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But we care about the filter's dynamic behavior -- how the response changes as we vary the parameters Fc and Q -- and two static examples give us little insight.
Fortunately, this isn't a physical book, so we aren't limited to static examples. The blue text indicates that there's something to play with. Try playing with it. We aren't restricted to the author's choice of examples -- we can see the filter's response for any parameters we want.
We can make discoveries that the author didn't bother to mention. For instance, we see that this filter can have stability problems at low Q.
As we play, we think of questions In which regions is this filter stable? Where do we start losing the lowpass response? Intuition By the way, this frequency response is not simply plotted from the transfer function.
Instead, the impulse response of the actual filter is simulated, and its FFT is shown. I think this is more honest, and would work even if we allowed the reader to change the filter topology.
The z-plane pole positions are from the transfer function, however. By watching the result change as we adjust parameters, we can develop an intuition for the system's behavior.
This is helped by the figure's use of multiple representations. We are shown six different ways of characterizing the filter: Each representation gives a unique insight. By watching how they all respond to our experimentation, and how they dance with one another, we can develop a deep understanding -- of not just this filter topology, but digital filtering in general.
Exploring the filter space becomes a game. Incidentally, non-engineers may appreciate yet another representation.
Flip the switch to the left, and try playing again. Trust I've talked about trust, and verifying the author's claims. You may be surprised that this concern is relevant even in an engineering textbook. Playing with the filter response, we see that our author hasn't been entirely honest. The formula for Fc is actually an approximation.
To the right, notice that the blue line the nominal Fc doesn't line up with the peak the actual resonant frequency. By playing with the parameters, we can get a sense for where the approximation holds.
It's actually pretty good at high Q, which is where we typically care about exact frequency. In fact, the entire premise of the filter, as stated in the sidebar that the parameters are separable might be considered marketing-speak.
It's not strictly true at all, although it appears to be fairly close for 0. Explanation It's tempting to be impressed by the novelty of an interactive widget such as this, but the interactivity itself is not really the point.
The primary point of this example -- the reason I call it an "explorable explanation" -- is the subtlety with which the explorable is integrated with the explanation. Like the proposition example earlier, the filter description works as a static explanation -- it can be read like normal text.
The reader is not forced to interact in order to learn. The reader interacts if he wants to go deeper, if he has piqued curiosity or unanswered questions.
There are no UI elements screaming for attention. The reader is not transported off to a separate "interactive" context.
Instead, the reader simply nudges the examples that the author has already presented. Most interactive widgets dump the user in a sandbox and say "figure it out for yourself".
Those are not explanations. To me, an essential aspect of the "explorable explanation" concept is that the author holds up his end of the conversation. The author must guide the reader, and provide a structure for the learning experience.
Only then can the reader respond, by asking and answering the questions that the author provokes.
Contextual Information As much as we might wish authors to write explorable explanations, many won't.A sense of immediacy: Although Twain's narrative is couched in the past tense, we sense that whatever is going on is happening in the very recent past or even now, as we speak.
This is especially true as he goes from jeweler to jeweler to get his watch fixed. The appalling movement of his watch after each repair feels real .
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Headline News continues Thursday, November 1 – Poll shows support is waning for Question BOSTON — Support is dwindling for a ballot question that would impose mandatory limits on the maximum number of patients that can be assigned to one nurse, according to a new poll out Wednesday.