Determine if $ y[n] = ny[n-1] + x[n]$ is linear time invariant and BIBO stable

1. How do you prove linear time invariant?
2. How do you know if a system is linear or time invariant?
3. Is Y n )= x (- n time invariant?
4. Are linear time invariant system is stable?

How do you prove linear time invariant?

A system is time-invariant if its output signal does not depend on the absolute time. In other words, if for some input signal x(t) the output signal is y1(t)=Trx(t), then a time-shift of the input signal creates a time-shift on the output signal, i.e. y2(t)=Trx(t−t0)=y1(t−t0).

How do you know if a system is linear or time invariant?

One test to verify time invariance/variance property of a system is to shift the response of the system to an input signal and apply a shifted input, to the same system and compare the two waveforms, so obtained. If the system is time invariant, the two waveforms will match when the input and output shifts match.

Is Y n )= x (- n time invariant?

A system that reverses the signal cannot be time-invariant because when you shift the input, the output is shifted the other way. k and −k are not the same amount.

Are linear time invariant system is stable?

In other words, the system is stable if the output is finite for all possible finite inputs. For the particular case of continuous-time LTI systems, it can be proven that a system is (BIBO) stable, if and only if, the impulse response ℎ(��) is absolutely integrable.