Estimation of phase for noisy linear phase signals

It is well-known that a discrete-time symmetric signal has a linear-phase Fourier transform. This paper describes a procedure for estimating the parameters associated with a linear-phase signal from noisy measurements. When the data being modeled is composed of a linear-phase signal corrupted by additive Gaussian noise, the approach taken results in maximum-likelihood estimates of the linear-phase parameters. The Fisher information matrix determining the achievable accuracy for the estimates is derived. The proposed estimation procedure is applied to the image processing problem of determining the inclination of the axis of symmetry of a reflection-symmetric object. The effectiveness of the procedure is tested on both synthetic and real images