EE5410 Signal Processing -- The multiplication property
1. The convolution property states that convolution in the time domain corresponds to multiplication in the frequency domain.
2. Because of duality between the time and frequency domain, we would expect a dual property also to hold (i.e., that multiplication in the time domain corresponds to convolution in the frequency domain.)
3. Multiplication of one signal by another ( r(t) = s(t)p(t) ) can be thought of as using one signal to SCALE or modulate the amplitude of the other, and consequently, the multiplication of two signals is often referred to as amplitude modulation.
4. For this reason, it is sometimes referred to as the modulation property.
5. We see that ALL the information in the signal s(t) is preserved when we multiply this signal by a sinusoidal signal, although the information has been shifted to higher frequencies.
6. This fact forms the basis for sinusoidal amplitude modulation systems for communication.
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