Discrete time signal to continuous time signal

  • #1

Homework Statement


Suppose that a discrete-time signal x[n] is given by the formula

x[n] = 10cos(0.2*PI*n - PI/7)

and that it was obtained by sampling a continuous signal at a sampling rate of fs=1000 samples/second.

Determine two different continuous-time signals x1(t) and x2(t) whose samples are equal to x[n]; ie. find x1(t) and x2(t) such that x[n] = x1(nTs) = x2(nTs0 if Ts = 0.001. Both of these signals should have a frequency less than 1000Hz. Give a formula for each signal.


The Attempt at a Solution



Since x[n] = 10 * cos ( 0.2 * PI * n - PI / 7)
The same signal would be represented by

x[n] = 10 * cos(2.2 * PI * n - PI/7)

Is this assumption correct?

Now I would need to convert these two x[n] equations to time-domain x(t), and I am not sure how I would go about doing this part.
 

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