Hello,
Intuitively (I hope) you could simply think of a low shelving filter as
a parallel of a lowpass + a scaled amount of the input, and conversely
of a high shelving filter as a parallel of an highpass + a scaled amount
of the input.
E.g., in case of a low shelving whose output = (1 - k) * lowpass output
+ k * input, with 0 < k < 1, at DC you have gain = 1 and at freq=infty
you have gain = k. (Actually, you have to scale the lowpass/highpass too
if you want gain=1 at DC or infinity).
Cheers,
Stefano
Il 26/11/23 07:32, brianw ha scritto:
Can anyone explain how a shelving filter is able to maintain a flat frequency
response both above and below its center frequency?
I have a sense of first-order low-pass filters that have analogs in the
physical world - it somehow makes sense that the frequency response continues
to drop off as the frequency increases above the cutoff. However, while a high
shelving filter has a similar drop in frequency response just above its cutoff,
eventually the response levels off and remains flat as frequency increases. For
example, a high shelf set for -10 dB would have a 0 dB response for frequencies
significantly below the cutoff, a transition around the cutoff with first order
response, and then once the response reaches -10 dB for high frequencies, the
response remains at -10 dB as frequency increases.
I'm trying to understand how this is possible. The Wikipedia article for audio
EQ has a section that seems to hint at how this is achieved.
https://urldefense.proofpoint.com/v2/url?u=https-3A__en.wikipedia.org_wiki_Equalization-5F-28audio-29-23Shelving-5Ffilter&d=DwIFAg&c=009klHSCxuh5AI1vNQzSO0KGjl4nbi2Q0M1QLJX9BeE&r=TRvFbpof3kTa2q5hdjI2hccynPix7hNL2n0I6DmlDy0&m=upGIdDKIRsFXJZNFq2HDaJZ3o2g4X_MUDEt6vyMkQUWMkMzq2MaNL8TGk2mG7h3U&s=GWUlmLkjr9OLMrPKS-R0jAEZJ5TrrXSRi1VVGxm20Dc&e=
This section mentions that there is both a pole and a zero in a shelving
filter. Is that how the response becomes flat in that region? Is it because the
first-order slopes of both the pole and zero add together and end up being flat
as frequency increases, albeit at a loss of 10 dB in the example above?
By the way, I tried to search the internet for an answer, but 99% of the hits
are articles about how to use a shelving filter, or what it does, but none on
how it does it. The remaining 1% of the articles are about the detailed
mathematical transfer functions for shelving filters, without any simple
overview of how they work, or what they're doing mathematically at a high level
rather than formula level.
Thanks for any insight,
Brian Willoughby
