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**"Fourier Transform"****Related Terms:**Fourier analysis, Fast fourier transform, Fft, Phase noise, Discrete cosine transform, Audio signal, Power spectrum, Spectrum analyser, Spectrum analyzer, Phase locked loop, Intermediate frequency, Modulation transfer function, Local oscillator, Fourier series, Phase modulation, Modulate, Downconverter, Analog signal, Modulation, Signal processing, Amplitude modulation, Phase lock loop, Graphic equalizer, Lfo, Frequency modulation, Equalization, Intermodulation, Nyquist frequency, Equalizer , Analogue, Heterodyne, Resonant frequency, Phase distortion, Quantization, Frequency response, Detection, Sine wave, Tuner , Discriminator, Correlator, De-emphasis, Digital filter, Multiburst, Waveform , Group delay, Phase-locked loop, Chirp, Oversampling, Superheterodyne receiver

Description and detailed explanation on Fourier Transform, some FFT, LPC etc. Runable project demonstrates DCT transform on continuous audio, show and edit audio source with different zooming and view.

A mathematical procedure that changes "time" information into "frequency" information.

The Fourier transform of an object is the transformation to the Fourier basis. If the object comprises pixels or voxels, the Fourier basis also has components. Given a dimensional object vector , the components in the Fourier basis are obtained by multiplying by the DÃ—D unitary matrix . In the simple case where all the array sizes of the object are equal to , the elements of are given by Fq r = exp( i 2Ï€ qâ‹…r / N ) / âˆšD. For general rectangular arrays, qâ‹…r / N is replaced by qx rx / Nx + qy ry / Ny + .... In keeping with standard notation, the Fourier transform of is denoted in this glossary by F(A).

Frequency space transform that decomposes a spatial image into a set of sinusoidal frequency components.

A mathematical function which when applied to a dataset generates a new dataset that identifies the frequencies contained in the data.

(MRI) Mathematical calculation performed in MRI which allows the computer to transform the radio signal into data that can be used to generate an image.

a bit of maths which is based on the principle that any signal can be constructed from a sum of sine waves

a frequency spectrum display of the sampled data

a mathematical method where a complex wave, or a complex pattern is broken down and converted into a basically longer, but precise signal of simpler frequencies

a mathematical operation that transforms a signal from the time domain to the frequency domain , and vice versa

a mathematical operation which decomposes a time varying signal into its complex frequency components (amplitude and the phase or real and imaginary components)

a mathematical tool that provides a means of transforming information from the time domain to the frequency domain, and vice versa

an example of doing the SMe thing in a function space, with a basis made of sinusoids

an operation based on Fourier's theorem, which states that any harmonic function can be represented by a series of sine and cosine functions, which differ only in frequency, amplitude, and phase

an operation which converts functions from time to frequency domains

a representation of some function in terms of a set of sine-waves

a special case of a wavelet transform with basis vectors defined by trigonometric functionssine and cosine

the spectrum of an aperiodic waveform which can contain all frequencies, rather than discrete harmonics. See also Fourier series.

A graph of sound pressure vs. time is an illustration of a time-domain function. Sound can also be described as a frequency-domain function, as the superposition of a group of sinusoidal waves spanning the audio frequency spectrum. Mathematically both functions contain exactly the same information and each function perfectly defines the sound. A Fourier transform, and inverse transform, convert functions back and forth between the time and frequency domains. This is a error-free transformation, but the width of the frequency range and frequency resolution (fine-grain detail) is limited by the time resolution and duration. The longer the duration, the finer the detail, and the finer the time detail, the wider the frequency range. A fast Fourier transform is a technique for performing these mathematical operations very quickly with a computer. See the Signal Processing Section for more detail.

any of various functions (as F(u)) that under suitable conditions can be obtained from given functions (as f(x)) by multiplying by eiux and integrating over all values of x and that in scientific instrumentation describe the dependence of the average of a series of measurements (as of a spectrum) on a quantity of interest (as brightness) especially of a very small magnitude -- called also Fourier transformation

mathematical technique for interconverting data between the time or space domain and frequency or wavenumber domain. ( See Spectral analysis.) back

a mathematical technique for converting time dependant data into frequency data. Most often used in Fourier transfrom infrared spectrometry (FTIR). The conversion from frequency to time is performed by the inverse Fourier transform function.

a mathematical transform that converts a time series of data that has been collected at a specific sample interval into a series of frequency energy data. Ie data in meters is converted into m2/Hz. A FFT or Fast Fourier Transform is a computationally efficient method of doing a Fourier Transform. For Wave analysis it assumes that a time series of wave height data is the sum of many waves of different frequencies. For example a time series of 512 samples is converted into 256 wave energies of frequencies from 1/(sample interval *512) Hz to 256/(sample interval *512) Hz.

Developed by a French mathematician in the early 1800's, the Fourier transform basically separates a waveform into sinusoids (pure tones) of different frequencies, storing the data as amplitude and phase as a function of frequency. These sinusoids can be added together to reconstruct the original waveform. The transformation, therefore, is between the time-domain waveform and the frequency-domain spectrum of a signal or sound. Both are complete descriptions of the signal, and one can be computationally converted into the other. See: Transform, Spectrum, Transfer Function. Impulse Response, FFT, Spectrum Analyzer.

Calculation performed on an interferogram to turn it into an infrared spectrum.

mathematical representation of an image as a series of two-dimensional sine waves. The smaller the wavelength, the higher the spatial frequency, the higher the resolution of features in the image represented. Each Fourier component is indexed by its spatial frequency (kx, ky) and is given as a pair of numbers: amplidude (describing the strength of the sine wave) and phase (describing the position of the sine wave).

An optical or digital means of transforming an image from the spatial to the frequency domain.

A mathematical procedure used in MR that converts a time-domain signal into a frequency- or spatial-domain signal or image. It is analogous to the way that our ear distinguishes or separates out separate sounds or frequencies from noise we hear. Our eyes do not work this way. If we see a mixture of blue and yellow we see the color green, not the original blue and yellow.

(FT) - a mathematical procedure to separate the frequency components of a signal from its amplitudes as a function of time, or vice versa. The Fourier transform is used to generate the spectrum from the FID in pulse NMR techniques and is essential to most imaging techniques.

the mathematical transformation used in FT spectroscopy to convert an interferogram into an infrared spectrum.

Fourier transform at mathworld.com

A mathematical technique capable of converting a time domain signal to a frequency domain signal and vice versa. [ Chapter 5

Technique used to evaluate the importance of various frequency cycles in a time series pattern.

A mathematical technique for analysing a complex waveform into its component frequencies and thus expressing it as a sum of a continuous series of sine and cosine (fixed frequency and amplitude) waves. The Fourier transform is central to many kinds of signal processing, including the analysis and compression of all types of frequency-based information. In oil analysis, the "FT" portion of "FTIR".

A mathematical technique that resolves a given signal into the sum of sines and cosines. Widely used as the FFT (Fast Fourier Transform), which is the basis for spectrum analysis.

An analytical transformation of a function () obtained (if it exists) by multiplying the function by âˆ’ iux and integrating over all , where is the new variable of the transform () and 2 = âˆ’1. If the Fourier transform of a function is known, the function itself may be recovered by use of the inversion formula: The Fourier transform has the same uses as the Fourier series: For example, the integrand F() exp ( iux) is a solution of a given linear equation, so that the integral sum of these solutions is the most general solution of the equation. When the variable is complex, the Fourier transform is equivalent to the Laplace transform. See also Fourier integral, spectral function.

The mathematical transformation that allows a function in time or space to be examined in terms of its frequency components.