Fourier Synthesis

Fu-Kwun Hwang

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Fourier Synthesis

« on: January 29, 2004, 06:04:29 PM »

Registed user can get files related to this applet for offline access.
If java program did not show up, please download and install latest Java RUN TIME
or

How to play:

Left click and drag the [ball, green] circles to change the magnitude of each Fourier functions [Sin nf, Cos nf].

Right click the mouse button to change the magnitude between 0 and 1.0

Click Play to turn on the sound effect, Stop to turn it off.

The coefficient of sin(0f) is used as amplification factor for all modes.

(Use it to change the sound level)，the coefficient of cos(0f) is the DC component.

Click the checkbox at the top(after stop) will show square the the amplitude of the signal.

The default value for base frequency is f=2200Hz, you can change it from the TextField. (20 < f < 2000). The ear is 1000 times more sensitive at 1kHz than at 100Hz.

	frequency range
	speech	song
adult male	80-240	up to 700
adult female	140-500	up to 1100

How to play:

Left click and drag the [ball, green] circles to change the magnitude of each Fourier functions [Sin nf, Cos nf].

Right click the mouse button to change the magnitude between 0 and 1.0

Click Play to turn on the sound effect, Stop to turn it off.

The coefficient of sin(0f) is used as amplification factor for all modes.

(Use it to change the sound level)¡Athe coefficient of cos(0f) is the DC component.

Click the checkbox at the top(after stop) will show square the the amplitude of the signal.

The default value for base frequency is f=2200Hz, you can change it from the TextField. (20 < f < 2000). The ear is 1000 times more sensitive at 1kHz than at 100Hz.

	frequency range
	speech	song
adult male	80-240	up to 700
adult female	140-500	up to 1100

Registed user can get files related to this applet for offline access.
If java program did not show up, please download and install latest Java RUN TIME
or


« Last Edit: September 23, 2008, 12:18:41 AM by Fu-Kwun Hwang »	Logged

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topic17

« Reply #1 on: January 30, 2004, 07:44:50 AM »

Subject: java and sound
Date: Fri, 12 Sep 1997 14:19:41 +0800
From: "Harlan W. Lefevre" <hwl@solconch.uoregon.edu>
To: hwang@phy.ntnu.edu.tw
Dear Dr. Hwang,
I have used several of your applets in my physics courses here.
And I asked our people to mirror your site here for fast access.
The applets are really useful. Thank you.
I usually roll an NCD Xterminal into my classroom and use a remote Sun as server.
Unfortunately java only writes audio to /dev/audio and Xwindows won't deliver the audio to the Xterm.
So the beauty of your Fourier Synthesis program is largely lost when one can't do the sound.
Do you have a solution to this problem?
Sincerely yours,
Harlan Lefevre


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topic17

« Reply #2 on: February 28, 2004, 02:35:53 PM »

Hello,

I've just played around with your Fourier-Synthesis-Applet which realy is great. Just the best I've found in the net :-)
I could use it very well for my students. How can I let it run an my stand alone PC?
It would be great for me, if I could let it run until thuesday.
Please, can you help me?
Thanks you

Have a nice weekend

Daniel

daniel.forrer@swissonline.ch


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topic17

« Reply #3 on: September 06, 2004, 07:55:24 PM »

Ditto!
I could really do to have this run offline on my PC.
Ta!


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Spirit

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Posts: 3

topic17

« Reply #4 on: October 26, 2005, 07:56:39 PM »

Hi,

I am an A-level student, studying further mathematics, and physics and have seen 'fourier series' listed as a module in one of the university prospectus, by chance i came accross this and thought i'd ask if anyone would mind giving a brief expllanation to what it actually is. What can i say, it has sparked my curiosity!

Thank you for reading.


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Fu-Kwun Hwang

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Posts: 1162

topic17

« Reply #5 on: October 27, 2005, 07:11:15 AM »

All the wave (no matter what kind of shape) can be decompositive into series of wave with the same base frequency(or period).
For example: You can look at sound wave of your voice with oscilloscope or recored with computer.
You know everyone sound differently. But it not easy to find out the difference from the waveform.
If we make a Fourier transform of the sound wave, i.e., calculate the weighting of each frequency component.
Then, the ratio of those components are characteristic of each person.
So it can be used as voice recognition.

You should be able to find detail information from physics textbook.


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Spirit

Newbie

Posts: 3

topic17

« Reply #6 on: October 27, 2005, 07:48:19 AM »

Thank you very much for your help and time. Cheesy


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chef

Newbie

Posts: 3

Hi i need help

« Reply #7 on: May 21, 2006, 04:32:00 AM »

Hey so i am doing this lab for my school and i don't know how to put sound in it so i was thinking maybe someone could help thanks!!!!!!!!!!!!!!


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Fu-Kwun Hwang

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Posts: 1162

topic17

« Reply #8 on: May 21, 2006, 09:55:57 AM »

Try to check out JSresource.org.


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Fu-Kwun Hwang

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Posts: 1162

Re: Fourier Synthesis

« Reply #9 on: February 28, 2007, 10:50:20 PM »

The following copy of email messages from one of the user:
**********************************************

Quote

Dear Sirs,

Congratulations for the excellent page http://www.phy.ntnu.edu.tw/java/sound/sound.html

I have 3 questions

1.Any periodically repeating wave - however complex its shape is - can be resolved into sine and cosine waves. okay. It is possible to resolve any complex shaped signal similarly into sines and cosines, even if it is not periodically repeating - considering wave length as infinity and approximating..
Now consider a recorded wave form of a song (amplitude vs time) lasting say 5 minutes. This wave when resolved into component sines and cosines shall contain a lot of harmonics. Each with its specific frequency. If all the important components are selected and replayed the sound produced will be an approximate reproduction of the original sound. This is done posteriori.
Now consider a small intervel of time. say one second. after say 2 minutes from the start. The portion of the signal in this small duration if seperately considered and resolved (done in the current running time) the condition of the constituent harmonics will be same as that of the original signal of 5 minute duration considered for this particular one second.

But while we do this, we donot know what is going to happen after say the 3rd minute. But the happenings after the 3rd minute (or all the instants after the 2nd minute and one secondth instant) decide what should be shape of this particular one second - being part of the larger 5 minute duration. There is an apparent anomaly of having the future already getting fixed or a future event determining the present condition. What is the wrong in this argument?

Please check out the following URL :Fourier Analysis of Time Series

It is just a superposition of linear signal. For different time interval, the sume of the contribution is not the same. It is a relation between two different representations. It is not one of them determined another one.

Quote

2. High level languages like Basic etc. have words for sound. But can, at a time, produce only one sound of only one frequency. A complex wave after resolving into its components can be heard faithfully only if the multiple frequencies weighted with its respective amplitudes are heard simultaneously. In your programme how it is achieved?

The program was written many years ago with JDK1.0.2. At the time, it was an undocumented java library (I found out how to generate single frequency sound with java code from the web. However, I can not remember where I found it).

Quote

3. The amplitude Vs time wave form of a song (vocal) if resolved into components, will contain what range of harmonics?
Thanking you,

Mathematically, there are infiniite number of possible frequency. However, we can not hear it if it's requency is not within 20Hz-20000Hz.


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