On Fractional Fourier Transform Moments Based On Ambiguity Function

The fractional Fourier transform can be considered as a rotated standard Fourier transform ingeneral and its benefit in signal processing is growing to be known more. Noise removing is oneapplication that fractional Fourier transform can do well if the signal dilation is perfectly known. Inthis paper, we have computed the first and second order of moments of fractional Fouriertransform according to the ambiguity function exactly. In addition we have derived some relationsbetween time and spectral moments with those obtained in fractional domain. We will prove thatthe first moment in fractional Fourier transform can also be considered as a rotated the time andfrequency gravity in general. For more satisfaction, we choose five different types signals andobtain analytically their fractional Fourier transform and the first and second-order moments intime and frequency and fractional domains as well.