6. We have a signal x(n) = xa(t)]t=nTi where T1 7 msec, and we wish to convert x(n) to y(m) such that %3D y(m) t=mT2 with T2 = 5 msec. Develop a system to do this, being sure to specify the frequency re- sponse of any filters that are used (ideal responses are okay). Are there any restrictions on xa(t) that should be imposed so that this is possible?

Let Ap be the difference between the phase shift a Helium-Neon laser beam expe- riences on traversing a given length of vacuum and on traversing the same length of plasma. What is Ad when the laser beam passes through 10 cm of plasma having a density of n = 102? m?? How could this be used as a density diagnostic? The wavelength of the He-Ne laser radiation is 632.8 nm

5. Assume an MRI scanner imaging 'H with the following specifications: Bo = 3.0 T. Assume that with the Z-gradient on, the magnetic field strength is B0 at location Z = Zc: a. With a bandwidth of 1500 Hz, what is the gradient strength (G2) that would allow us to image a slice with 0.75 mm thickness? b. Using the gradient calculated in (a), we need to acquire an MR slice with the same slice width and positioned at 2.5 cm above the Z. position (Z = Z. +2.5 cm). What is the required RF excitation pulse center frequency (in MHz) for the slice selection pulse?

A spherical power light source of (7.566x10^1) watts is (6.1000x10^-1) metres from a photodiode detector of area (4.70x10^-1) cm². Find the power at the detector, in watts, to 3 sf. Hint find the intensity of the wave at the detector first.