<p>This paper proposes representing finite-energy signals observed within a given bandwidth as parameters of a probability distribution and employing the information-geometric framework to compute the Fisher–Rao distance between these signals, considered as distributions. The observations are described by their discrete Fourier transforms, which are modelled as complex Gaussian vectors with known diagonal covariance matrices and parametrised means. These parameters define a coordinate system on a statistical manifold. We investigate the possibility of deriving closed-form expressions for the Fisher–Rao distance. We employ established results from the Riemannian geometry of the multivariate normal model and extend the analysis to complex Gaussian variables representing the finite-energy signal observations. Expressions for the Christoffel symbols and the geodesic tensor equations in the Fisher metric are derived, leading to geodesic equations expressed as second-order differential equations. Although these equations depend on the parametric model, they combine the magnitude and phase of the signal and their gradients with respect to the parameters. Two cases are examined: (1) the general case for any finite-energy signal observed in a given bandwidth and (2) the observation of a finite-energy signal with a known magnitude spectrum and unknown phases and attenuation coefficient. The manifold of finite-energy signals corresponds to the manifold of the multivariate normal model with a known diagonal covariance matrix, while the set of finite-energy signals with a known magnitude spectrum constitutes a submanifold. Closed-form expressions for the Fisher–Rao distances are obtained for both cases. We show that the submanifold is not geodesic, because the Fisher–Rao distance measured on the submanifold exceeds that on the entire manifold.</p>