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Re: sorry for the ignorance but what do notch filters really do?

Posted by Jacques (A) on July 24, 2005 at 08:49:55

In Reply to: sorry for the ignorance but what do notch filters really do? posted by adkins on July 23, 2005 at 19:51:46:

They isolate some audio frequency and its surroundings, then they increase or decrease the level of this audio frequency (and its surroundings) in the output audio signal.

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! PARAMETERS !
! !
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So, they have four settings (called parameters) possible:
-the frequency (often called "middle" or "center" frequency" because it is in the middle of the processed band).

- the width of the "surroundings" called "bandwidth". A narrow bandwidth means that mainly only the center frequency will be processed.
A wide bandwidth means that a wider frequency span arounf the center frequency will be processed.
(Notch filters are narrow bandwidth filters).

- the gain in the processed band. When positive, it means you _boost_ the center frequency and the surrounding
band.
When negative, you decrease the level in the processed band.

- shape: it sets how in the bandwidth are individual frequency processed.
An example: let you have a center frequency 2,000Hz with a bandwidth
100Hz, and a gain +12dB. So, 2,000Hz is boosted 12dB, and (2,000 - 100)Hz =
1,900Hz and (2,000 + 100)Hz = 2,100Hz are boosted +3dB (by definition ofthe bandwidth.
How much will be (2,000 - 50)Hz = 1,950Hz and (2,000 + 50)Hz = 2,050Hz boosted?
And other frequencies in the bandwidth
It can be between +12dB and +3dB.
Many filters hace 2 presets for this parameter, one giving a low-order
action, the other a higher order action.
In the above example, let say that response at 1,950Hz and 2,050Hz is +6.0dB with low-order action and still +10db with high-order action

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! OTHER CONSIDERATIONS !
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(1) So, what is a notch filter? A narrow bandwidth filter, with bandwidth
and shape not modifiable, and even gain in some cases.

(2) Often the bandwidth is referred as the 'Q' of the filter. The reason is
historical. A filter is made of electronic devices in which energy swings from one form
(electrostatic in a capacitor) to another form (magnetic in an inductor)
while being dissipated.
In other words, it resonates. Any resonating system, would it be electronic or
mechanical (springs and masses), when feed with an input excitation at its
resonance frequency, oscillates stronger and stronger until it settles at
some level, greater than the excitation.
One defines the Q as the ratio between this later steady level and the
excitation level. It depends of the damping of the oscillation. Under 1 means there is no oscillation
(because it was damped before it could build up), above, it oscillates.
For reasons that are above this short explanation, the bandwidth of a
filter depends on the Q . A small Q gives a wide bandwidth (damped
behavious), a high Q gives a narrow bandwidth (less damped behaviour)

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! DIFFERENT GEARS... !
! !
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(3) Depending on the kind of gear, you have or you don't have all the
settings above:
- a parametric equalizer is built around a number of filters (3 to 5),
chained. You can modify all the four parameters above on each filter. So,
the name. Most often, a low pass and an high pass are addred to help
shaping the audio curve. The highpass can have its cut frequency settable
(often 2 or 3 discrete frequencies, chosen by a thumbswitch, for example
35, 55, 100Hz), and its cutrate too (18 or 24dB/octave is the standard).
Same with the lowpass, which can cut from 8KHz up

- a graphic equalizer has split the band in 31 subbands (why 31, because
studies in physioacoustics show that abobe is useless, because
undiscernable), so the center frequencies are fixed, the bandwidth is fixed
too, and tweaked in a way that the settings adds smoothly on adjacent
subbands (in other words, that the graphic shownonto the EQ's faceplate is
similar to the real gain curve. You just can set the gain, + or -
- an anti-feedback (Larsen Effect) uses a narrow notch filter to fade away the
"feedback". This notch filter is continuously set by a control computer
which tracks any sustaining whistle, calculates its frequency, and sets the
notch filter just enough for it to make the "feedback" fade away.
BTW, I prefer to use "Larsen Effect" instead of "feedback", because "feedback" is
used in other domains of audio electronics with completely different use
-in a PA for example-, and it's pure confusing for non-specialized people
to use the same word (we say Larsen in French, but also Italian, German,
Spanish, Dutch, so I can avoid any accusation of french arrogance)

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
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! ...FOR DIFFERENT USES !
! !
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

(1) The parametric equalizer can build any audio curve you need. Its
drawbacks are : difficult to set (you must understand what you do), and
large sonic consequence of misusing it. It is great to correct "at the
source" a mike, an instrument, a couple milke/instrument (for example, for
a given velocity mike, there is a given bass boost when you sing in it too
close. You can preset your paramEQ to the cut/boost frequency of _this_
mike, withj, and just adjust "on the live" the gain depending on the
singer. But you have to know before what you want.

(2) the graphic equalizer is more used to coorect rooms. There are on the
net many curses about graphic EQ. Refer to them.

(3) Instrument filters are built into instruments, synthetizers or organs.

(4)anti-feedback system can be great or a great source of audio
degradation. Well,built, they can work in a somehow efficient way. But:
they can avoid all relexion induced Larsens. Once the main Larsen faded
away, other can build up, from reflexion onto different walls, etc. The
problem is that this modes are numerous, and the anti-feedback cannot beat
them all..
Another consideration is about conversion ADC and DAC. It should be done at
96KHz to avoid expensive (or insufficient if not) filtering. DSP should
work in integer mode, with a wide accumulator. I just really wonder by
which miracle can people offer such equipement for $150. Even with workers
and technicians working as slaves, I would be unable, just because of the
price of components, even in quantities about 10,000 a month.. Maybe I
missed something, or maybe it's many pro ears that are missing something...
just a question.

Hope it helps your understanding ;-)

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