Signal Representations and Mathematica Operationsl

The unit step function u(t) has a value of 1 when:

• t<0

• t=0

• t>0

• All of the above

The mathematical expression for a shifted unit step function that turns on at t=a is:

• u(t+a)

• u(t−a)

• u(a−t)

• u(t)×a

For a rectangular pulse that starts at t=a and ends at t=b, the correct expression is:

• u(t−a)+u(t−b)

• u(t+a)−u(t+b)

• u(t−a)−u(t−b)

• u(t)−u(t−a)

The general form of a sinusoidal signal is:

• A cos (ωt+ϕ)

• At sin (ω+ϕ)

• Ae^jt

• A/(ωt)

In engineering, the step function is used to represent:

• A continuous process

• Voltage or current switched on at a specific time

• A random signal

• A sinusoidal wave

A ramp signal represents:

• A signal increasing linearly with time

• A signal decreasing exponentially

• A constant pulse

• A periodic signal

The exponential function e^at represents:

• A sinusoidal wave

• Exponential growth or decay

• A step signal

• An impulse

The impulse function δ(t) has which of the following properties?

• Zero everywhere except at t=0

• Infinite at t=0

• Total area = 1

• All of the above

The SI unit of frequency is:

• Hertz (Hz)

• Joule (J)

• Watt (W)

• Volt (V)

The operation used to combine two signals X₁(t) and X₂(t) is:

• X(t)=X1​(t)−X2​(t)

• X(t)=X1​(t)+X2​(t)

• X(t)=X1​(t)×X2​(t)

• X(t)=∫X1​(t)dt