Question

Problem 7.1 A real-valued signal xx(????????) is known to be uniquely determined by its samples when the sampling frequency is ????????????????=10,000????????. For what values of ω is ????????(???????????? ) guaranteed to be zero? Please note that frequency can be positive and negative

Answer 1

Answer:

IωI > 5000π rad/s

Explanation:

Step 1  

The value of ω at which X(jω) is assumed to be zero is given by,  

IωI > ω_M

where ω_M  is the maximum frequency of the original signal.

Assume that the sampling frequency we equals the Nyquist rate ω_N  

Step 2  

Then the value of ω is given by,  

IωI > ω_M

     > ω_s/2

     > 10000π/2

     > 5000π

thus,

IωI > 5000π rad/s