Test: Basic Operations on Signals - Electronics and Communication Engineering (ECE) MCQ

Amplitude scaling refers to multiplication of a constant with the given signal.
It is given by y (t) = a x (t). It can be both increase in amplitude or decrease in amplitude.

AM radio signal is an example for y (t) = x₁ (t) * x₂ (t) where, x₁ (t) consists of an audio signal plus a dc component and x₂ (t) is a sinusoidal signal called carrier wave.

Audio mixer is a device which combines music and voice signals. It is given by
Y (t) = x₁ (t) + x₂ (t).

Inductor performs differentiation. It is given by y (t) = L d/dt i(t) where, I (t) denotes current flowing through an inductor of inductance L.

y (t) = x (at), comparing this with the given expression we get a = 1/5. If 0 < a < 1 then it is expanded (stretched) version of x (t).

Capacitor performs integration. V (t) developed across capacitor is given by
v (t) = (1/C)* ∫^t_-∞ i (∂).d∂, I (t) is the current flowing through a capacitor of capacitance C.

By comparing the given equation with y (t) = x (at) we get a = 2. If a > 1 then it is compressed version of x (t).

For discrete time signal y [n] = x [k x n] and k > 1, it will be compressed signal and some samples will be lost. The samples lost will not violate the rules of sampling theorem.

The given y (t) is integral of x (t) and amplitude 3 remains constant for t > 1.
It is because of the properties of integration.