enter image description heremaybe 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. enter image description here


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    \$\begingroup\$ The shifted LPF will be a band pass filter. \$\endgroup\$ Jun 27, 2023 at 17:27
  • \$\begingroup\$ but band pass filter has two squares, I mean, two places like LPF How is it possible? \$\endgroup\$
    – user323806
    Jun 27, 2023 at 17:28
  • \$\begingroup\$ @StefanWyss Hi, edited in post the BPF, that is not logical to me how it will be BPF, please explain to me \$\endgroup\$
    – user323806
    Jun 27, 2023 at 17:30
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    \$\begingroup\$ Forget about negative frequencies. They have no relevance other than math. \$\endgroup\$ Jun 27, 2023 at 17:32
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    \$\begingroup\$ This filter passes a band from 100 - 200 Hz. \$\endgroup\$
    – tobalt
    Jun 27, 2023 at 17:58

1 Answer 1


The filter response cannot be shifted this way.

The negative values of angular velocity are a mirror image of the positive values.

The definition for a low pass filter is based on the positive values of \$\omega\$. The 0 Hz boundary cannot be shifted.

When a corner frequency of a filter is shifted to the right, the image corner frequency is shifted to the left, and vice versa.

Perhaps frequency should be calculated as \$f=\left|\frac{\omega}{2\pi}\right|\$.

  • \$\begingroup\$ Hmm, if I am understanding correct. When you said that if I shift it, it cannot be shifted. So when I shift it, I basically make it BPF ( as before it was LPF ). Am I right? \$\endgroup\$
    – user323806
    Jun 27, 2023 at 19:54
  • \$\begingroup\$ You can draw whatever you like. In a real filter, there is only one corner frequency. The negative sign indicates 180 degree phase shift. \$\endgroup\$
    – RussellH
    Jun 27, 2023 at 20:20

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