|This thesis presents the process of designing, building, and testing a system that will be referred to herein as the Digital Guitar Amplifier. The Digital Guitar Amplifier is a real time digital audio signal processing unit that implements a signal processing algorithm that emulates the sound of a Fender Blues Jr. The Digital Guitar Amplifier fits within a reasonable footprint for a guitar effects pedal. The digital signal processor has CD level audio quality. The signal processing algorithm attempts to maintain the legacy of the vacuum tube within the math and processing of the algorithm by physically modelling the vacuum tube circuit. A mathematical comparison and human hearing survey is presented, which demonstrates that the sound of the Digital Guitar Amplifier compares favorably to the sound of a real Fender Blues Jr. amplifier. The algorithm that is developed can be extended to emulate any tube amplifier.