Test: The Impulse Function - Electrical Engineering (EE) MCQ

Using the definition of the Heaviside function, we can come to this conclusion

Arises from the definition of the delta function. There is a clear difference between just the functional value and the impulse area of the delta function.

The spread of the impulse can never be restricted to a single point in time, and thus, we cannot achieve a perfect impulse.

The integral reduces to the the integral calculated at a single point, determined by the centre of the delta function.

sgn(0)=0, and d[n] = 0 for all n not equal to zero. Hence the sum reduces to zero.

The function gets shifted by the center of the delta function during convolution.

Using the corollary, if we take d[n] to be the ‘x’ function, it will be shifted by -1 when convolved with d[n-1], thus rendering d[n-1].

Using the definition of the Heaviside function, we can come to this conclusion.

The bilateral LT is different from the aspect that the integral is applied for the entire time axis, but the unilateral LT is applied only for the positive time axis. Hence, the u(t) [unit step function] differs in that aspect and hence can be used to differentiate the same.

Now, d = du/dt and u = dr/dt. Hence, we obtain the above answer.