In many engineering applications, including radar, sonar, communications and seismology, the direction of impinging signal wavefronts can be used to discriminate between competing sources. Often these source signals cover a wide bandwidth and conventional narrowband beamforming techniques are ineffective, since spatial resolution varies significantly across the band. In this thesis we consider the problem of beamforming for broadband signals, primarily when the spatial response remains constant as a function of frequency. This is called a frequency invariant beamformer (FIB).¶ Rather than applying the numerical technique of multi-parameter optimisation to solve for the beamformer parameters, we attempt to address the fundamental nature of the FIB problem. The general philosophy is to use a theoretical continuous sensor to derive relationships between a desired FI beampattern and the required signal processing structure. Beamforming using an array of discrete sensors can then be formulated as an approximation problem. This approach reveals a natural structure to the FIB which is otherwise buried in a numerical optimisation procedure.¶ Measured results from a microphone array are presented to verify that the simple FIB structure can be successfully implemented. We then consider imposing broadband pattern nulls in the FI beampattern, and show that (i) it is possible to impose an exact null which is present over all frequencies, and (ii) it is possible to calculate a priori how many constraints are required to achieve a null of a given depth in a FIB. We also show that the FIB can be applied to the problem of broadband direction of arrival (DOA) estimation and provides computational advantages over other broadband DOA estimators.¶ Through the theoretical continuous sensor approach, we show that the FIB theory can be generalised to the problem of designing a general broadband beamformer (GBB) which realizes a broadband angle-versus-frequency beampattern specification. Coupled with a technique for radial beampattern transformation, the GBB can be applied to a wide class of problems covering both nearfield beamforming (in which the shape of the impinging wavefront must be considered and farfield beamforming (which is simplified by the assumption of planar wavefronts) for a broadband beampattern specified over both angle and frequency.