You will find everything in this class super-hard if you just want to plug-and-chug.<\/p>\n<\/blockquote>\n
Having you plug the functions and numbers into the definitions and go work through the long math\u00a0is not the point of a signals-and-system class. In fact it’s quite the opposite:<\/p>\n
\nThis class tries to teach you all the tricks available to AVOID the tedious math.<\/p>\n<\/blockquote>\n
That means if you get the essence, the problems are\u00a0supposed to be easy. A hard-working mentality is the biggest obstacle to doing well in signals-and-systems. It’s not uncommon for professors to come up with ‘hard’ problems with dead easy solutions, which devastates and infuriates students enough that the ones who didn’t make it will hate it from the bottom of their hearts.<\/p>\n
\nFrom the previous posts, I repeatedly emphasized superposition as the #1 trick (property to exploit)\u00a0in this class. For most of the problems in the class, they are not arbitrary signals. Professors synthesize\u00a0them from\u00a0a common set of ‘building blocks’:<\/p>\n
\n
- Dirac-delta function <-> sinusoids (complex exponentials)<\/li>\n
- Rectangular waveform <-> sinc functions<\/li>\n
- (Occasionally) triangular waveform and ramps.\u00a0<\/li>\n
- (Laplace and z-transforms): decaying\/growing exponentials.\u00a0<\/li>\n
- (Controls) Heaviside step function<\/li>\n<\/ul>\n
Namely, they linearly combine (and window) the above building blocks to form the signals you see on exams.\u00a0They are basically testing whether you can break their synthetic waveform into the building blocks to apply the properties shown in the class.\u00a0<\/p>\n
\nNote that other than\u00a0exponentials (sinusoids are considered complex exponentials) and sinc, most of the building blocks are discontinuous functions that needs to be described mathematically. Here are 3 typical ways that I know:<\/p>\n
\n
- Split cases: the favorite for most textbooks and typed up solutions.\u00a0Drawing vector graphics (pictures) with LaTeX is such a huge pain.<\/li>\n
- Indicator function: only after you get savvy with breaking functions into partitions (over different time segments) or add up overlaying blocks. Just a heads up that not all professors like it (because most likely you’re breaking up the cases in a different way than theirs), but they are obliged to accept the answer as it’s technically complete and correct.\n
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