Final answer:
The frequency translation property of the Fourier transform is a property that shifts the frequency spectrum of a signal in the frequency domain, which is fundamental in communications and signal processing.
Step-by-step explanation:
The frequency translation property of the Fourier transform refers to the effect that modulating a signal by a cosine or sine wave in the time domain has on its corresponding Fourier transform. Specifically, this property implies that if a time-domain signal is multiplied by a cosine or sine wave at a frequency ω0, the Fourier transform of the resulting signal will be shifted in the frequency domain by ω0. In more technical terms, multiplication of a time-domain signal by ejω0t results in a frequency-domain spectrum that is shifted by the frequency ω0.
This property is also known as the modulation property, and it is fundamental in communications and signal processing, as it allows for the shifting of signals to different frequency bands. The correct answer to the student's question is 1) A property that shifts the frequency spectrum of a signal.