Fourier Analysis And Audio Synthsizing, An important assingnment |
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Fourier Analysis And Audio Synthsizing, An important assingnment |
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Dec 7 2009, 03:52 AM |
that's quite interesting, I just watched this video
Good luck with that This post has been edited by Daniel Realpe: Dec 7 2009, 03:54 AM -------------------- Visit my:
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Dec 7 2009, 12:05 PM |
I had that module at school but nothing like this guy on the video We just had to produce synthetic sounds by using software for it. No equations
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Dec 7 2009, 01:16 PM |
Please don't call me a nerd but I did study it 7-8 years back, even gave a paper on it .. but I'm SO glad i remember nothing of it !!
You should be able to find a lot of articles on it online.. Apologies im not much help now .. maybe a few years back I wouldve been All the best on the project !! -------------------- "If the need is deep, you WILL find a way , if it isn't, you'll find some excuse"
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Dec 7 2009, 01:24 PM |
Shhhh .. u shouldnt say that or you wont get any replies
And somehow the word fourier sent chills down my spine .. so I'm thinking i must've come very close to failing the test , -------------------- "If the need is deep, you WILL find a way , if it isn't, you'll find some excuse"
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Dec 7 2009, 02:09 PM |
Yeah, its a hard nut to crack
great post audiopaal |
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Dec 7 2009, 03:33 PM |
There are many approaches to synthesis but here are a few simple ideas and building blocks.
So called "Subtractive Synthesis" in the old analog syas consisted of generating a waveform then filtering it in various ways. Nowaday in the digital domain, you can still do the same thing in a few steps. Firstly, you need to generate a waveform. This is a simple mathematical function such as sin(). When you are working as a VST plugin, all you have to do is give the host a sequence of numbers that represent the amplitude of the waveform you want to create, once for each sample. So, a little math allows you to work out how the voltage evolves over time. For instance: 440hz is a particular pitch of the note A. You know that the sinewave needs to cycle every 1/440th of a second, and that your sample rate is for example 44,000 khz. 44,000/440 = 1000, so we want to split our wave into 1000 steps. Each complete wave consists of 360 degrees, so we divide 360 by 1000 to get .36. Now all we need to do is start at zero, and add .36 for each sample, and take the sine of that to get the amplitude - that gives you a basic sound. Of course you would want to read the keyboard and check which note is being asked for and then do the appropriate math as above but with a different frequency for each note - that is the basis of getting a sound out. You may need to do this for several notes at once if you are writing a polyphonic synth, and you would then need to mix the resulting signals together. That is simply a case of multiplying each by a scaling factor (to represent the overall loudness) and adding them. Next, you may want to filter, and that is where the fourier analysis comes in. Fourier analysis basically looks at a section of samples, for instance a second, or a millisecond, and performs a calculation that represents that data exactly, but broken down into frequency bands. When you write the algorithm you decide how many bands. If for instance you had 20 bands you would end up with a value for each band over that time period. Now we can play with frequency - pick a band and multiply it by a scaling factor and you have increased or decreased the amplitude of just that frequency. If you then subject it to a reverse fourier, you will end up with the original sound with an altered frequency balance - this is the basics of how digital EQs and graphic equalizers work. So now our simple synth has generated a sinewave and filtered it - Subtractive synthesis. The rest is just more complex math! -------------------- Check out my Instructor profile
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Dec 7 2009, 06:05 PM |
Thanks Andrew Nice input especially with the EQ. thats a really nice practical example to use. gives me the idea to talk about noisegating (which is eliminating to frequensies below a certain amplitude (a set value for the fourier coefficints) and filtering (removing a certain bandwith(frequency spectrum) of the signal?) Noise gating would simply be based on the amplitude of the original signal - no fourier transforms needed for that. Although some noisegates listen to specific frequency ranges for the signal, and yes, you would use a fourier transform to figure that out -------------------- Check out my Instructor profile
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Dec 7 2009, 08:43 PM
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Soo, let's deal with every question separately
What "amount of numbers" is Z+ ? dunno the english tranlation and what is an interger? Integer is ummm... a number without decimal point Like 1, 3, 10000 but 10.12 and pi are not integers Z+ is 1, 2, 3,... It is the same thing as natural numbers, only 0 is not included . So the first expression is just math for what we have assumed? am i right? i had been wondering how they got that expression for long First of all, as the guy points out in the video, the expression in general is not true. However, for example if the function is continious at the point x, then the formula will yield correct result at that point (he says more on this stuff in some later lecture, about convergence theorems). The formula itself is something that has to be proved, it did not appear "out of thin air" . Here, we're just assuming that it holds. those funktions on the right of his board (those that equals zero, and pi) should they be obvious (if thats the case, then ill look at them and understand them) or are they to advanced? they seem simple, but i might be wrong. that the same area i below the graph as the one over the graph It is pretty easy to see that those integrals are zero, you just need to use some trigonometric identities . can you explain how you can interchange(meaning switch?) the sigma (at least for finite amounts)? i can see som sort of realtion. that integrals sums up. and sigma writes a lot of sums .. You just use the property of integral - "integral of sum is sum of integrals" Arghhh.. don't have latex here Here: think i have used something like that, by aproximation an unknow funktion with a lot of "tangets" is that the word? by using Eulers method (which is slow, and has to be done in small steps) therefore another method the "runge-kutta method" can be used (4 times as quick) but i can remember the procedure. I remember it as difficult, but once u got the method it went pretty fluidly To be honest I've never done numerical methods or any approximation algorithms But isn't Euler's method the method for solving differential equations? |
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