29:106/186 RADIO ASTRONOMY
Fourth Homework Set...February 17, 2000
Due: February 23, 2000
Note: In the following problems, try a crack at it using traditional analysis
first. If your brain begins to hurt, switch to numerical evaluation.
(1) A sine wave of frequency 
is modulated by a pulse,
What is the power spectrum of this signal?
(2) An instrument with a response function 
measures a signal
given by
What is the measured signal 
?
(3) If h(t) is a real function, what constraints does this place on the
properties of its Fourier transform H(f)?
(4) A signal in the time domain is given by 
.
What is its Fourier transform? What is the power spectrum? What is the autocorrelation
function?
(5) Use Fourier transforms to evaluate the second temporal derivitive 
of the function 
.