Proof of shift invariance

1. How do you prove shift invariant?
2. How do you prove a system is time invariant?
3. What is meant by shift invariant?
4. Is CNN shift invariant?

How do you prove shift invariant?

If g(x + x0) = H[f(x + x0)] then the system is shift invariant, otherwise it is not.

How do you prove a system is 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.

What is meant by shift invariant?

A shift-invariant system is one where a shift in the independent variable of the input signal causes a corresponding shift in the output signal. So if the response of a system to an input is , then the response to an input is .

Is CNN shift invariant?

Modern convolutional networks are not shift-invariant, as small input shifts or translations can cause drastic changes in the output. Commonly used downsampling methods, such as max-pooling, strided-convolution, and average-pooling, ignore the sampling theorem.