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
