A fast hardware based track trigger is being developed in ATLAS for the High Luminosity upgrade of the Large Hadron Collider. The goal is to achieve trigger levels in the high pile-up conditions of the High Luminosity Large Hadron Collider that are similar or better than those achieved at low pile-up conditions by adding tracking information to the ATLAS hardware trigger. A method for fast pattern recognition using the Hough transform is investigated. In this method, detector hits are mapped onto a 2D parameter space with one parameter related to the transverse momentum and one to the initial track direction. The performance of the Hough transform is studied at different pile-up values. It is also compared, using full event simulation of events with average pile-up of 200, with a method based on matching detector hits to pattern banks of simulated tracks stored in a custom made Associative Memory ASICs. The pattern recognition is followed by a track fitting step which calculates the track parameters. The speed and precision of the track fitting depends on the quality of the hits selected by the pattern recognition step. The figures of merit of the pattern recognition are measured by the efficiency for finding hits from high transverse momentum tracks and the power of rejecting hits from low transverse momentum tracks and fake tracks.