If you want your graph to have a title, enter it here. This is optional. If you leave this box empty, a suitable title is provided automatically. The length of the title is limited to 80 characters maximum. © 2025 Sooeet.com All rights reserved

Name for horizontal space-time axis (optional):

Name for Horizontal Space-Time Axis

If you want your graph to have a name for the horizontal space-time axis, enter it here. This is optional. If you leave this box empty, a suitable name for the horizontal space-time axis is provided automatically. The length of the name for the horizontal space-time axis is limited to 80 characters maximum. © 2025 Sooeet.com All rights reserved

Name for horizontal frequency axis (optional):

Name for Horizontal Frequency Axis

If you want your graph to have a name for the horizontal frequency axis, enter it here. This is optional. If you leave this box empty, a suitable name for the horizontal frequency axis is provided automatically. The length of the name for the horizontal frequency axis is limited to 80 characters maximum. © 2025 Sooeet.com All rights reserved

Name for vertical space-time axis (optional):

Name for Vertical Space-Time Axis

If you want your graph to have a name for the vertical space-time axis, enter it here. This is optional. If you leave this box empty, a suitable name for the vertical space-time axis is provided automatically. The length of the name for the vertical space-time axis is limited to 60 characters maximum. © 2025 Sooeet.com All rights reserved

Name for vertical frequency axis (optional):

Name for Vertical Frequency Axis

If you want your graph to have a name for the vertical frequency axis, enter it here. This is optional. If you leave this box empty, a suitable name for the vertical frequency axis is provided automatically. The length of the name for the vertical frequency axis is limited to 60 characters maximum. © 2025 Sooeet.com All rights reserved

Enter list of User-Data samples:

List of User Data Samples

To perform the Fast Fourier Transform on your data, enter a list of numbers, with each number in the list separated from the next number by a blank-space or a comma. Format of Input Data Your input data can be entered as a list of numbers, as in the following examples: s1, s2, ... sN-1, sN s1 s2 ... sN-1 sN where N is the total number of data samples. Fast Fourier Transform Your data samples are processed by a discrete digital version of the continuous Fourier Transform. The discrete or digital version is called a Fast Fourier Transform, or FFT. Number of User Data Samples For best results, the number of samples in your input list should be a power of 2, such as 1024, 4096, 32768, upto a maximum of: 2^18 = 262144 Each number in your data sample list should be in one of the following formats. You can mix the formats: Integer: 31457 Decimal: +9862.314 Scientific Notation: 2.7E+2 Your list should look like one of these: 2, 2.7E+2, 2.718, 0.35e03, ... 2 2.7E+2 2.718 0.35e03 ... © 2025 Sooeet.com All rights reserved

Enter sampling rate:

Sampling Rate of Input Data

Sampling Rate Enter the sampling rate of the input data, in Hertz, (i.e. samples per second.) Sampling Rate Format The sampling rate should be in one of the following formats: Integer: 8820 Decimal: 44100.9 Scientific Notation: 1.1025e04 Nyquist–Shannon Sampling Theorem The Nyquist–Shannon theorem is one of the principal elements of information theory. The theorem states that a bandlimited analog signal can be completely reconstructed via the inverse Fourier transform, only if the signal is sampled at a rate that exceeds 2F, where F is the highest frequency contained in the original signal. Therefore, when sampling a bandlimited analog signal intended for processing via the FFT, the sampling rate should exceed twice the maximum frequency that you wish to resolve with the FFT. For example, to capture a 3 Kilohertz frequency component in the original analog signal, the analog signal must be sampled at a rate that exceeds 6 Kilohertz. Limitations of the Fast Fourier Transform For best results, the number of samples in your input data list should be a power of 2, such as 1024, 4096, 32768, upto a maximum of: 2^18 = 262144 Due to the internal workings of the FFT, data sample lists larger than 2^18 require significant amounts of computer processor and memory resources, and are disallowed as of this writing. © 2025 Sooeet.com All rights reserved

User-Data Examples (optional):

User-Data Input Selector

This selector allows you to choose from several User-Data input signals, and to process your selected input signal with the Fast Fourier Transform (FFT). These User-Data input signals are provided as examples of real-world signals that are often processed by the FFT, including musical instrument sounds, human voices in audio recordings, and other signals. © 2025 Sooeet.com All rights reserved

