Which of the following statements is true?Question 4Select one or more:A signal will have the same energy in both the time and frequency domains.A signal that is limited in frequency has unlimited (infinite) extent in the time domain.A signal can have limited extent in both the time and frequency domains.A signal that is limited in time has unlimited (infinite) extent in the frequency domain.

The following statements are true:

1. A signal that is limited in frequency has unlimited (infinite) extent in the time domain. This is based on the principle of the Fourier Transform, which states that a signal cannot be simultaneously localized in both time and frequency domains. If a signal is limited in frequency, it means it contains only a certain range of frequencies, and thus must be spread out over an infinite amount of time.

2. A signal that is limited in time has unlimited (infinite) extent in the frequency domain. This is the converse of the previous statement. If a signal is limited in time, it means it exists only for a certain duration, and thus must contain an infinite range of frequencies.

The other two statements are false:

1. A signal will have the same energy in both the time and frequency domains. This is not necessarily true. The energy of a signal in the time domain is the square of its amplitude, while in the frequency domain it is the square of its Fourier Transform. These two quantities are not necessarily equal.

2. A signal can have limited extent in both the time and frequency domains. As mentioned above, the Fourier Transform principle states that a signal cannot be simultaneously localized in both domains.

The following statements are true:

1. A signal that is limited in frequency has unlimited (infinite) extent in the time domain. This is based on the principle of the Fourier Transform, which states that a signal cannot be simultaneously localized in both time and frequency domains. If a signal is limited in frequency, it means it contains only a certain range of frequencies, and thus must be spread out over an infinite amount of time.

2. A signal that is limited in time has unlimited (infinite) extent in the frequency domain. This is the converse of the previous statement. If a signal is limited in time, it means it exists only for a certain duration, and thus must contain an infinite range of frequencies.

The other two statements are false:

1. A signal will not have the same energy in both the time and frequency domains. The energy of a signal is preserved under the Fourier Transform (i.e., the total energy in the time domain is equal to the total energy in the frequency domain), but the energy is not distributed the same way in both domains.

2. A signal cannot have limited extent in both the time and frequency domains. This is known as the Uncertainty Principle in signal processing, which states that a signal cannot be simultaneously localized in both time and frequency domains.