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<math>\Rightarrow \frac{w_{o}}{2\pi} = \frac{K}{N} \Rightarrow</math>Rational number | <math>\Rightarrow \frac{w_{o}}{2\pi} = \frac{K}{N} \Rightarrow</math>Rational number | ||
<math>\therefore \frac{w_{o}}{2\pi}</math> shold be a rational number | <math>\therefore \frac{w_{o}}{2\pi}</math> shold be a rational number | ||
| + | |||
| + | (b) Show that the system described by | ||
| + | <math>y[n] = x[n] + x[n+1] + x[n+2]</math> is a LTI system. | ||
| + | |||
| + | <math>ax_{1}[n]+bx_{2}[n] \rightarrow ax_{1}[n]+bx_{2}[n]+ax_{1}[n+1]+bx_{2}[n+1]+ax_{1}[n+2]+bx_{2}[n+2] </math> | ||
| + | <math>=</math> | ||
Revision as of 15:23, 30 June 2008
(a) Derive the condition for which the discrete time complex exponetial signal x[n] is periodic.
$ x[n] = e^{jw_{o}n} $ $ x[n] = x[n+N] = e^{jw_{o}(n+N)} = e^{jw_{o}n}e^{jw_{o}N} $ to be periodic $ e^{jw_{o}N} = 1 = e^{j2\pi k} $ $ \therefore w_{o}N = 2\pi k $ $ \Rightarrow \frac{w_{o}}{2\pi} = \frac{K}{N} \Rightarrow $Rational number $ \therefore \frac{w_{o}}{2\pi} $ shold be a rational number
(b) Show that the system described by
$ y[n] = x[n] + x[n+1] + x[n+2] $ is a LTI system.
$ ax_{1}[n]+bx_{2}[n] \rightarrow ax_{1}[n]+bx_{2}[n]+ax_{1}[n+1]+bx_{2}[n+1]+ax_{1}[n+2]+bx_{2}[n+2] $ $ = $
