F(s) = 1/(s + a)

F(s) = 1/(s - a)

F(s) = a/(s + a)

F(s) = a/(s - a)

f(t) = sin(2t)

f(t) = cos(2t)

f(t) = e^(-2t)sin(2t)

f(t) = e^(-2t)cos(2t)

F(Ϲ) = πe^(-(Ϲ^2)/4)

F(Ϲ) = πe^(-4(Ϲ^2))

F(Ϲ) = πe^(-(Ϲ^2)/2)

F(Ϲ) = πe^(-2(Ϲ^2))

f(t) = δ(t - t_0)

f(t) = δ(t + t_0)

f(t) = δ(t)e^(-jϹt_0)

f(t) = δ(t)e^(jϹt_0)

To convert a signal from the time domain to the frequency domain

To convert a signal from the frequency domain to the time domain

To analyze the stability of a system

To determine the poles and zeros of a system

The Fourier Transform is a special case of the Laplace Transform

The Laplace Transform is a special case of the Fourier Transform

They are unrelated transforms

They are equivalent transforms

Linearity

Time-shifting

Convolution

Initial Value Theorem

They determine the system's stability

They determine the system's frequency response

They determine the system's time response

All of the above

To model and analyze continuous-time signals

To model and analyze discrete-time signals

To design filters and signal processing systems

All of the above

y'' + μk^2y = 0

y'' - μk^2y = 0

y'' + μk^2y' = 0

y'' - μk^2y' = 0

y(t) = Acos(μk^2t) + Bsin(μk^2t)

y(t) = Ae^(-μk^2t) + Be^(+μk^2t)

y(t) = Acosh(μk^2t) + Bsinh(μk^2t)

y(t) = Ae^(-μk^2t) + Be^(-μk^2t)

The solution is the convolution of the input signal with the impulse response

The solution is the product of the input signal and the impulse response

The solution is the derivative of the input signal with respect to the impulse response

The solution is the integral of the input signal with respect to the impulse response

The ratio of the output signal to the input signal in the frequency domain

The ratio of the output signal to the input signal in the time domain

The Laplace Transform of the impulse response

The Fourier Transform of the impulse response

To determine the cutoff frequency and bandwidth of the filter

To determine the order and type of the filter

To determine the stability of the filter

All of the above