Question

Determine the Fourier transform of the following signal. Furthermore, determine the signal's energy. What is the signal's power?

x(t) = sin(4)t-2))/π (t-2)

Answer 1

The student's signal requires clarification as the provided function seems to be incorrectly formatted. Once clarified, the Fourier transform, energy, and power of the signal can be determined following mathematical formulas for signals.

Step-by-step explanation:

The Fourier transform of a signal is used to determine its frequency spectrum and is especially useful in the field of signal processing. The student's question involves calculating the Fourier transform of the signal x(t) = sin(4t-2)/π (t-2). However, the signal expression provided seems to be incomplete or incorrectly formatted as x(t) = sin(4)t-2))/π (t-2) which doesn't represent a standard mathematical function.

To calculate the signal's energy, the formula E = ∫|x(t)|^2 dt is used, assuming the signal is energy finite. Power, which is defined for signals that exist for all time, is the average energy per unit time and is calculated using the formula P = lim(T → ∞) (1/2T) ∫_{-T}^{T} |x(t)|^2 dt. For the signal given, if we assume it's meant to be x(t) = (sin(4(t-2)))/π (t-2), it is an energy signal as it tends to zero as t goes to infinity, and hence its power is zero.