Number of data samples:

Number of Data Samples

This output field displays the number of data samples that where processed by the Fourier transform. If you provided an input list of data samples, the number of data samples displayed here should coincide exactly with the length of your input list. If it does not coincide, it is because your input list contained blank elements, such as: 1, 2, 3, , 5, 6 Calculator Memory You can save the result of this output field in the Calculator Memory, then use the saved result as input for other converters and calculators anywhere on the website. To save this result, click inside the output field, and then click the button entitled Save in the Calculator Memory. See the Calculator Memory for more details. TIP: Precision of the calculator is 15 significant digits, from left to right. Digits after the 15 left-most digits, are not significant. Numeric Range of the calculator is: +1.797e+308 ... -1.797e+308 +1.000e-311 ... -1.000e-311 © 2025 Sooeet.com All rights reserved

FFT real output:

FFT Real Output

When you press the Get FFT Data button, this output field displays the contents of the Real-FFT result, as a list of numbers separated by blank spaces. Calculator Memory You can save the result of this output field in the Calculator Memory, then use the saved result as input for other converters and calculators anywhere on the website. To save this result, click inside the output field, and then click the button entitled Save in the Calculator Memory. See the Calculator Memory for more details. TIP: Precision of the calculator is 15 significant digits, from left to right. Digits after the 15 left-most digits, are not significant. Numeric Range of the calculator is: +1.797e+308 ... -1.797e+308 +1.000e-311 ... -1.000e-311 © 2025 Sooeet.com All rights reserved

FFT imaginary output:

FFT Imaginary Output

When you press the Get FFT Data button, this output field displays the contents of the Imaginary-FFT result, as a list of numbers separated by blank spaces. Calculator Memory You can save the result of this output field in the Calculator Memory, then use the saved result as input for other converters and calculators anywhere on the website. To save this result, click inside the output field, and then click the button entitled Save in the Calculator Memory. See the Calculator Memory for more details. TIP: Precision of the calculator is 15 significant digits, from left to right. Digits after the 15 left-most digits, are not significant. Numeric Range of the calculator is: +1.797e+308 ... -1.797e+308 +1.000e-311 ... -1.000e-311 © 2025 Sooeet.com All rights reserved

FFT/IFFT graph data output:

FFT/IFFT Graph Data Output

When you press the Get FFT Data button, this output field displays the current FFT/IFFT graph data, as a list of numbers separated by blank spaces. The graph data that is output depends on the selection in the FFT Y-Axis Magnitude menu, and on the mode set by the FFT/Inv-FFT button, and on the mode set by the Fold ω / Un-Fold ω button, and on whether User-Data or Program-Data is currently selected. The FFT/IFFT Graph Data Output can be used to connect the output of one FFT operation to the input of a second FFT operation. Simply copy and paste the FFT/IFFT Graph Data Output to the User Data input. Then, in the Sampling Rate input field, enter the size of the output buffer from the first FFT, and finally, click the User Data button. Cepstrum Analysis The technique of using the output of one FFT operation as the input of a second FFT operation is used for example in Cepstrum analysis. Cepstrum analysis or Cepstral analysis attempts to detect periodic signals that may occur in the frequency spectrum of a time-domain or spatial-domain signal, or specifically, in the FFT of a time-domain or spatial-domain signal. Calculator Memory You can save the result of this output field in the Calculator Memory, then use the saved result as input for other converters and calculators anywhere on the website. To save this result, click inside the output field, and then click the button entitled Save in the Calculator Memory. See the Calculator Memory for more details. TIP: Precision of the calculator is 15 significant digits, from left to right. Digits after the 15 left-most digits, are not significant. Numeric Range of the calculator is: +1.797e+308 ... -1.797e+308 +1.000e-311 ... -1.000e-311 © 2025 Sooeet.com All rights reserved

