Lossy compression is a form of compression that slightly degrades a signal in ways that are ideally not detectable to the human ear. This is opposite to lossless compression, in which the sample is not degraded at all. While lossless compression may seem like the best option, lossy compression, which is used in most audio and video, reduces transmission time and results in much smaller file sizes. However, this compression can affect quality if it goes too far. The more compression there is on a waveform, the more degradation there is, and once a file is lossy compressed, this process is not reversible. This project will observe the degradation of an audio signal after the application of Singular Value Decomposition compression, a lossy compression that eliminates singular values from a signal’s matrix.

This project examines the dynamics and design of control systems for a rocket in propulsive ascent and descent using a simplified model with motion constrained to a vertical plane. The governing differential equations are analyzed. They are then linearized, after which transfer functions are derived relating controllable input variables to controlled output variables. The effect of changes in various parameters as well as other aspects of the system are examined. Methods for controller design based on the derived transfer functions are discussed. This will include the discussion of control of the final descent and landing of the rocket. Lastly, there is a brief discussion about both the successes and limitations of the model analyzed.