Is $y(t) = \cos(t) + x(t)$ a time-invariant system?

1. How do you check system is time invariant or not?
2. Is COSX time invariant?
3. What is the example of time-invariant system?
4. Is sin t time invariant?

How do you check system is time invariant or not?

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 COSX time invariant?

Yes, since it is memoryless, it only depends on the present input (For a system to be causal, its present output must not depend on future values of the input). (v) Is the system time-invariant? Yes, since y(t+τ) = cos(x(t+τ)), for any t and τ.

What is the example of time-invariant system?

b) y(T)=sin[x(T)]

Similarly, if the system is passed through the time delay first then through the system then output will be sinx(T−t). We can see clearly that both the outputs are same. Hence, the system is time invariant.

Is sin t time invariant?

Lemma 1: Therefore, sin(x(t)) is a time-invariant system.