Exponentials Steps Impulse Signals Exercises

The symbol $u(t)$ denotes a $\_\_\_\_\_\_\_\_\_\_\_$  signal.

The symbol $\delta(t)$ denotes a $\_\_\_\_\_\_\_\_\_\_\_$  signal.

A signal $x(t) = e^{st}$ is a  $\_\_\_\_\_\_\_\_\_\_\_$.

An exponential signal is defined as $x[n] = Az^n$. Which value for $z$ results in the signal whose magnitude decays the fastest as $n$ increases?

A signal $x[n] = (0.9)^n\cos(\frac{\pi}{8} n)$. Write this signal as a sum of two exponentials, $x[n] = A_1 z_1^n + A_2 z_2^n$ and identify the correct values of $A_1, z_1, A_2, z_2$.

The signal depicted below is an exponentially-damped sinusoid of the form $x(t) = e^{at} \cos(2\pi f t)$.  The value $x(1) = 0.4493$. Enter $f$.

The signal depicted below is an exponentially-damped sinusoid of the form $x(t) = e^{at} \cos(2\pi f t)$.  The value $x(1) = 0.4493$. Enter $a$.

Which of the following choices describes the signal shown below?

Which of the following choices describes the signal shown below?

Use the sifting property of the impulse to evaluate

$b = \int_{-\infty}^\infty x(t) \delta(t-a) dt$

for $x(t) = 2e^{-t}\cos(\pi t)$ if $a = 1$.