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).
Sorry about the confusion.. Thanks

For part(a) : using you will end up with one unknown constant. Choose that constant so that for all .

Why choose this solution? You can think of as a time-type variable, and choosing the output that is zero (eg: where nothing happens) until the input 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 , but that misses the point.

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).

Sorry about the confusion.. Thanks

For part(a) : using you will end up with one unknown constant. Choose that constant so that for all .

Why choose this solution? You can think of as a

time-type variable, and choosing the output that is zero (eg: where nothing happens) until the input 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 , but that misses the point.

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, .

For 3b: does the basic example still work if the denominator is ?

Will the answer be ?

Yes, exactly.