The next basic signal operation performed on the dependent variable is multiplication. In this case, you may have guessed that two or more signals will be multiplied to get a new signal.

Mathematically, this can give:

Y(t)= x 1(t)× x 2(t) ... For continuous-time signals x 1(t) and x 2(t).

Y [n] = x 1 [n ]× x 2 [n] ... For discrete-time signals x 1 [n] and x 2 [n].

When n = -0.8, the value of y [n] seems to be 0. 17, and it is found that the product of the values of x 1 [n] and x 2 [n] is equal to n = -0.8, which are 0.75 and 0.23 respectively. In other words, following the green dotted line, we get 0.75×0.23 = 0. 17.

Similarly, if we move along the purple dotted line (at n = 0.2) and collect the values of x 1 [n], x 2 [n] and y [n], we find that they are -0.94, 0.94 and -0.88 respectively. Here we also find that -0.94×0.94 = -0.88, that is to say, x 1 [0.2]× x 2 [0.2] = y [0.2].

Therefore, we can draw a conclusion that the multiplication operation leads to a signal whose value can be obtained by multiplying the corresponding value of the original signal. This is true whether we are dealing with continuous-time signals or discrete-time signals.

When amplitude modulation (AM) is performed, signal multiplication is used in the field of analog communication. In AM, a message signal is multiplied by a carrier signal to obtain a modulated signal.

Another example where signal multiplication plays an important role is frequency shift in RF (Radio Frequency) systems. Frequency shift is a basic aspect of RF communication, which is realized by using a mixer, which is similar to an analog multiplier.