MATLAB and the discrete Fourier transform

I have previous experience with MATLAB, but the problem that I face is some problems in applying a problem in (DSP: Digital signal processing) which is not my study field, but I must finish those problems in days to complete my project.

All I want is help with a method and steps of solving this problem in MATLAB and then I can write the code with myself.

The problem is about the signal

x(t) = exp(-a*t);

1) What's the discrete Fourier transform of the sampled signal with sample rate fs?

2) If a=1 and fs=1开发者_如何学编程, plot the amplitude spectrum of the sampled signal

3) Fix the sampling frequency at fs = 1 (Hz) [what does it mean?] and plot the magnitude of the Fourier Transform of the sampled signal at various values of a

The DFT is used to bring a discrete (i.e. sampled) signal from the time domain to the frequency domain. It's an extension of the Fourier transform. It is used when you are interested in the frequency content of your data. The DFT { x(t) } yields an expression X(F); sample rate (fs) is a term in its expression... This will be your answer to part 1.

You can find tables for the example expression exp(-a*t), but you really should study the electrical engineering (and perhaps math) background for this concept. If you have ability in MATLAB AND you get the basics of the Fourier transform/discrete Fourier transform, then these problems will be straightforward.

MATLAB actually has a tutorial for this subject matter: http://www.mathworks.com/help/techdoc/math/brenr5t-1.html. Good luck...