Always and all.

Always bat not all.

Always using the correct filter.

low pass and high pass.

Band reject and band pass

The frequency central in the border between band pass and reject band.

The lowest frequency rejected.

The high frequency of the filter.

Not delete low and high frequencies.

Delete low frequencies.

Delete high frequencies.

Butterworth

Chebyshev 1

Elliptic

Delete high frequencies.

Delete low frequencies.

Delete low and high frequencies.

Laplace Transform (LT)

Fast Fourier Transfrom (FFT)

Discret Cosinus Transform (DCT)

Use input and output samples

Use a transfer function  like a quocient with denominator different of 1

only use the value of the input samples

To reduce the error of the signal in frequency domain.

To divide a signal in several parts in time.

To use a reduce number of samples and make easy to work.

if a time shift in the input results

in the same time shift in the output.

if it does not change

its behavior in time.

the two previous statements are correct.