y y y y

x y x y

– ω +

+ ω –

Control Buttons

User Data Button Click this button to perform the Fast Fourier Transform (FFT) using data from the User Data source. The FFT calculator will render a graph in the frequency domain, or in the time-domain, depending on which of those modes is currently active. Program Data Button Click this button to perform the Fast Fourier Transform (FFT) using data from the Program Data source. The FFT calculator will render a graph in the frequency domain, or in the time-domain, depending on which of those modes is currently active. Get FFT Data Button When you click the Get FFT Data button, the three FFT output fields display the current FFT/IFFT graph data, as lists of numbers separated by blank spaces. The three FFT output fields are: FFT Real Output FFT Imaginary Output FFT/IFFT Graph Data Output yyyy Radio Button Sets the data format for the FFT results that are retrieved when you click the Get FFT Data button. When this radio button is set, the FFT results that are retrieved contain y-values only. The x-values are implied. xyxy Radio Button Sets the data format for the FFT results that are retrieved when you click the Get FFT Data button. When this radio button is set, the FFT results that are retrieved contain x-values and y-values as x y pairs. – ω + Radio Button Sets the data format for the FFT results that are retrieved when you click the Get FFT Data button. When this radio button is set, the FFT results that are retrieved are organized so that the most-negative frequencies are given first, then the least-negative frequencies are given, then the zero frequency is given, then the least-positive frequencies are given, and finally the most-positive frequencies are given. + ω – Radio Button Sets the data format for the FFT results that are retrieved when you click the Get FFT Data button. When this radio button is set, the FFT results that are retrieved are organized so that the zero frequency is given first, then the least-positive frequencies are given, then the most-positive frequencies are given, then the most-negative frequencies are given, and finally the least-negative frequencies are given. This is the natural format of the FFT results. Screen Shot Button This button allows you to save a JPEG image of the currenly displayed graph, to your computer. Fold ω / Un-Fold ω Button This button folds or unfolds the x-axis of the frequency-domain spectrum, so that the negative frequencies are shown or hidden. Zoom In Button This button enables and disables Zoom In mode. When enabled, the mouse cursor changes to the "+" cursor, and you can click and drag on the graph area to zoom in. Zoom Out Button This button enables and disables Zoom Out mode. When enabled, the mouse cursor changes to the "-" cursor, and you can click and drag on the graph area to zoom out. Show Points / Hide Points Button This button displays the individual data samples on the time-domain graph, and on the frequency-domain graph. When the button is clicked, it changes to the Hide Points mode. Clicking the button in the Hide Points mode, hides the individual data samples. Inv-FFT / FFT Button This button runs the FFT (forward Fast Fourier Transform), or the IFFT (inverse Fast Fourier Transform), on the input data. © 2025 Sooeet.com All rights reserved

How to use the FFT calculator:

