Skelly

04-04-2007, 12:12 AM

I have been looking at some past scholarship papers and had been scratching my head over this problem from quite a while. It was hinted that a similar question to this will be in the scholarship exam. Any help would be greatly appreciated as I am sitting for my papers in 2 days. The question is as follows:

High fidelity sound can recorded digitally by sampling a sound wave at the rate of 44,100 times a second. Thus a 10-second segment of sound can be represented by a vector in R441000. A sound technican at a jazz festival plans to record sound vectors with 2 microphones, 1 sound vector s from a microphone next to the saxophone player, and a second concurrent sound vector g from a microphone next to the guitar player. A linear combination of the two sound vectors will then be created by a "mixer" in a studio to produce the desired result.

Suppose that each microphone picks up all of the sound from its adjacent instrument, so the actual recorded vectors are u=s+0.06g for the saxophone, and v=g+0.12s for the guitar.

a) What linear combinations of u and v will recover the saxophone vector s?

b) What linear combinations of u and v will recover the guitar vector g?

c) What linear combination will produce an equal mix of s and g, that is 0.5(s+g)?

Thanks,

Jay.

High fidelity sound can recorded digitally by sampling a sound wave at the rate of 44,100 times a second. Thus a 10-second segment of sound can be represented by a vector in R441000. A sound technican at a jazz festival plans to record sound vectors with 2 microphones, 1 sound vector s from a microphone next to the saxophone player, and a second concurrent sound vector g from a microphone next to the guitar player. A linear combination of the two sound vectors will then be created by a "mixer" in a studio to produce the desired result.

Suppose that each microphone picks up all of the sound from its adjacent instrument, so the actual recorded vectors are u=s+0.06g for the saxophone, and v=g+0.12s for the guitar.

a) What linear combinations of u and v will recover the saxophone vector s?

b) What linear combinations of u and v will recover the guitar vector g?

c) What linear combination will produce an equal mix of s and g, that is 0.5(s+g)?

Thanks,

Jay.