Data Window With Tunable Side Lobe Ripple Decay

The Fourier transform of the proposed data window is given by the inverse of the product of two Gamma functions. Main lobe bandwidth and side lobe ripple decay can be controlled by a single continuous parameter alpha. The side lobe ripple decay is -20(2alpha - 1) dB/decade. It is proved that the inverse Fourier transform is a time-limited function. For alpha being an integer multiple of 1/2, the window parameters can be directly derived from Pascal´s triangle. For alpha = 2, the Hann window is obtained as a special case.