Convolution and Unit Step Function

The video tutorial explains how to calculate the convolution of two signals using the unit step function. It begins with an introduction to the problem, followed by a detailed explanation of the unit step function and its properties. The tutorial then simplifies the integral by ignoring parts that result in zero, evaluates the integral from zero to infinity, and concludes with the final calculation and result, showing that y(t) equals 1 minus cosine of t.

What is the main objective of the problem discussed in the video?

• To determine the Fourier transform of a signal

• To calculate the derivative of a signal

• To find the convolution of two signals

• To solve a differential equation

What does the unit step function u(t) equal when t is less than zero?

• 1

• 0

• Undefined

• t

How does the unit step function simplify the convolution integral?

• By making the integral zero for certain ranges

• By changing the limits of integration

• By converting the integral to a sum

• By eliminating the need for integration

What is the role of the unit step function in the convolution process?

• To add complexity

• To simplify the integral

• To change the function

• To eliminate the need for limits

In the context of the video, what is the significance of the range from zero to infinity?

• It is where the integral is undefined

• It is where the sine function is zero

• It is where the unit step function is zero

• It is where the unit step function is one

Why is the integral from minus infinity to zero ignored?

• Because it is zero

• Because it is negative

• Because it is infinite

• Because it is undefined

What is the integral of sine of tau with respect to tau?

• sine of tau

• -cosine of tau

• cosine of tau

• -sine of tau

What happens to the integral from t to infinity in the convolution calculation?

• It is doubled

• It is ignored

• It becomes one

• It becomes zero

What is the final expression for y(t) as derived in the video?

• y(t) = 1 - cosine(t)

• y(t) = sine(t)

• y(t) = cosine(t)

• y(t) = 1 + sine(t)

What is the value of cosine of zero?

• Undefined

• -1

• 1

• 0