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I moved this sentence from the article, because I don't understand what it is trying to say, irritation of whom (the listener?), could the contributor please clarify the meaning and it can be added back. --
Lexor|
Talk 13:07, 24 Jun 2004 (UTC)
There is often irritation when you actively want to cut low frequencies with a high pass....
With the given equations, if the time interval is the same as the RC time constant, alpha calculates as 0.5. But this is incorrect, after one time constant of time the output should reduce to 1/e, not 1/2. Surely the correct equation is e^(-dt/RC).
Richard whitehead (
talk)
20:48, 13 June 2008 (UTC)reply
I didn't realise I was being that clever! I just imagined the input signal varying as a sequence of steps. In this case, the current decays between steps according to exponential decay, and then a new lot of current is added on when the step happens (both ends of the capacitor changing voltages by the same amount because the step is instantaneous, so the new current is delta-V / R). I expect the result is very similar unless the simulation time step is too long (too similar to RC).
Richard whitehead (
talk)
13:09, 14 June 2008 (UTC)reply
See the new comments about the relationship between α and RC. As you can see, the decay truly is exponential, but the mapping from "continuous-time frequencies" to "discrete-time frequencies" is not linear, and so the "time constant" isn't going to match especially for α that large. Keep in mind that whenever you go from CT to DT, you're wrapping an infinite line (i.e., from 0 Hz to ∞ Hz) to a finite line (i.e., the semicircular circumference from 0 radians/sample to π radians/sample). There's no way to do that linearly, and so the frequencies only "match" in a small region. That's why we have different CT-to-DT methods; sometimes we need them to match in different ways. For example, we might need to make sure all CT poles land inside the unit circle, or we might need to make sure that the match is very close near the corner frequency... or lots of other things. There's always going to be mismatch, and that's why it's always best to do your design in your target context. If it's going to be realized in discrete-time, it should be designed there too. —TedPavlic (
talk)
20:46, 8 January 2009 (UTC)reply
One more thing. As you can see on the new sections of the page, this method approximates the derivative by taking the slope over one sampling period. Each CT-to-DT method approximates the derivative in a different way. Put another way, each CT-to-DT method deals with the space "in between" samples in different ways. As you can see, there are tradeoffs. Lots of people like approximating the derivative as the slope between time points. A consequence of that is that your impulse response doesn't have the same time constant (however, there is a qualitative relationship between the DT and CT time constants; as one gets bigger, so does the other). —TedPavlic (
talk)
21:17, 8 January 2009 (UTC)reply
High-pass vs. 1st order LTI high-pass
The title of this article is high-pass filter. You can implement a discrete-time high-pass filter without attempting to match the characteristics of any particular continuous time high-pass filter. So the emphasis on matching the 1st-order continuous time version seems misplaced to me.
Ccrrccrr (
talk)
17:03, 28 May 2009 (UTC)reply
For example, the statement, "the effect of a high-pass filter can be simulated on a computer," seems misplaced. You can implement a high-pass filter in discrete time, and it actually is a high-pass filter, not an approximation of one.
Ccrrccrr (
talk)
17:05, 28 May 2009 (UTC)reply
I'd like to see a summary for less technical people.
It would be nice to include a sample audio clip showing what something sounds like before and after a high pass filter is applied.
Kevink707 (
talk)
18:44, 5 February 2010 (UTC)reply
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Please add a section covering resonance. Also, please explain the difference between a single-pole filter and a 2-pole filter (is the latter simply two of the former in series?)
174.106.34.169 (
talk)
14:11, 26 January 2023 (UTC)reply