Which method mathematically converts the time function into a sine wave of different functions?

The fast Fourier transform (FFT) is a powerful computational algorithm used to analyze the frequency components of a time-domain signal. It converts the time function, which represents how a signal varies over time, into its constituent frequencies in the form of a sine wave. This transformation allows us to see the different frequency components that make up the original signal, highlighting how they contribute to the overall shape and behavior of the waveform.

The FFT is extensively used in various fields including engineering, audio signal processing, and communication systems because it provides insights into the frequency content of signals. By breaking down the time-domain signal, we can analyze phenomena such as noise, harmonics, and the frequency spectrum, thus enabling better interpretation and manipulation of signals for applications like filtering, modulation, and system analysis.

The other methods listed do not primarily focus on frequency transformation:

• An A/D converter is responsible for converting an analog signal into a digital form, which involves sampling and quantizing the amplitude but does not analyze frequency content.

• An impedance meter measures electrical impedance at specific frequencies but does not perform a transformation of time functions into sine wave representations across a spectrum.

• A differential amplifier amplifies the difference between two electrical signals without inherently providing a frequency analysis or transformation of time