This thesis reports studies based on the concept of characterising a band-limited signal by the locations of its zeros In a ‘complex time' plane (whose real axis is the real variable t). The relations between the zeros of a signal and more conventional descriptors such as Nyquist samples, Fourier coefficients or spectral samples are investigated. Added noise or linear filtering changes the zeros of a signal in a complicated way. The problems which arise are discussed. Signals can be synthesised directly from a specified zero pattern. The properties of signals having a certain class of zero pattern (‘angle coded signals') are studied. A method is presented by which zero patterns can be produced which yield signals (suitable for radar use) having desired properties.