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i need to sketch y[n] where * denotes the convolution operator and delta is the unit impulse. I know how to sketch x[n-1] and delta[n-2] but i have problems with the convolution. In my script i only found this formula for convolution with delta pulses.

\begin{aligned} z[n] * \delta[n-n0] & = z[n-n0] \\ \end{aligned}

But it doesn't help me at all...

\begin{aligned} x[n] & = (\frac{1}{2})^n (u[n+1]-u[n-3]) \\ y[n] & = x[n-1] * \delta[n-2] \end{aligned}

Maybe someone can help me. ;-)
And is there an easy way to prove my sketches?
Wolfram Alpha doesn't work i think.

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1 Answer

up vote 2 down vote accepted

Write explicitly $X[m] = x[m-1]$ as a function of $n$ and put $m = n-2$.

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Well, i am a beginner in dsp. I do not know exactly what u mean. Shall i just sketch x[n-3] ? –  madmax Apr 14 '11 at 13:11
    
Sure, but I just described the logics which leads to this result. –  Ilya Apr 14 '11 at 13:17
    
That's all? Ok, i trust u. ;-) Till now i don't really know what i am doing ... –  madmax Apr 14 '11 at 13:26
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