# How to identify low pass, bandpass, band reject, high pass filter etc from given $|H(e^{j\omega})|$?

1) How is this a low pass filter?

$$0.99 \leq |H(e^{j\omega})|\leq1.01 {\rm\ for\ } 0\leq|\omega|\leq0.19\pi$$

$$|H(e^{j\omega}\;)|\leq0.01{\rm\ for\ } 0.21\pi\leq|\omega|\leq\pi$$

2) What kind of filter is this? Low pass, high pass, band pass, band reject or what? $$0.99 \leq |H(e^{j\omega})|\leq1.01 {\rm\ for\ } 0\geq|\omega|\geq0.19\pi$$

$$|H(e^{j\omega}\;)|\leq0.01{\rm\ for\ } 0.21\pi\leq|\omega|\leq\pi$$

I am really confused on how to identify if a filter is high pass, band pass, low pass, band reject from given specifications. Can you make me understand this concepts?

• If you have trouble reading the math, why don't you just draw it ? It becomes blatantly obvious then. Sep 5, 2021 at 6:47
• Yeah I got it now(the first one). Can you tell me about the second question? How can sth be lesser than 0 yet greater than $0.19\pi$, is that second question wrong? Sep 5, 2021 at 8:20
• The second one is clearly a typo, that's pretty obvious. Sep 5, 2021 at 10:51
• oh thanks a lot. i was geting confused due to that. Sep 5, 2021 at 10:52