The exciting result is that a constant motion round a circle centered at the origin of the complex plane (real +ve to the right, imaginary +ve straight up) is the same as cos(wt) + i sin(wt) where w is rate of rotation. The ties complex numbers to sine/cosine, and with the wonderful realisation of the exp funxton or value e, exp(iwt) = cos(wt) + i sin(wt) As a result we can work in the complex plane where things are easier (exp is a nice function) znd then take the real part at the end. I do agree with Michael about the Princeton book of audio DSP. I started there (DSP not being in the Maths Tripos) and my students, both maths and non maths found it a good introduction. ==John ff (Not sure I am coherent about maths -- it is so exciting!) Quoting Anders Genell : > Well, sort of... > If complex number are on the vertical axis and real number are on the > horizontal, the resulting plane (called the z-plane) is a tool that is > essential for all matters of problems. A problem that is mapped onto that > plane (by using what is called z-transform) allows for its solution where > it otherwise would be impossible. > > Also, the m ost beautiful equation in the world is related to complex > numbers: > http://en.wikipedia.org/wiki/Euler's_identity > > Regards, > Anders > > > > On Mon, Apr 28, 2014 at 5:04 PM, Askwazzup wrote: > >> genell wrote >> > Complex numbers are usually denoted by an i or a j, which is defined as >> > i^2=-1 >> > A ordinary (not complex) number is either positive or negative, and if >> you >> > multiply such a number with itself it is always positive (-1 * -1 = 1 and >> > 1 >> > * 1 = 1), so there is no ordinary number that you can multiply by itself >> > and obtain a negative number. Enter the complex numbers. They seem >> strange >> > but are very useful for many somewhat advanced problems. One such problem >> > is the solution to the wave equation which governs the properties of >> sound >> > waves. >> > >> > Othogonal functions (such as Chebyshev as well as sin and cos) are >> > functions that in a simplified analogy are independant in the sam way >> that >> > width, length and height are independent. You can move straight up (e.g. >> > in >> > an elevator) without needing to move left, right or forward,backward. >> > Orthogonal functions are also useful as solutions to complicated >> equations >> > of motions, thermodynamics and not the least sound (or quantum physics, >> > which also uses the wave equation). So, in essence, chebyshev funtions >> are >> > good for e.g. physical modelling (e.g. make tones vary in a manner >> > descibed >> > by how heat spreads in a solid object) or for just having numbers varying >> > in a fashion more interesting than a straight line. >> > >> > John's example above is how to calculate numerical values of the >> chebyshev >> > function, and is (i assume) how it is implemented in the csound source >> > code. >> > Now I'll let John and his esteemed colleagues here point out all my >> errors >> > - I'm not a mathematician... >> > >> > Regards, >> > Anders >> >> Ah, i was mixing up complex numbers with irrational numbers.. >> >> Thanks, that cleared up some things (both paragraphs). So i guess part of >> why we need this is because the the sinusoid moves between values of - to + >> and so the calculation needs complex numbers? >> >> >> >> >> -- >> View this message in context: >> http://csound.1045644.n5.nabble.com/Csound-and-Math-tp5734740p5734757.html >> Sent from the Csound - General mailing list archive at Nabble.com. >> >> >> Send bugs reports to >> https://github.com/csound/csound/issues >> Discussions of bugs and features can be posted here >> To unsubscribe, send email sympa@lists.bath.ac.uk with body "unsubscribe >> csound" >> >> >> >> > > Send bugs reports to > https://github.com/csound/csound/issues > Discussions of bugs and features can be posted here > To unsubscribe, send email sympa@lists.bath.ac.uk with body > "unsubscribe csound" Send bugs reports to https://github.com/csound/csound/issues Discussions of bugs and features can be posted here To unsubscribe, send email sympa@lists.bath.ac.uk with body "unsubscribe csound"