Intro to Linear Time-Invariant Systems Exercises

A linear system satisfies the principle of  $\_\_\_\_\_\_\_\_\_\_\_$.

The output of a causal system depends on $\_\_\_\_\_\_\_\_\_\_\_$ values of the input.  Select the best answer.

A system has input $x[n]$ and output $y[n]$.  Which of the following systems are causal?  Select all that apply.

A system has input $x[n]$ and output $y[n]$.  Which of the following systems are linear?  Select all that apply.

A system has input $x[n]$ and output $y[n]$.  Which of the following systems are time invariant?  Select all that apply.

System 1 evaluates the output $y_1[n]$ from the input $x[n]$ as

$y_1[n] = b_0x[n]+b_1x[n-1] + b_2 x[n-2] + b_3 x[n-3]$

where $b_0 = 0.25; \;\; b_1 = 0.25; \;\; b_2 = 0.25; \;\; b_3 = 0.25$.

System 1 forms the  $\_\_\_\_\_\_\_\_\_\_\_$ input values.

System 1 evaluates the output $y_1[n]$ from the input $x[n]$ as

$y_1[n] = b_0x[n]+b_1x[n-1] + b_2 x[n-2] + b_3 x[n-3]$

where $b_0 = 0.25; \;\; b_1 = 0.25; \;\; b_2 = 0.25; \;\; b_3 = 0.25$.  System 1 will  $\_\_\_\_\_\_\_\_\_\_\_$ rapid fluctuations or high-frequency components of the input signal.

System 2 is of the same form but with different coefficients

$y_2[n] = c_0x[n]+c_1x[n-1] + c_2 x[n-2] + c_3 x[n-3]$

The $c_k$ are $c_0 = -0.5; \;\; c_1 = 0.5; \;\; c_2 = 0; \;\; c_3 = 0$.  System 2 forms the  $\_\_\_\_\_\_\_\_\_\_\_$ input values.

System 2 is of the same form but with different coefficients

$y_2[n] = c_0x[n]+c_1x[n-1] + c_2 x[n-2] + c_3 x[n-3]$

The $c_k$ are $c_0 = -0.5; \;\; c_1 = 0.5; \;\; c_2 = 0; \;\; c_3 = 0$.  Therefore, System 2 will attenuate  $\_\_\_\_\_\_\_\_\_\_\_$ components of the input.