# Ideal Low Pass Filter shifted is still ideal Low Pass Filter?

maybe a stupid question. But let us say we have a ideal LPF filter like this: $$H\left(j\omega \right)=\begin{cases}1&-\omega _m<\omega <\omega _m\\ 0&else\end{cases}$$ If I shift it , which means like that: $$H\left(j\omega \right)=\begin{cases}1&\omega _m<\omega <3\omega _m\\ 0&else\end{cases}$$ Is it still ideal LPF filter? Because we know the "shape" of LPF fitler is like a step function of $$u(t+1)-u(t-1)$$

I know my question is a little stupid, but it is important to me.

EDIT: I was said in comments it will be Band Pass Filter, but how? band pass filter looks like double shifted LPF, not one.

EDIT:

• The shifted LPF will be a band pass filter. Jun 27, 2023 at 17:27
• but band pass filter has two squares, I mean, two places like LPF How is it possible? Jun 27, 2023 at 17:28
• @StefanWyss Hi, edited in post the BPF, that is not logical to me how it will be BPF, please explain to me Jun 27, 2023 at 17:30
• Forget about negative frequencies. They have no relevance other than math. Jun 27, 2023 at 17:32
• This filter passes a band from 100 - 200 Hz. Jun 27, 2023 at 17:58

The definition for a low pass filter is based on the positive values of $$\\omega\$$. The 0 Hz boundary cannot be shifted.
Perhaps frequency should be calculated as $$\f=\left|\frac{\omega}{2\pi}\right|\$$.