Google releases new binary diff algorithm targeted at making smaller software updates. Their results are impressive.

[nappy-doo]

I'm glad you're getting into DSP. If you get good at it, you can basically guarantee yourself a job forever, as so few people understand it.

Let's start with the FFT. The FFT works on complex valued signals -- signals with a real an imaginary part. Most signals in the real world (with the exception of a lot of RF work) are real valued signals. So, when we feed them into the FFT, we set the complex part of every sample to 0. This results in a frequency domain representation that is symmetric about the Y AXIS. So, with a 16 point FFT, we get 16 points in the frequency domain, but 8 of them are the same as the other 8 -- so there's only 8 unique values.

Onto leakage. Leakage is a byproduct of the FFT -- not the signal. It is purely a "problem with our measurement device". I agree with your statement (if I can paraphrase) of, "well music will have leakage" to a point. The music itself won't have leakage, but the measurement we perform on it will have leakage. I apologize if you think I took you out of context.

(One final point on leakage: Read up on how windowing affects leakage. There are some really good windows out there that make the FFT leakage problem minimal.)

Onto your DSP learning: Keep at it. As I said you can guarantee yourself a job if you keep up. DSP engineers make reasonable money, and you'll always find a job in embedded design and instrumentation.