Fourier Synthesis is a small, easy to use application, specially designed to enable you to adjust the first seven coefficients of the Fourier series (both for the cosine and the sine terms). In addition, a few predefined wave forms can be selected.
Fourier synthesis represents the summation of cosine and sine waves at different frequencies and amplitudes.
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Fourier Synthesis For Windows
A Fourier series is defined by the formula below:
Where and are the Fourier coefficients, which are found by successive approximations.
The Fourier coefficients can be uniquely calculated from the envelope and the amplitude of the excitation function.
A Fourier series can be considered as the superposition of sine waves of the form
The first approximation to the Fourier coefficients is given by:
are the Fourier coefficients.
The latter can be found by the following relation, derived from the above relation for the first approximation to the Fourier coefficients:
Once the first seven coefficients of the cosine and the sine components are determined, Fourier synthesis gives the coefficients of the following expansion:
By comparing the latter expansion with the previous one, it can be observed that and is the envelope of the excitation and sine components.
At last, after this summary you can see the link between the coefficients of the Fourier series and the first seven coefficients of the Fourier Synthesis of the excitation wave function, as reported in the following table:
Input File of Fourier Synthesis
Fourier Synthesis in the input file of the above example is as follows:
— Sine model:
— Cosine model:
— Sine model:
— Cosine model:
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The first part of the application consists of three main windows, called the Tool Bar, the Database and the Display. The Tool Bar window (see picture) contains the buttons and entries that are used to adjust the frequency, amplitude and number of waves, chosen in the Database window, the wave forms and the time between waves.
The Display window contains a graph where you can view the calculated Fourier series (see figure).
Fourier Synthesis Tips:
You may want to increase the frequency and number of waves, to provide the best fit to your audio wave form, however the only the first seven coefficients (coefficients a to h in picture) can be adjusted.
Each of the wave forms is centered on 1 second in the Display window.
All the items in the Tool Bar, Database and Display windows are editable.
If you find your audio recording is flat, you can apply a lot of correction using Fourier Synthesis.
Fourier Synthesis has been rated as a “pro” application by PCWorld Magazine.
In the entry “What’s New in Windows Media Player 8, Windows Media Player 9 Beta”, published in Windows Media Magazine, March 2002 issue (WMM03), version 8.0 of the Windows Media Player was rated as “excellent”, while version 9.0 Beta 1 was rated as “good”.
Category:Windows multimedia software
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What’s New in the?
Simplify the complexity of a Fourier Series by allowing you to adjust the first seven coefficients of the Fourier Series using the “Waveform” window. Use the “Coefficient” window to change the number of coefficients, their amplitudes and frequencies.
Fourier Series is an extremely useful technique for creating complex wave forms. By generating sinusoidal and cosinusoidal terms, the complex wave form can be built up. This application will allow you to adjust the first seven coefficients of the Fourier Series. A Fourier Series is usually built up by Fourier Synthesis. This is a process of building up a Complex Wave Form or Complex Wave With by adding Cosinusoidal and Sine Waves at different frequencies and amplitudes. These waves are separated by using the Frequency Range and Amplitude windows. Finally, you can use the “Fourier Series” window to put together the different waves to form a complex wave form. You can check the resultant wave form by dragging the cursor from one end of the complex wave form to the other.
Use the “Waveform” window to adjust the first seven coefficients of the Fourier Series. You will be able to select the number of coefficients to use and the frequencies at which each coefficient will vary. You can use the “Cosine” window to adjust the cosine components and the “Sine” window to adjust the sine components.
Can be used to record macro files. Requires RT-Tower 1.3 or later.
Simple 3D Background
Option to add a 3D background behind the synthesis window.
Simple 3D Background Description:
This application has three features, each of which is described below.
Simple 3D Background can be used to add a 3D background behind the synthesis window. With this background enabled, you can click and drag the cursor away from the synthesis window to bring a selected part of the screen into focus.
3D Bg Monitor
3D Bg Monitor is a small utility, specially designed to let you view a 3D transparent background behind the interface and help you see what is being synthesized when you are playing around in the parameter windows. You will need the RT-Tower 1.3 or later to use this feature.
Simple 3D Background Description:
With this feature enabled, you will see a 3D transparent background behind the interface, and any selected parts of the
Processor: Dual Core CPU 3GHz or higher
RAM: 1GB or higher
OS: Windows 7 or later.
DirectX: Version 9.0c
Network: Broadband Internet connection
Storage: 500MB or higher
The minimum system requirements for the game are:
Processor: Intel Core 2 Duo
OS: Windows 7 or later