Question

When are dummy variables used in continuous time convolution?

(a) To change the limits of integration

(b) To change the domain of integration

(c) To substitute time analysis

(d) To substitute frequency analysis

The question was asked in an international level competition.

The above asked question is from Continuous Time Convolution in portion Time-Domain Analysis of CT Systems of Signals and Systems

Answer 1

Right answer is (b) To change the domain of integration

The explanation: Dummy variables are used in continuous time convolution to change the domain of integration i.e the input and response are first changed into a dummy variable domain before convolution.

Suppose x(t) is the input and h(t) is the impulse response so to find the convolution, the domain is changed to a dummy variable e(suppose).

So, x(t)*h(t)=x(τ)*h(τ).