subtraction, thus achieving a significant speed advantage. The power-of-two window is shown to offer comparable leakage reduction and spectral resolution properties to conventional windows such as the Hamming, Hanning and Parzen but with a greatly reduced computation time