How to Use the FFT Calculator

The Fourier Transform Calculator performs FFT and IFFT transforms of input data, and displays time-domain, spatial-domain and frequency-domain representations of that data in graphical form. The Fourier Transform Calculator accepts three different sources of data. Source 1: Program Data The first source of data for the Fourier Transform Calculator is the time-domain Program Data source. A large number of Program Data objects are programmed into the calculator. Any Program Data object may be loaded by the user whenever that data object is required. The menu entitled "Program-Data" provides the list of all the available time-domain Program Data objects. To use this source of data, select one of the Program Data objects from that menu. The Fourier Transform Calculator will automatically process the selected Program Data object via the FFT, and display the frequency-domain spectrum, or the time-domain function, for that Program Data object. The menu entitled "FFT Number of Samples" applies only to the Program Data objects. Use that menu to choose the number of samples that are taken from the Program Data object currently selected in the menu entitled "Program-Data". Source 2: User Data The second source of data for the Fourier Transform Calculator is User Data. This is simply a list of time-domain data samples that the user provides to the calculator for processing via the FFT. To employ the User Data source, enter a list of time-domain data samples in the first input box, then enter the sampling rate of that data in the second input box, and click the User Data button. The Fourier Transform Calculator will automatically process your input data via the FFT , and display the frequency-domain spectrum, or the time-domain function, for the given User Data. The number of samples is automatically obtained from the list of data samples you provide. For best results in the FFT, you should provide a number of data samples that is a power-of-2, such as 256, 512, 1024, 2048, 4096, 8192, etc. However, if the length of your data list is not a power-of-2, the calculator will automatically zero-pad your input data to the next higher power-of-2. Source 3: User Data Examples The third source of data for the Fourier Transform Calculator is User-Data Examples. Many examples of User-Data are provided in the selector box entitled "User-Data Examples". To employ the User Data Examples source, simply select one of the items in the selector box entitled "User-Data Examples". The Fourier Transform Calculator will automatically process your selected User-Data example via the FFT , and display the frequency-domain spectrum, or the time-domain function, for your selected User-Data Example. How to Change the Source of Data To change to the User Data source, simply enter a list of data samples in the first input box, enter the sampling rate of that data in the second input box, and click the User Data button. To change to the Program Data source, simply click the Program Data button, or select a new Program Data object from the menu entitled "Program-Data". To change to the User Data Examples source, simply select one of the items from the selector box entitled "User-Data Examples". The FFT calculator will operate on the newly selected data source until you change to another data source. Graphing Mode The FFT calculator uses Sooeet Graph v 1.5F to plot the frequency-domain spectrum of the Fourier Transformed output, and the time-domain representation of the input data. Sooeet Graph v 1.5F is preset to "Automatic" grid mode. In that mode the x and y grids are automatically scaled to fully contain the frequency-domain spectrum of the Fourier Transformed output, or the time-domain representation of the input data. Decimal and Scientific Notation The FFT calculator automatically outputs in Decimal Notation, or in Scientific Notation, depending on the magnitude of the input data, and depending on the magnitude of the Fourier Transform output in the frequency-domain. © 2025 Sooeet.com All rights reserved

FFT frequency domain output:

FFT Frequency Domain Output

FFT Frequency Domain Spectral Graph The result of FFT processing is a frequency domain spectrum, diplayed as a graph. The peaks that may appear in the frequency domain spectral graph indicate the presence of important frequency components in the original analog signal. X-Axis of the Spectral Graph The x-axis represents frequency in cycles per second, or in cycles per unit length. However, the actual units of the x-axis depend on the nature of the input data. For example, if the input data represents an electrical signal or a mechanical signal, the units of the x-axis are cycles per second, or Hertz, but if the input data represents a row or a column from a 2-dimensional image, then the units of the x-axis are cycles per unit of length. Y-Axis of the Spectral Graph The y-axis represents the magnitude of the frequency components in the spectral output of the FFT. The magnitude of the frequency components can be expressed in either of two ways: Amplitude-Units-Peak Decibels of Amplitude-Units-Peak Amplitude-Units-Peak (Apk) This is a direct linear representation of the FFT output magnitude. Use Apk when you need to see the actual magnitude of large spectral components. However, when using the Apk scale keep in mind that small spectral components are likely burried in the presence of much larger spectral components. Amplitude-Units-Peak (Apk) is calculated as follows: Apk = Sqrt( Re-FFT()^2 + Im-FFT()^2 ) / N Decibels of Amplitude-Units-Peak (dBV) This is a logarithmic (log base-10) measure of the ratio of the FFT output Amplitude-Units-Peak to a reference value of 1-Amplitude-Unit. Use dBV when you need to easily see small spectral components in the presence of large spectral components. dBV is calculated as follows: dBV = 20 log( Apk / 1-Amplitude-Unit ) © 2025 Sooeet.com All rights reserved

FFT y-axis magnitude:

