Optical Sound Track

[xcthulhu]

Here is a little problem I stumbled across from Bracewell's The Fourier Transform and Its Applications.

 

I don't know the answer, so if anyone can help me out I would be grateful (this is just for self-study).

 

The optical sound track on old motion-picture film has a breadth b, and it is scanned by a slit of width w. With appropriate normalization, we may say that the scanning introduces convolution by a rectangle function of unit height and width w. In a certain movie theatre the projectionist clumsily dropped the whole projector on the floor and after the slit was always inclined at a small angle [math]\epsilon[/math] to the striations on the sound track instead of making an angle of zero with them.

 

(a) What function now describes the convolution that takes place?

(b) Describe qualitatively the effect on the sound reproduction.

 

I have a theory what the answer is like but I'm not altogether sure.