Matrix ultrasound transducers for medical diagnostic purposes are commercially available for a decade. A typical matrix transducer contains 1000 + elements, with a trend towards more and smaller elements. This number renders direct connection of each individual element to an ultrasound machine impractical. Consequently, it is cumbersome to employ traditional focusing and beamforming approaches that are based on transmit and receive signals having an individual time delay for each element. To reduce cable count during receive, one approach is to apply sub-arrays that locally combine the element signals using programmable delay-and-sum hardware, resulting in reduction by a factor 10. In transmit, achieving cable count reduction while keeping focusing and steering capabilities turns problematic once it becomes impossible to locally equip each element with its own high voltage pulser. To overcome this bottleneck for decreasing element size, here we present a Fresnel-inspired hardware and beam forming approach that is based on transmit pulses consisting of several periods of an oscillating waveform. These will be derived from one oscillating high voltage signal by using local switching and timing hardware. To demonstrate the feasibilities of our approach, we will show beam profiles and images for a miniature matrix transducer that we are currently developing.@en