A mathematical analysis that attempts to find cycles within a time series of...
The mathematical process of resolving a given function, f(x), into its frequency components, which means finding the sequence of constant amplitudes to plug into a Fourier series to reconstruct the original function.
A method of dissociating time series or spatial data into sets of sine and cosine waves.
A method of finding he frequencies (or periods) present in a time series by decomposing it in to a series of sine waves as demonstrated by the mathematician Fourier.
analysis of a periodic function into a sum of simple sinusoidal components
the process of using the terms of a Fourier series to find a function that approximates periodic data
The decomposition of a signal into its simplest harmonic curves (sines and cosines). Galaxy: A large system of stars. Our galaxy, the Milky Way, is a spiral galaxy containing some 100,000 million stars, 100,000 light years in diameter and 10,000 light years thick.
the method of analysis in which a complex wave is regarded as a suitable combination of a number of pure tones. a mathematical theorem that any periodic vibration can be analyzed into a set of single sinusoid waves. In turn, the superposition of the sinusoid waves will reproduce the original vibration. (H:552)
is a mathematical technique for turning a time series into a set of coefficients which are the amplitudes of a set of sine waves of various frequencies so that those sine waves add up to the original data.
A technique, usually performed using a DSP algorithm, that allows complex, dynamically changing audio waveforms to be described mathematically as sums of sine waves at various frequencies and amplitudes. See DSP.
The use of the Fourier series to evaluate the harmonic components of a complex wave.
The process of analyzing a complex wave by separating it into a plurality of component wave, each of a particular frequency, amplitude and phase displacement.
The determination of the harmonic components of a complex waveform, i.e. the terms of a Fourier series that represents the waveform.
The representation of physical or mathematical data by the use of the Fourier series or Fourier integral.
Mathematics. Most often the approximation of a function through the application of a Fourier series to periodic data, however it is not restriced to periodic data. The Fourier series applies to periodic data only, but the Fourier integral transform converts an infinite continuous time function into an infinite continuous frequency function, with perfect reversibility in most cases. The DFT and FFT are examples of the Fourier analysis.
Fourier analysis, named after Joseph Fourier's introduction of the Fourier series, is the decomposition of a function in terms of a sum of sinusoidal basis functions (vs. their frequencies) that can be recombined to obtain the original function. That process of recombining the sinusoidal basis functions is also called Fourier synthesis (in which case Fourier analysis refers specifically to the decomposition process).