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| Signals and systems class, why? |
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| T3sl4co1l:
--- Quote from: prophoss on October 22, 2020, 12:15:15 am ---Part of the reason I went the direction I did was to understand how things work from the bottom up. I have learned all about circuits from the electron up. --- End quote --- Have you? Excuse my skepticism -- Fourier transforms show up frequently in physics, especially the statistical mechanics that underlies semiconductor theory! Indeed, a transformation is incredibly useful when applied to repeating structures -- in this case, crystalline solids. The physics application is to integrate over a periodic structure, instead of trying to add up each and every 10^26 or so particles' contributions, surely a hopeless endeavor. ;D So you see terms like "phase space" or "k space", which plot wavenumber -- that is, spacial frequency (units of 1/length). The transform works just the same with respect to space, as it does to time (hertz == 1/time) -- anywhere you have a repeating structure with respect to some parameter, you can do a transform, and you'll probably find something meaningful. :) Even more fundamental than that, matter itself is made of waves (quantum mechanics); FT is often used in QM solutions, though the boundary conditions are often more complex, so that an approach from differential equations is necessary. (For example, the field in a hydrogen atom gives rise to discrete energy levels; but the orbital parameters (spin and angular momentum) give rise to spherical harmonics -- the FT of waves on a spherical shell.) Understanding wave-particle duality, is simply understanding the Fourier transform -- and once you have an intuitive understanding of wave mechanics, my friend, you can understand literally 90%, maybe 98% or more, of all phenomena in the universe, from the smallest subatomic to the largest galactic-cluster scale! --- Quote ---I asked my teacher and he just said so that we can analyze circuits. That didn't exactly answer my question and that is why I asked the same question here. --- End quote --- Speaking of analysis, and periodic structures, an interesting application of FT is the classic nerd snipe: https://xkcd.com/356/ By symmetry, the nearest-neighbor pair of points is easy to solve; but the knights-move pair shown here is surprisingly challenging. A typical solution is to consider the infinite array of nodes -- we're just doing nodal analysis like we would any other circuit -- and take the (2-dimensional) Fourier series of that entire system, with respect to position. The two points in question are the boundary conditions, and, crank crank crank, out pops a... factor of pi? :D Tim |
| Tomorokoshi:
For a small view into this topic, and to spend some time on a cold winter day, watch this series: |
| Electro Fan:
You might be too close to the trees to see the forest. A huge part of the forest is what we refer to as Information Systems. Information Systems are used to collect, distribute, and manage information. Information Systems are comprised of computer systems (that input, process, and output information) and networks (that move information, both with wires and wirelessly within and between machines). Information comes in various forms including text, sound, images, and video. In order to design and build and maintain information systems it is necessary to move information back and forth among the analog and digital realms. This requires ADCs, DACs, bandwidth, and much more to manage the signals that represent the information as it moves within and between machines and as the machines interface to the applications and humans they support. The ability to reliably make all this happen requires the concepts, math, and physics that are being taught in the lessons and projects in your class. You might think you are abstractly learning about frequency, amplitude, and phase but you are learning how to manage information comprised of many signals in the analog (continuously variable) and digital (binary) realms - all riding on the microscopic control of nature including electromagnetics. Unfortunately it is a common approach to teach university students about lots of parts without teaching the big picture of the systems that are made from the parts but you should accept that what you are learning is a bunch of powerful building blocks that will help you design the vegetation and trees that make the forest of information technology. Whether it’s signals in a circuit board like I2C or signals across the Internet with TCP/IP or any other type of signal it’s ultimately about the ability to reliably and ever more efficiently and cost-effectively transmit, process, and receive information. Almost everything in your signals class should fit into this framework if you zoom out to see and assemble the big picture. With signals machines and people get and give information and with information machines and people make decisions that lead to actions that drive productivity that drives profitability that creates the ROI that can be recycled back into R&D. How we harness signals is fundamental to much of technology across all industries (energy, transportation, healthcare, you name it) and throughout the private and public sectors of human society. Challenge your dynamic range to keep learning the details and the big picture at the same time. |
| prophoss:
Excellent stuff, thanks. |
| Benta:
--- Quote from: Electro Fan on October 23, 2020, 07:38:40 am ---Unfortunately it is a common approach to teach university students about lots of parts without teaching the big picture of the systems that are made from the parts but you should accept that what you are learning is a bunch of powerful building blocks that will help you design the vegetation and trees that make the forest of information technology. --- End quote --- Very true and well phrased. I remember the situation from my university days. In retrospect I understand the issue: the lecturers on the basic stuff (maths, physics, transformations etc.) were all theorists from the maths/physics faculty and would present ridiculous examples using farads, henrys etc. in what they were lecturing. All highly knowledgeable people with a deep knowledge in their field, but only in that (there's a limit to how much one person can handle) It wasn't until we got to the higher level courses that the lecturers were actually engineers with practical experience. From then on things just got better. But their math knowledge was not at the level of the maths/physics guys, just much more application oriented. Normal for all studies, I guess. |
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