Question

What is the purpose of determining normalized energy in Parseval's theorem?

1) To calculate the total energy of a signal
2) To normalize the energy of a signal
3) To determine the frequency components of a signal
4) To calculate the power of a signal

Answer 1

Parseval's theorem is used to calculate the total energy of a signal, enabling comparisons between signals of varying amplitudes or power levels and providing a standardized way to analyze signal energy. Option 1 is correct.

Step-by-step explanation:

The purpose of determining normalized energy in Parseval's theorem is to calculate the total energy of a signal. Parseval's theorem, which ties the Fourier transform to the energy of a signal, states that the energy calculated in the time domain is equal to the energy calculated in the frequency domain.

Normalizing the energy allows for comparisons between signals of different amplitudes or power levels and provides a consistent basis for analyzing signal energy regardless of the signal's scale.

When applying Parseval's theorem, it is important to note that energy in a wave is related to amplitude squared. In the context of electromagnetic waves, which are assumed to be sinusoidal for these calculations, the peak intensity (Io) is twice the average intensity (Iave), which can be expressed as Io = 2 * Iave. This highlights why the normalized energy found through Parseval's theorem is critical for an accurate representation of the signal's energy.

In summary, determining normalized energy using Parseval's theorem serves to enable the calculation of total energy of a signal, using either its time domain representation or its frequency domain representation, while also standardizing this measurement for comparison.