Superposition principle on key markets

The superposition principle states that, for a linear system the superposition of stimuli yields a superposition of responses.

where x is some sort of stimulus, r is some sort of response and F(x)=r is the linear relationship.

In other words, in a linear system,

The net response at a given place and time caused by two or more independent stimuli is the sum of the responses which would have been caused by each stimulus individually.

Waves are usually described by variations in some parameter through space and time (for example, height in a water wave, pressure in a sound wave, or the electromagnetic field in a light wave). If the linear approach is true, the superposition principle says that the net variation in that parameter caused by two or more waves traversing the same space, is the sum of the variations of that parameter which would have been produced by the individual waves separately.

Maxwell's equations imply that the distributions of charges and currents are related to the electric and magnetic fields by a linear transformation. Thus, the superposition principle can be used to simplify the computation of fields which arise from given charge and current distribution and vice versa.

Interference is a consequence of the superposition principle. When two or more waves are superimposed, the net wave displacement is just the algebraic sum of the displacements of the individual waves. Since these displacements can be positive or negative, the net displacement can either be greater or less than the individual wave displacements. The former case is called constructive interference, while the latter is called destructive interference.

Beamforming digital processing takes advantage of interference to improve SNR signal. A transmitter beamformer controls the signal of an array of transmitters, in order to create a constructive and destructive interference pattern at the receiver. A receiver beamformer combine delayed signals from an array of sensors, in order to create a constructive signal.

Conventional beamformers use a fixed set of weightings and time-delays (or phasings) to combine the signals from the sensors in the array, primarily using only information about the location of the sensors in space and the wave directions of interest.

Adaptive beamforming techniques, generally combine this information with properties of the signals actually received by the array, typically to improve rejection of unwanted signals from other directions.

Sensor array signal processing have wide band of interest on remote sensing and image processing, the   areas of interest of Starlab, Environment, Energy, Health and Space. These key markets will have great impact in the future and the superposition principle maybe will be on the base of the solutions.