Selection of dimensional normalization parameters in fractional Fourier transform

Dimensional normalization is required in the digital computation of the fractional Fourier transform, but how to select a suitable dimensional normalization parameter is not studied yet. For this reason, the influence of the dimensional normalization on the initial frequency, the chirp rate and the peak's position on the (p, u) plane is analyzed. And the relationship between the dimensional normalization parameter and the distance between two chirp signals' peaks at the p axis and the u axis is deduced. It is discovered that the distance between two peaks varies with the dimensional normalization parameter and it has maximums. A method is presented to choose the dimensional normalization parameter. By changing signals' observation time and sampling frequency, a suitable dimensional normalization parameter is selected to increase the distance between two signals' peaks and reduce the mutual influence among multi-component chirp signals. The effectiveness of this method is verified by the simulation results.