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I found a decent free textbook that explains DSP fundamentals for
non-specialists. Here's the author's definition of a transform (e.g. Discrete Fourier Transform).

Suppose you have a signal composed of 100 samples. If you devise some equation, algorithm, or procedure for changing these 100 samples into another 100 samples, you have yourself a transform. If you think it is useful enough, you have the perfect right to attach your last name to it and expound its merits to your colleagues. (This works best if you are an eminent 18th century French mathematician).
Mark Branson's profile photoDavid Jedlicka's profile photoRichard Tollerton's profile photoJames Loftus-Mercer's profile photo
I take it the title of this textbook is a secret?
Yeah, you need to click "Add"... you'd think it would know after you paste it in there, right?
A transform is just a change of basis in a Hilbert space. What's so difficult to understand about that?
+Michael Soland, sorry to bruise your Google pride, but this was a real bug, I think. I truly did explicitly add it. Twice. Ah well; insert "at least it's not Facebook" jab here.
I'm sad that it tries to be low math. But math is how it works! =(
Oops, I've exposed myself as anti-math. Damn.

Really, I think this author strikes a reasonable balance. He doesn't deny the math is important (and actually includes quite a bit), but he's careful to introduce concepts in more concrete, applied terms. Many DSP texts really do go too far the other direction, assuming readers work with sinusoids, exponentials, complex numbers, and probability every day. Honestly, most of us don't.
Yeah, I cannot deny that even during grad school I really liked it when our books/profs would give us both definitions. The mathematical one and the concrete one. Sometimes it is hard to get an intuitive grasp of something from just a mathematical definition. is great, especially for non-specialists. But it only covers discrete-time systems. In the wider scope of things, I find that hugely limiting. I can think of several good reasons why the author more or less ignores continuous-time systems -- not the least of which is that the whole topic is generally meaningless if all you're doing is manipulating signals on a computer -- but I think a firm grasp of continuous-time systems (and the continuous Fourier transform) is essential to understanding aliasing, reconstruction, IIR filter design based on the bilinear transformation, etc.
Agreed. The aliasing section I read might have benefitted from a bit more grounding on continuous signals. In practice, though, my world right now is, in fact, entirely discrete, so I'm quite comfortable in my ignorance... :)
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