Why do I need to multiply the frequencies with a number, to get correct shift in the bode plot?

1. How do you calculate frequency response?
2. How do you find the stability of a Bode plot?

How do you calculate frequency response?

This can be solved for the frequency response, H(ω) = e ^jωn (b₁ + b₂ e ^-jω + b₃ e ^-2jω)/ e ^jωn (a₁ + a₂ e ^-jω + a₃ e ^-2jω). This form of the frequency response can be generalized to LTI difference equations with an arbitrary number of terms.

How do you find the stability of a Bode plot?

If both the gain margin GM and the phase margin PM are positive, then the control system is stable. If both the gain margin GM and the phase margin PM are equal to zero, then the control system is marginally stable. If the gain margin GM and / or the phase margin PM are/is negative, then the control system is unstable.