In some cases a real signal may be known a priori to be always positive. If this positive signal is later band‐limited, the knowledge of its original positivity can be used to help in recovering the lost frequencies. Specifically, the frequency‐domain values for members of this special class of signals have the interesting property that they are related to each other via the self‐convolution of Hermitian functions. This relationship is the basis for some current deconvolution approaches and can be generalized for the case of a signal of arbitrary sign. A steepest descent formulation in the frequency domain can determine these Hermitian functions while maximizing the fit to the known in‐band data and to estimated dc values. This formulation allows for the explicit calculation of the step size and is also easily modified to include finite support or penalty/reward constraints. Simulated data tests indicate good bandwidth extension for this method, while actually sometimes improving the signal‐to‐noise ratio of the in‐band values.
