Perfectly Flat-Top and Equiripple Flat-Top Cosine Windows

Abstract

This paper describes a new method for designing flat-top cosine time windows. New perfectly flat-top windows, i.e., having monotonically decaying main lobe, and new equiripple flat-top windows, i.e., with some minor ripples of equal amplitude in the main lobe, are proposed. Perfect flatness (monotonic main lobe) is obtained by zeroing frequency derivatives of the window’s spectrum at the origin. Perfect flatness is a new quality in flat-top windows, as all known flat-top windows have some ripples in the main lobe. New equiripple flat-top windows are designed based on the conditions imposed on the window’s frequency response. The new flat-top windows are compared with the existing ones through the figures of merit, amplitude estimation example, and noise propagation analysis, showing superior performance of the former. The new windows are an excellent choice for popular digital waveform (spectrum) analyzers, as sine-waves amplitudes can be accurately estimated directly from the discrete Fourier transform spectrum without any further postprocessing.