Final answer:
The modulation property of Fourier transform is important for understanding how the characteristics of signals change when modulated, relevant in AM and FM radio transmissions where amplitude or frequency are altered to encode information.
Step-by-step explanation:
The modulation property of Fourier transform is a mathematical concept that explains how the characteristics of a Fourier transform change when the input signal is modulated. In terms of electromagnetic waves, like those used in AM and FM radio transmission, this property is crucial. For amplitude modulation (AM), the amplitude of the carrier wave is varied in accordance with the information being sent, whereas in frequency modulation (FM), it is the frequency that is varied. These changes in modulation translate to a superposition of waves with different frequencies in the context of Fourier transform, meaning that we can analyze and reconstruct the original signal through its Fourier components. The modulation property of Fourier transform hence allows the analysis of these changes in the context of the frequency domain, providing a critical tool for understanding and processing signal transmissions.