Shift-Invariance of Dirac Comb?

1. How do you know if shift is invariance?
2. What is the Fourier transform of a comb?
3. What is the property of shift invariant system?
4. What is linear shift invariant?

How do you know if shift is invariance?

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

What is the Fourier transform of a comb?

The Fourier Transform of the comb function is a comb function. When peaks occur with distance T in time domain, they occur with distance 1/T in frequency domain. Or, equivalently: The Fourier Transform of a comb with peak frequency F is a comb function with peak distance F.

What is the property of shift invariant system?

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.

What is linear shift invariant?

Linear, shift invariant, discrete time system are invariant regarding shifts in their independent variables. This property permits the initial value of the independent variable to be arbitrarily set to zero ( ) during the analysis of such systems. This can often simplify the analysis.