FFT Frequency Domain Y-Axis Magnitude

The Y-Axis Magnitude Options The y-axis of the frequency domain graph is set to represent magnitude in decibels, as discussed above. However, you can change that setting via this menu: FFT Y-Axis Magnitude Menu This menu has the following options: Apk = Sqrt( R^2 + I^2 ) / N Square root of the sum of the squared Real component (R) of the FFT result and the squared Imaginary component (I) of the FFT result, divided by the number of samples in the FFT input buffer (N). Amplitude-Units-Peak (Apk) is a direct linear representation of the FFT output magnitude. Use Apk when you need to see the actual magnitude of large spectral components. However, when using the Apk scale keep in mind that small spectral components are likely burried in the presence of much larger spectral components. Sqrt( R^2 + I^2 ) Square root of the sum of the squared Real component (R) of the FFT result and the squared Imaginary component (I) of the FFT result. Real^2 + Imag^2 The sum of the squared Real component (R) of the FFT result and the squared Imaginary component (I) of the FFT result. Real^2 The square of the Real component of the FFT result. Imaginary^2 The square of the Imaginary component of the FFT result. Real The Real component of the FFT result. Imaginary The Imaginary component of the FFT result. dBV = 20 log( Sqrt( R^2 + I^2 ) / N ) The decibel of the square root of the sum of the squared Real component (R) of the FFT result and the squared Imaginary component (I) of the FFT result, divided by the number of samples in the FFT input buffer (N). This is a logarithmic measure of the ratio of the FFT output Amplitude-Units-Peak (Apk) to a reference value of 1-Amplitude-Unit. Use dBV when you need to easily see small spectral components in the presence of large spectral components. 20 log( Sqrt( R^2 + I^2 ) ) The decibel of the square root of the sum of the squared Real component (R) of the FFT result and the squared Imaginary component (I) of the FFT result. 20 log( R^2 + I^2 ) The decibel of the sum of the squared Real component (R) of the FFT result and the squared Imaginary component (I) of the FFT result. 20 log( Real^2 ) The decibels of the squared Real component of the FFT result. 20 log( Imag^2 ) The decibels of the squared Imaginary component of the FFT result. Norm(20 log( ... )) Similar to the above decibel values, but normalized so the peak value is at 0 dB. Phase( FFT() ) in radians Phase spectrum in radians, derived from the FFT output. © 2025 Sooeet.com All rights reserved

FFT window functions:

The Window Functions

FFT Window Functions¹ The FFT can pre-multiply the input time-domain data with any of several window functions. Window functions are commonly used in signal processing to reduce the "spectral leakeage" caused when the FFT is applied to a non-periodic finite-length sequence of input data. To apply a window function, simply select one of the window functions from the menu entitled "FFT Window Function". The selected window function is automatically applied to the sample data prior to the FFT. Program-Data Input time-domain data for the FFT can be supplied as a Sample List of User Data, or by one of the Program Data objects available in the menu entitled "Program-Data". That menu contains an assortment of preset Program Data objects, including all of the window functions. The window functions are provided in the menu entitled "Program-Data", so that users may analyze the time-domain and frequency-domain characteristics of the window functions. However, to pre-multiply a window function with FFT input data, use the menu entitled "FFT Window Function" to select a window function of your choice, rather than the menu entitled "Program-Data". The FFT Window Functions The following window functions are provided: Rectangle, Triangle, Hann (aka Hanning), Raised Cosine (1-4), Hamming, Riesz, Tukey, Riemann, de La Vallee Poussin (aka Parzen), Bohman, Poussin, Hanning-Poussin, Cauchy, Cosine, Gaussian, Kaiser-Bessel, Blackman Exact, Blackman, Blackman-Harris, Lanczos, Bartlett, Bartlett-Hann, Nuttall, Blackman-Nuttall, Flat Top . References: [1]
Harris, Fredric J. "On the Use of Windows for Harmonic Analysis with the Discrete Fourier Transform." Proceedings of the IEEE. Vol. 66, No. 1 (January 1978). © 2025 Sooeet.com All rights reserved

Sampling rate for User Data:

Sampling Rate of User Data

Sampling Rate When providing User Data to the FFT, you must also enter the sampling rate of that data, in Hertz, (i.e. samples per second.) This only applies to User Data. The sampling rate for Program Data is set automatically. Sampling Rate Format The sampling rate value that you enter must be in one of the following formats: Integer: 8820 Decimal: 44100.9 Scientific Notation: 1.102536e04 Nyquist–Shannon Sampling Theorem The Nyquist–Shannon theorem is one of the principal elements of information theory. The theorem states that a bandlimited analog signal can be completely reconstructed via the inverse Fourier transform, only if the signal is sampled at a rate that exceeds 2F, where F is the highest frequency contained in the original signal. Therefore, when sampling a bandlimited analog signal intended for processing via the FFT, the sampling rate should exceed twice the maximum frequency that you wish to resolve with the FFT. For example, to capture a 3 Kilohertz frequency component in the original analog signal, the analog signal must be sampled at a rate that exceeds 6 Kilohertz. Limitations of the Fast Fourier Transform For best results, the number of samples in the input data list should be a power of 2, such as 1024, 4096, 32768, upto a maximum of: 2^18 = 262144 Due to the internal workings of the FFT, data sample lists larger than 2^18 require significant amounts of computer processor and memory resources, and are disallowed as of this writing. © 2025 Sooeet.com All rights reserved

