Approximate Fourier transform using square waves
R.D. Hughes, Mal L. Heron · IEE Proceedings A Physical Science Measurement and Instrumentation Management and Education Reviews · 1989
The technique of spectral analysis, by truncated approximations to the sine and cosine functions, is evaluated using a three-level approximation (−1, 0, +1), where the −1 and +1 sections are of equal length, and the length of the zero level is variable. An optimum ratio is found where the zero levels together cover 120° of the cycle length, to give the least amount of ringing, or leakage. The transform that converts the square-wave spectral estimates to the Fourier coefficients is evaluated. In applications where spectral estimates are required only for limited frequency bands, the technique is flexible and efficient. This analysis is also well suited to irregularly spaced samples, and for direct application to analogue signals.