Advanced DSP

Homework: Least Squares Matrix Inversion

Problem 1. There are six actors on stage – Andy, Bob, Charlie, Dan, Eliza and Ganpat – standing in a straight line. I have four spotlights, directly over the heads of Bob, Charlie, Dan and Eliza. Each spot transfers 20% of its light to the actor standing below, but there is 10% light seeping to each of the two nearest neighbors. (Leakage to further actors is minimal.)

(a) The director claims she wants flat lighting – each actor lighted with exactly 1 unit of light. How well can I meet her requirements?

(b) The director claims she wants flat lightling, but does not tell me exactly how many units of light she wants on each actor. What can you tell me about my solution?

Problem 2. There are three actors on stage, and two spotlights. The transfer matrix is

Prove that, as long as the director makes “reasonable” demands, we can definitely satisfy them “to some extent”.