FFT parametric controls:

FFT Parametric Controls

Slider Controls Some of the Program Data objects allow the user to control phase, frequency, pulse-width, and other parameters that drive the Program Data object. One of the parametric controls is the Slider, which allows the user to modify one parameter, by clicking and dragging the Slider button. The Slider provides a quick way to modify the parameter it controls, but it does not provide fine control over that parameter. Other Parametric Controls For precise control over frequency and other parameters, the following buttons are provided: F/2 Button This button lowers the current frequency, dividing that frequency by 2. For example, if the current frequency is 120 Hz, clicking this button lowers the frequency to 60 Hz. Clicking and holding this button, causes this action to be repeated until the button is released. 2F Button This button raises the current frequency, multiplying that frequency by 2. For example, if the current frequency is 150 Hz, clicking this button raises the frequency to 300 Hz. Clicking and holding this button, causes this action to be repeated until the button is released. -0.1 Button This button lowers the current frequency by subtracting 0.1 Hz from that frequency. For example, if the current frequency is 60 Hz, clicking this button lowers the frequency to 59.9 Hz. Clicking and holding this button, causes this action to be repeated until the button is released. +0.1 Button This button raises the current frequency by adding 0.1 Hz to that frequency. For example, if the current frequency is 60 Hz, clicking this button raises the frequency to 60.1 Hz. Clicking and holding this button, causes this action to be repeated until the button is released. -0.01 Button This button lowers the current frequency by subtracting 0.01 Hz from that frequency. For example, if the current frequency is 60 Hz, clicking this button lowers the frequency to 59.99 Hz. Clicking and holding this button, causes this action to be repeated until the button is released. +0.01 Button This button raises the current frequency by adding 0.01 Hz to that frequency. For example, if the current frequency is 60 Hz, clicking this button raises the frequency to 60.01 Hz. Clicking and holding this button, causes this action to be repeated until the button is released. FLR Button This button Floors the current frequency to the nearest lower integer value. For example, if the current frequency is 60.759 Hz, clicking this button Floors the frequency to 60.000 Hz. Clicking and holding this button, causes this action to be repeated until the button is released. Arrow Keys on the Keyboard The Left and Right arrow keys on the keyboard can also be used to lower and raise the current frequency. To use these buttons, first click the frequency slider button to select it, then press the Left or Right arrow keys on the keyboard. Holding down an arrow key, causes this action to be repeated until the arrow key is released. © 2025 Sooeet.com All rights reserved

FFT sound:

