Fourier Visualizations

The first day, the teacher walked in, wrote an equation (FFT) on the board, and spent the next 90 minutes manipulating it into different forms (from his in-hand notes), with no explanation of what or why we were doing so. Occasionally he would stop, say something along the lines of "and you can convert what we have here to this..." and write another equation on the board, and continue "which is one of your homework problems for next time."

The next class was identical. When the third class started the same way, I walked out 40 minutes into it and dropped it. I had zero incentive to continue, the teacher hadn't explained at all what the purpose of what we were doing yet. It had literally been us writing down his math notes for three straight hours while he explained how the mathematical manipulations worked, but not why it mattered or how it was relevant.

I've vacillated over the years between being upset with myself for abandoning that class, and not "getting" fourier related things, and being mad at the teacher at being so horrible at teaching, at least for the portion I was there for.

This is simple. This is obvious. Something like this would have gone a long way towards explaining what the fuck I was doing. I'm no longer upset at myself. I am doubly upset at that teacher now.

One set of two small phasors (one rotating CW relative to the main phasor, and one rotating CCW to the main phasor) is useful for thinking about amplitude and phase modulation. But I find it hard to believe that having four phasors stacked on top of each other strengthens anyone's intuition about Fourier transforms.

It was offered as a double elective for CS and CEE, which meant it was supposed to be accessible to both majors (if admittedly harder for CS majors). I can accept the class being hard, I can't accept the first three hours of class time being spent copying notes of his math notes as he copied them out of his binder onto the board, with a total of class discussion being less than 10 minutes in total for those two class periods. There wasn't even and explanation of what our goal in this was, just "Here's an equation. It's useful. Now we are going to derive some other useful forms of it."

Never before or since have I ever been in a class where the teacher walks in, introduces himself, says what we'll be covering (FFT), turns to the board and starts copying his math notes onto the board, and doesn't stop until the class is over, keeping in mind, it wasn't how to solve an equation, it was how to transform a given equation into another given form with no explanation as to why. Things have come close in some of the more dry history classes I've had, but even then you generally get some additional context from the teacher expanding on the notes presented.