What is the primary purpose of the Fourier Transform?

To represent aperiodic signals as a continuous function of frequencies.

Which of the following statements about the Fourier Transform is true? A) It only applies to periodic signals. B) It can represent a larger class of functions than Fourier series. C) It cannot be used for continuous signals. D) It is only applicable in electrical engineering.

B) It can represent a larger class of functions than Fourier series.

Riddle: I can turn time into frequency, providing insight into components unseen. What am I?

Fourier Transform

True or False: The Fourier Transform of a periodic signal results in a continuous function.

False. The Fourier Transform of a periodic signal results in a train of impulses.

The conditions for the existence of the Fourier Transform include that the signal must be ______ integrable.

Absolutely

What mathematical operation is used to recover the original function from its Fourier Transform?

Inverse Fourier Transform

Which property of the Fourier Transform states that the transform of a linear combination of signals is the same linear combination of their transforms?

Linearity

Fill in the blank: The Fourier Transform of the unit impulse is the ______ function.

Identity

In the context of Fourier Transforms, what does the term 'duality' refer to?

The relationship between a signal and its Fourier Transform, where the Fourier Transform of a signal can be treated as a signal itself.

What happens to the spacing of frequencies in the spectrum as the time period T of a periodic signal increases?

The spacing between adjacent frequency components decreases.