FFT Sound

WARNING: RISK of HEARING DAMAGE The FFT calculator generates sounds which may cause permanent hearing damage in humans and animals who are exposed to those sounds at high amplification, and/or for extended periods of time. Do not expose yourself, or other people, or animals, to the FFT calculator sounds, at high amplification, or for extended periods of time even at low levels of amplification. Do not expose yourself, or other people, or animals, to the FFT calculator sounds, via headphones, at high amplification, or for extended periods of time even at low levels of amplification. Fourier and Sound Priciples The forward Fourier Transform, implemented by this calculator as the FFT, produces a frequency-domain power spectrum. The inverse Fourier Transform, implemented by this calculator as the IFFT, produces a time-domain or spatial-domain signal or function, that can be interpreted as a time-varying voltage. If we interpret the time-domain or spatial-domain function or signal that is produced by the IFFT, as a time-varying voltage, then we can use that function or signal to drive an audio amplifier, and we can use the output of the amplifier to drive an electro-mechanical audio transducer, otherwise known as a "Speaker". Sound in air is produced by compression and rarefaction of air molecules, by a mechanical agent. In an electronic audio system, the mechanical agent is an electro-mechanical audio transducer. Vibrations of the transducer produce a sound wave that humans can perceive, when the frequency of vibration is in the range of 15 Hz to 20 KHz. The FFT calculator uses the audio system of the computer on which it is running, to generate audio signals in the frequency range of 0.001 Hz to well above the 20 KHz upper frequency limit of human hearing. Generally, audio frequencies below 15 Hz are considered infrasonic, meaning that humans generally cannot hear such low frequencies, and frequencies above 20 KHz are considered ultrasonic, meaning that humans generally cannot hear such high frequencies. Sound and the Fourier Series Perhaps the best way to illustrate the use of sound in the FFT calculator, is by way of an example. The menu entitled "Program-Data" contains an item entitled "Synthesis - Square Wave". Please choose that item from that menu. You should see three new Sliders and several new Buttons. These controls are used to manage the synthesis of a square wave from the sum of a series of trigonometric sine waves. The series of trigonometric sine waves that the FFT calculator uses to synthesize a square wave, is a so-called Fourier Series, a mathematical series directly related to the development of the continuous and discrete Fourier Transforms. Move the Slider entitled "Fund. (Square Wave)". This Slider controls the so-called Fundamental Frequency of the synthesized square wave. Choose a fundamental frequency of about 16 Hz. Now move the Slider entitled "Harm. (Square Wave)". This Slider controls the number of so-called Odd Harmonics that are summed to produce the synthesized square wave. Choose 10 harmonics. Now click the button entitled Play. If the audio system on your computer is working properly, you should hear a low pitched hum, which contains some higher pitched sounds within it. Now click the button entitled Inv-FFT / FFT. You should see the graphical representation of the audio signal in the Spatial-Domain, and the frequency components that make up that audio signal in the Frequency-Domain. To stop the sound click the button entitled Stop. Limitations of the FFT Sound System Due to the limitations of the FFT sound system, the sound buffer that is used for FFT sound output always generates 8192 sound samples at a sampling rate of 44.1 KHz, regardless of the setting in the menu entitled "FFT Number of Samples". Due to this limitation, sound frequencies above 8.192 KHz will be distorted to the degree that they exceed 8.192 KHz. However, in practical use, this limitation is of little consequence, because most audio amplifiers and speakers cannot accurately reproduce high frequencies. This limitation is a factor if the sound output from the FFT calculator is reproduced over a high quality audio system, which includes a high quality preamplifier, a high quality power amplifier, and high quality speakers. © 2025 Sooeet.com All rights reserved

FFT additive synthesis:

FFT Additive Synthesis

Fourier and Additive Synthesis As explained in the "FFT Sound" help topic, using Square Wave Synthesis via the Fourier sine series it is possible to synthesize an approximation of a square wave by summing a specific series of sine waves. However, more generally, it is possible to synthesize an approximation of any periodic function by summing a carefully crafted finite series of sine waves and/or cosine waves. The menu entitled "Program-Data" contains an item entitled "Sinusoid Component 1". Please choose that item from that menu. You should see four new Sliders and several new Buttons. These controls are used to manage the synthesis of an arbitrary function from the sum of a series of trigonometric sine and cosine waves. The item entitled "Sinusoid Component 1" is the first of 16 sinusoid components that can be used to approximate many arbitrary functions by means of Fourier Synthesis. The button entitled Sinusoid / Component allows you to see and hear either the entire synthesized sinusoid, or the individual component sine or cosine wave. The item entitled "Synthesis - Sinusoid" in the menu entitled "Program-Data", is the synthesized master-sinusoid, which is composed of upto 16 components. The item entitled "Synthesis - Sinusoid" also allows the addition of random white Gaussian noise to the synthesized function, via the slider entitled "Noise Level (Sinusoid)". © 2025 Sooeet.com All rights reserved

« Previous Page

Contact Sooeet:

Your name (required if you want a reply): Your eMail address (required if you want a reply): Your message: Type the Security Code in the box, then click Send:

About Contact Donate Link Share Press Site Map RSS Terms SMS Terms Privacy Home Top

By using this site you acknowledge having read and accepted our terms of service and privacy policy.

© 2025 Sooeet.com All rights reserved