What is Reddit's opinion of Signals and Systems?

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If you want something introductory and accessible on both the discrete and continuous Fourier transform (and Laplace and z), I can recommend Oppenheim & Willsky.

I always found the text very understandable and the notation more tight and self-consistent than in most textbooks -- I don't really understand the negative reviews on Amazon. I wouldn't be surprised if they were actually from competing publishers.

Full disclosure though: I got through this text with the aid of a really great prof, so I used it mostly to reinforce concepts I more or less already understood from lecture. But also it is one of the (very) few textbooks I actually remember in a positive light.

Amplitude of displacement is the thing a microphone measures**: sound waves create a time variable pressure front which displaces the diaphragm in the microphone. The pitch (frequency) and timbre (simultaneously occurring frequencies) of the signal can be recovered using the Fourier Transform. If you are unfamiliar this technique this is a reasonable introduction, though for a thorough treatment of the subject look to Oppenheim and Willsky.

Translation: it’s a totally reasonable tattoo that does capture the information (albeit at low resolution) of the sound.

** I’m not a expert on the operation of every type of microphone in existence. I am leaving space for the possibility that a microphone exists which does something completely different but I am totally unaware of it and it’s mechanism of operation.

Oppenheim gives a really great explanation for the motivation and derivation behind the Laplace and Fourier Transforms in is book Signals and Systems.

I know he also has some lectures on MIT Open Courseware, but I haven't seen them. I've heard good things.

I was really happy to have read that book before my Diff Eq class. Because that text just threw the Laplace Transform at us like it was handed down from the gods.

Hmm if you don't have a solid background on probability I'd start with that. Then it might be worth it to look into the basics of stochastic processes and review linear algebra. In a week studying an hour a day you can probably get it covered, more if you want to do many exercises. Do you know the basics of Linear Systems theory too? They're probably worth it.

Then you should be ready to pick up any basic image processing book. Look for ones containing on transforms and linear filtering that should be a good start. Once you're familiar with the aformentioned math basics those books are quite easy to follow. This theory gives great insights on the basics of removing noise from images, compressing, etc.

I actually don't know which books to recommend. I learn mostly from classes, and looking into random books now and then. If I have to recommend (and if you have access to a library):

http://www.amazon.com/Signals-Systems-Edition-Alan-Oppenheim/dp/0138147574

http://www.amazon.com/Introduction-Linear-Algebra-Fourth-Edition/dp/0980232716

http://www.amazon.com/Introduction-Probability-Edition-Dimitri-Bertsekas/dp/188652923X/ref=pd_sim_14_15?ie=UTF8&refRID=1D5V9Q9C92FCMAWJCRKM

This is what I use: http://www.amazon.com/Signals-Systems-2nd-Alan-Oppenheim/dp/0138147574

~~Also add any Signal Processing Book in there. That will give you the sense of the level of math required.~~

Edit: After reading some comments, That's a bad choice. Go with an Intro to Electric Circuits book to help refine your math. Try to get the one that has no or little calculus in it. I used this one during my circuit theory class. It might be too much, but it does challenge your algebraic and pre-calculus skills.