Question

Let x(t)=e^(30pi it/7) be a signal the frequency of x(t) is

a) 30/7
b) 15/7
c) 7/15
d) signal not perijdic

Answer 1

b) 15/7

Explanation:

The frequency of a signal is a measure of how often the signal repeats over time. In this case, x(t) is a complex exponential signal, represented by the equation x(t) = e^(30πit/7). The variable "t" represents time, and the variable "i" represents the imaginary unit, which is equal to the square root of -1.

The "30πi" term in the exponent represents the angular frequency of the signal, which is a measure of how rapidly the signal oscillates. The "t/7" term in the exponent represents the time scaling of the signal, which determines how quickly or slowly the signal repeats over time.

When we combine these two factors, we can see that the signal repeats every 7 units of time. Therefore, the frequency of the signal is 1/7, which is equivalent to 15/7 in decimal form. Therefore the answer is (b) 15/7