Selection of dimensional normalization parameter in digital computation of the fractional Fourier Transform

In the digital computation of the fractional Fourier Transform, the dimensional normalization is needed. The initial frequency and chirp rate of a chirp signal are changed by the dimensional normalization parameter, and the position of the chirp signal's peak on the two-dimensional parameter (p, u) plane is also changed. This influences the detection of the multi-component chirp signals. In order to decrease the influence, a method is presented to choose the dimensional normalization parameter, based on the distance between two chirp signals' peaks. First, the coordinates of the chirp signal's peak is educed on the (p, u) plane. And the relationships between the dimensional normalization parameter and the distances between two chirp signals' peaks on p axis and on u axis are analyzed. It is discovered that the distances varies with the dimensional normalization parameter and they both have their own maximums. By changing signals' observation time and sampling frequency, selecting a reasonable dimensional normalization parameter can increase the distances between two signals' peaks. It can improve multi-component chirp signals' resolution ability and reduce the shading effect between strong signals and weak signals. The effectiveness of the method is verified by the computer simulations.