# Does a filter need to completely attenuate high frequencies to be considered low-pass?

I'm looking at a system with a frequency response that is: $$H(e^{j\omega})=\tfrac{1}{4}(2\cos(\omega)+\cos(2\omega)+2)$$

I think the magnitude of this system looks like this (not sure what is the proper name for a function like this):

Would this be considered a low-pass filter even though the output is always greater than zero? If not, what would be the proper name for it?

• looks lowpass to me. – robert bristow-johnson Jan 28 '17 at 4:01
• someone in audio might call it a "low shelf" filter. – robert bristow-johnson Jan 28 '17 at 4:03