Homework #4

[Julius Smith]

Hi Hiroko,

At 10:04 PM 10/20/2002 -0700, Hiroko Shiraiwa wrote:
>Hi Julius,
>
>For me, the definition of x_k[n] seems really funny. You said,
>x_k[n] = e^j \omega n is just in the special case, T = 1.
>
>But if you define it as x_k[n] = e^j \omega nT, the dimension
>of left side and right side doesn't match. The left side is in
>"sample space" though the right side is in t-domain, which is
>converted from sample space using fs.

It is fine to use any function of n on the right-hand side.

>I think that the definition
>would be one of following;
>
>x_k[n] = e^j \omega n

This is fine, provided \omega is in [-\pi,\pi].

>OR
>x_k(t) = e^j \omega nT  (where t = nT).

This is ok too, except we would normally write nT in place of t above.

Cheers,
Julius