High resolution images from reflected wave energy

A process and apparatus for producing signals for controlling a display to produce an image in an imaging system employing a plurality of transducers. First and second beam signals are produced in response to delayed channel signals associated with respective transducers, the delayed channel signals representing real and imaginary components of time domain signals associated with respective transducers suitably delayed to focus a receive beam pattern of the transducers at a beam angle, each of the first and second beam signals including separate real and imaginary component representations. The real and imaginary components of the first and second beam signals are combined to produce a composite beam signal, the composite beam signal including separate real and imaginary component representations. A trigonometric expansion is performed on normalized values of the real and imaginary component representations of the composite beam signal to produce a plurality of expanded values and illumination signals are produced in response to the expanded values, for illuminating pixels on the display.