See Saw Margery Daw
I remember a time when everything seemed possible. I could perhaps have gone anywhere and been anything. This was almost scared out of me by truisms, such as nursery rhymes, that cautioned me to specialize in one thing – to pick a trade and get good at it. I tried, but I couldn’t do it. I just couldn’t find one thing and be the best at it.
So now, I am the master of nothing…
But is that so bad, really? I like hanging out with math-nerds and machinists. I can’t do what the best of them can do, but I can see their complementarity. Hanging out in the space between them is pretty cool (to me). I get to see things this way…
Basis functions are the building blocks of electrical circuits, not, as one might suppose, resistors capacitors and coils. Many, many years ago I began to learn and repeat this fascinating story (see here) that I recently revisited. The grand sense of wonderment I get from electrical engineering is like the feeling one might get from other adventure stories like Alice in Wonderland, Peter Pan and so many more. (Lewis Carroll, the person who first met adventurous Alice was also Charles Dodgson, the Oxford mathematics lecturer, a coincidence of significance.) The electrical engineering story goes something like this: We use mathematics to create machines to create mathematics to create …
We use mathematics to create machines to create mathematics to create…
- Lumped element lossy bandstop (5, 7, 9 poles)
- Lumped element lossy LPF || lossy HPF combo, with and w/o Wilkinsons
- PI inverter coupled shunt resonators
- TL coupled shunt resonators
A machinist or trim carpenter will sometimes create a special tool with a profile that mirrors a portion of the project she needs to produce. Individual profiling operations can be performed in series, so that their sum creates the desired shape.
You can also view individual resonators or individual antenna elements as special tools. By combining a bunch of them together you can possibly create the filter shape or antenna pattern you desire.
Machinists and carpenters accrue many thousands of dollars worth of cutters of different sizes and profiles in the course of their careers. Understanding (and remembering) that basis functions – each represented by one or more physical structures – are closely analogous ‘tools’ for shaping signals is the math-nerd equivalent.