Notch/Bandbass filter curves differ?

prometh

prometh

Power User
Is it just me, or shouldn't these 2 curves be identical in shape aside from vertical direction?
 

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well in a sense yes, one is pass everything but this, the other don't pass anything but this. Q makes dip or spike narrower or broader. Maybe I stated the obvious but yes, one is the mathematical inversion of the other.
 
The graphs represent a desired (relative) amplitude of the signal. Imagine a graphic EQ with a 1000 bands spaced at 10hz per band. Set all of them to zero except one band, set that one to its max. You now have a band-pass at that freq. Now set all the bands at their max except one, set that to its minimum. This is a band-stop or notch filter. Q would be represented by how many adjacent bands to the one in the examples above and the level you set them to.
 
The curves in Axe-Edit aren't same thing as what is actually happening inside the Axe-FX. Try and adjust the slope in the delay filter, notice how it doesn't change in the little window?
 
Ok, so they are mathematical inversions of each other, but just aren't accurately displayed as such in Axe-Edit?
 
If you put those filters in parallel their sum will match the original signal exactly. (Tested on an Ultra; I assume 2nd order filters on the II will give the same result.) You can verify that by inverting the signal at both filters and putting the original signal in parallel.

The graphs seem accurate & about the same in Axe-Edit & hardware. The reason one doesn't look like a flipped version of the other is because the Y axis is linear in dB. If it was linear in voltage instead, one curve would be an inverted version of the other.
 
mmcm4 said:
Notch filters are not mathematically equal to the inverse of band pass filters.

I've tried to upload images of the different transfer functions, but something keeps messing up.

Here's a handout from a class that should show the difference. See pp. 6-8. http://users.ece.gatech.edu/mleach/ece4435/sp07/dp03sp07.pdf

Eq. 11 and 17 show the differences.
Click to expand...

That paper seems to show that because the notch has one linear axis and one log that the notch has a much steeper curve. It has the same numbers represented but the notch falls away much quicker.
 
What would be the names of the filters that are the mathematical invert of a notch and bandpass filter? Then we/I can make a request to Cliff for them :)
 
I imagine you can sum (ie., not placed in series) the outputs of a low pass filter and a high pass filter into a mixer?? If the lowpass cutoff freq is lower than the high pass cutoff freq, it will reject a band that is the difference between the two cutoff freqs. Strictly speaking I believe notches deal with one center frequency where band reject deals with a range, splitting hairs perhaps.

|reject|
____ ____
\ /
\ /
^ LPf ^ HPf

prometh said:
Would a "band reject" filter be a possible addition?
Click to expand...
 
bobby_g said:
I imagine you can sum (ie., not placed in series) the outputs of a low pass filter and a high pass filter into a mixer?? If the lowpass cutoff freq is lower than the high pass cutoff freq, it will reject a band that is the difference between the two cutoff freqs. Strictly speaking I believe notches deal with one center frequency where band reject deals with a range, splitting hairs perhaps.

|reject|
____ ____
\ /
\ /
^ LPf ^ HPf
Click to expand...


A bandpass or notch filter is a high-pass and a low-pass combined together in series. The difference between the two is determined by where the -3dB cutoff frequencies are for the high and low pass filters.
 
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