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<math>X[n] = 6\cos(3 \pi n + \pi)\,</math> | <math>X[n] = 6\cos(3 \pi n + \pi)\,</math> | ||
| − | <math>x[n] = \sum^{ | + | <math>x[n] = \sum^{2}_{k = -1} a_k e^{jk\frac{\pi}{2} n}\,</math> |
Revision as of 07:57, 26 September 2008
Obtain the input impulse response h[n] and the system function H(z) of your system
Defining a DT LTI:
$ y[n] = x[n+5] + x[n-3]\, $
So, we have the unit impulse response:
$ h[n] = \delta[n-5] + \delta[n-3]\, $
Then we find the frequency response:
$ F(z) = \sum^{\infty}_{m=-\infty} h[m+5]e^{jm\omega} + h[m-3]e^{jm\omega}\, $
find m value to make the value inside the bracket zero
m = -5 for the first set and 3 for the second set
$ F(z) = e^{-5j\omega} + e^{3j\omega} \, $
Compute the response of your system to the signal you defined in Question 2 using H(z) and the Fourier series coefficients of your signal
Signal defined in Question 1:
$ X[n] = 6\cos(3 \pi n + \pi)\, $
$ x[n] = \sum^{2}_{k = -1} a_k e^{jk\frac{\pi}{2} n}\, $
