Question

Evaluate the convolution: f(t) = 1.r(t – 1) * 3. uſt – 1). Use d(t+A), u(t+B), r(t+A) to represent the delay, step and ramp functions respectively. A is a positive or negative constant. If you need to scale a function use B*u(t) for a step function (for example), with zero delay scaled by B.

Keep your answers in the form of d(t), u(t), and r(t). If you need to to raise the power of the time available t use r(t)ᴬ, where A is the constant you want to raise r(t) to. Do not multiply r(t)'s together, it will be marked incorrect in myopenmath.

f(t) = ______

Answer 1

Given the convolution: f(t) = 1.r(t – 1) * 3. uſt – 1), the evaluation of the convolution results in the value of f(t) = 3.

Step-by-step explanation:

The given convolution is f(t) = 1.r(t – 1) * 3. u(t – 1).

To evaluate this convolution, we need to understand the functions represented by d(t), u(t), and r(t).

d(t) represents a delay function, where d(t+A) means a delay of A units in the positive x-direction.

u(t) represents a step function, where u(t+B) means a step of height B at time t=0.

It is multiplied by another function to introduce a scaled step.

r(t) represents a ramp function, where r(t+A) means a ramp of slope 1 starting at x=A.

It can be used to represent a linear increase or decrease in value.

Using these functions, we can evaluate the convolution as:

f(t) = 1.r(t – 1) * 3. u(t – 1) = 3. r(0). u(0) = 3. u(0) = 3

So therefore the convolution results is f(t) = 3.