# Homework #9

## 6 thoughts on “Homework #9”

1. Hi! for question 5, it says” choose the solution with y[n]=0 for n<0, does it mean we compute y[n] for n<0 and set it equal to 0? What's the significance of this? And also, I got the solution for all y0 for part (a). So shouldn’t I just obtain the solution for part (b) using the same method, why would I need the impulse response from part (a).

• For part(a) : using $x[n]=\delta[n]$ you will end up with one unknown constant. Choose that constant so that $y[n]=0$ for all $n<0$.

Why choose this solution? You can think of $n$ as a time-type variable, and choosing the output $y[n]$ that is zero (eg: where nothing happens) until the input $x[n]$ is nonzero.

For part(b) : Impulse responses are used the same way every time, whether its continuous variable or discrete.
“Output = Impulse Response Convolved with Input”

You can answer part(b) by plugging in $x[n]=u[n]$, but that misses the point.

2. For question 3c, is (1^n) / 2 and (1^n) / 3 meant to be (1/2)^n and (1/3)^n respectively?

• That’s correct, $\frac{1}{2}^n = \left(\frac{1}{2}\right)^n$.

3. For 3b: does the basic example $a^nu[n] \rightarrow dtft \rightarrow \frac{1}{1-ae^{-iw}}$ still work if the denominator is $1+ae^{-iw}$ ?

Will the answer be $(-a)^nu[n]$?