Amplitude modulation (AM) is a method of transmitting a signal by varying the amplitude, or strength, of a carrier wave according to the information in the original signal. This allows the original signal to be conveyed over long distances without degradation, as the carrier wave can be much stronger than the original signal.

To calculate the amplitude modulation of a signal, we first need to determine the carrier wave frequency and amplitude. The carrier wave is typically a sinusoidal wave with a frequency much higher than the original signal, and its amplitude is typically set to a fixed value.

Next, we need to determine the modulation index, which is a measure of the depth of modulation. The modulation index is calculated as the ratio of the amplitude of the original signal to the amplitude of the carrier wave. For example, if the amplitude of the original signal is 10 units and the amplitude of the carrier wave is 100 units, the modulation index would be 0.1.

Once we have determined the carrier wave frequency, amplitude, and modulation index, we can then calculate the amplitude of the modulated signal at any given point in time. This is done by multiplying the carrier wave amplitude by the sum of 1 and the product of the modulation index and the original signal at that point in time.

For example, if the original signal is a sine wave with an amplitude of 10 units and a frequency of 1 Hz, and the carrier wave has an amplitude of 100 units and a frequency of 10 Hz, the modulated signal at a given point in time t can be calculated as follows:

Modulated signal = 100 * (1 + 0.1 * sin(2 * pi * 1 * t))

This equation shows that the modulated signal will have an amplitude that varies between 90 and 110 units, depending on the value of the original signal at that point in time.

In conclusion, amplitude modulation is a widely used method for transmitting signals over long distances, and it can be calculated by determining the carrier wave frequency and amplitude, as well as the modulation index. By using these values, we can calculate the amplitude of the modulated signal at any given point in time.