Question

Σₓ =√σ²ₓ =√5 = 2.3361

LINEAR SYSTEMS
Classify the following system (input x(t), output y(t), impulse response h(t)) as: linear or non-linear, time varying or time invariant, casual or non-casual, memoryless or non-zero memory.
(N.B. u(t) is the heave-step function.)

3.1.1 y(t) = 4.7x(t).
3.1.2 y(t) = 4.7x(t - 2.2).
3.1.3 y(t) = [4.7x(t - 2.2)] + 0.01.
3.1.4 y(t) = x(t)cos(2π50t).
3.1.5 y(t) = x(t) + y(t - 1).

Answer 1

The student is inquiring about characteristics of sinusoidal waves and how to classify a set of linear systems in physics. This topic is commonly addressed in high school level physics classes.

Step-by-step explanation:

The student is inquiring about various characteristics of sinusoidal waves and wave functions, which fall under the subject of physics, particularly within the wave motion or oscillations topic. This is typically taught in high school or early college physics courses.

In regards to 3.1.1 to 3.1.5, the student is asking to classify a set of linear systems based on their time variance, causality, and memory characteristics. The equations provided are examples of input-output relationships in these systems. For example, equation 3.1.1 suggests a simple linear transformation, 3.1.2 implies a time delay, 3.1.3 introduces a constant term, 3.1.4 contains a time-varying function, and 3.1.5 represents a recursive relationship.