Fractional Fourier Transform: A Tool for Signal Analysis In Time-Frequency Plane

--The fractional fourier transform(FRFT) which is a generalisation of classical fourier transform, was introduced number of years ago in the mathematics literature but appears to have remained largely unknown to a signal processing community to which it may, however, be a potentially useful. The fractional fourier transform depends on a parameter ‘α’ and can be interpreted as a rotation by an angle ‘α’ in the time frequency plane. An FRFT with α=π/2 corresponds to the classical fourier transform and an FRFT with α=0 corresponds to the identity operator. On the other hand angles of successively performed FRFT’s simply add up as do the angles of successive rotations. The FRFT’s is an orthogonal transform with chirp as a basis signal. Thus a chirp signal becomes an impulse in certain ‘α’ domain. In this paper we briefly introduce FRFT and a few of its properties and then discussion and interpretation of fractional fourier transform in time frequency plane is given with short-time fourier transform and spectrogram.