Random Vector Transformations
Two theoretical applications using a white random vector are the simulation and whitening of another arbitrary random vector. To simulate an arbitrary random vector, we transform a white random vector with a carefully chosen matrix. We choose the transformation matrix so that the mean and covariance matrix of the transformed white random vector matches the mean and covariance matrix of the arbitrary random vector that we are simulating. To whiten an arbitrary random vector, we transform it by a different carefully chosen matrix so that the output random vector is a white random vector.
These two ideas are crucial in applications such as channel estimation and channel equalization in communications and audio. These concepts are also used in data compression.
Read more about this topic: White Noise
Famous quotes containing the word random:
“We should stop looking to law to provide the final answer.... Law cannot save us from ourselves.... We have to go out and try to accomplish our goals and resolve disagreements by doing what we think is right. That energy and resourcefulness, not millions of legal cubicles, is what was great about America. Let judgment and personal conviction be important again.”
—Philip K. Howard, U.S. lawyer. The Death of Common Sense: How Law Is Suffocating America, pp. 186-87, Random House (1994)