June 29, 2014
I am first starting out and completed SimpleHPF exercise and while writing the code makes perfect sense I'm not quite sure why it works. I have taken a circuits lab and am familiar with a high pass filter in the analog sense however the concept of adding a one sample delay signal with the original signal seems like it would create a basic reverb rather than a high pass filter. Could anyone explain what specifically causes the attenuation of the low end by adding this delay? Does this have to do with slightly shifting the phase of the signal? In that case then I would imagine higher frequencies being attenuated because a small phase shift will result in more of the higher frequencies being degraded than the low frequencies. Also, in SimpleHPF the UI controls the coefficients a_0 and a_1 however why would increasing these scalars cause more attenuation in the bass to occur? Why is attenuation a function of intensity and not dependent on the phase / sample delay difference between the two streams?
January 29, 2017
There are several things regarding this filter: (1) as stated in the book, it is not an actual HPF, but rather more of a low-cutting shelving type filter and (2) its transfer function has all zeros.
To understand how it delivers the frequency response it does, you need to go through Chapter 5 and learn to plot the frequency response from the pole-zero plot, which you find with the difference equation. With that you can verify its functionality and frequency response. And you can get a feel for how the coefficients affect the location of the zeros and therefore the frequency response. This is an indirect approach; making sense of the coefficients as they relate to filter operation directly is more difficult.
One way to convert the analog circuits to digital versions is with the bilinear transform in Chapter 6. In that chapter, you will see an example RC lowpass circuit that I am sure you studied in circuits lab. The digital version is shown in Figure 6.15. You can see that it has a feedback path. But, the RC circuit itself does not have such a path. In order to understand that, you need to either solve the differential equation for the filter and generate a block diagram, or use analog signal flow graphing to reveal the signal flow. Both approaches show the feedback. However, with the bilinear transform feedback filters like this one, making sense of the coefficients as they relate to filter operation directly is not really possible. Instead, you should focus on how the coefficients affect the location of the poles and zeros, then use that to find the frequency (or phase) response.
In my new synth book, I go into much more analog theory as well as an alternate to the bilinear transform method.
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