Question

Consider the Power Spectral Density (PSD) of a signal x(t) given by Sₓ(f):

Sₓ(f) = { (f + 5000)/5000, -5000 ≤ f ≤ 0
(-f + 5000)/5000, 0 < f ≤ 5000 }

Express the PSD in mathematical form and describe the characteristics of the signal x(t) based on the given PSD.

Answer 1

The Sx(f) of the signal x(t) is characterized by a symmetric linear distribution, indicating that the signal is band-limited with the highest frequency at 5000 Hz. The PSD defines the power distribution over different frequencies.

Step-by-step explanation:

Considering the Power Spectral Density (PSD) of a signal x(t), the mathematical expression for the given PSD Sx(f) is as follows:

• For -5000 ≤ f ≤ 0, Sx(f) = (f + 5000)/5000
• For 0 < f ≤ 5000, Sx(f) = (-f + 5000)/5000

The characteristics of the signal x(t) based on the PSD can be inferred as exhibiting symmetry around the origin with a linear rise from -5000 to 0 Hz and a linear decline from 0 to 5000 Hz. This suggests that the signal is most likely band-limited with a maximum frequency of 5000 Hz. The PSD is used to describe how the power of a signal is distributed across different frequencies. Power Spectral Density, signal characteristics, and band-limited are important aspects of this PSD.