I'm not sure that patents can be represented in any simpler form. They're a sort of programming language of their own, in that they (in theory) encode precise legal claims. The patent system has a specified "language" for encoding that information. Because the information is inherently complex and nuanced, there may not be a way to encode it more simply than in the "programming language" patents currently use.
To make an analogy, C is hard to read for newcomers. But has anyone designed a simpler, better language for describing direct, low-level manipulation of memory? Is it even possible to describe such operations in a simpler way than in C?
That being said, any given patent isn't necessarily written well. Within the confines of the "patent programming language," one can write well or poorly. So I'm not claiming that individual patents can't be edited for clarity. Rather, I'm claiming that the fundamental way patents are written--which is admittedly intimidating--may not admit of much simplification.
To revisit the above analogy, one can write bad C. One can even write deliberately obfuscated C.
That's because the patent you linked isn't for a detection algorithm, it's for Shazam's entire business model - namely, a way for a customer to on the fly transmit a segment of recorded music, have the music identified (the claims are agnostic to the method of detection), have the identified match fedback to the user, and also providing a method for the user to also purchase the identified track.
I mean, this is actually a bad patent to pick on, because in the scheme of things, it's actually really clear. Just read the claims.
If you want to look at what an algorithmic patent looks like, take a look at http://www.audiblemagic.com/pdf/US5918223.pdf this is a Patent cited by the Shazam patent as an example of a music matching algorithm. The bulk of the patent is basically a mix of block diagrams, pseudo-code, and background into the art. It's certainly not phrased like normal papers, but it's hardly 'mired'. It gets trickier when you get to the claims (which is actually the only parts that are binding), but if you read and understood the preferred embodiment (which I believe any reasonable literate and patient programmer can), it's nowhere as bad, as long as you understand that claims are nearly always structured from broadest to narrowest, with successive claims typically carving out specific 'implementations' of prior, broader claims.
To make an analogy, C is hard to read for newcomers. But has anyone designed a simpler, better language for describing direct, low-level manipulation of memory? Is it even possible to describe such operations in a simpler way than in C?
That being said, any given patent isn't necessarily written well. Within the confines of the "patent programming language," one can write well or poorly. So I'm not claiming that individual patents can't be edited for clarity. Rather, I'm claiming that the fundamental way patents are written--which is admittedly intimidating--may not admit of much simplification.
To revisit the above analogy, one can write bad C. One can even write deliberately obfuscated C.