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This Concept Map, created with IHMC CmapTools, has information related to: a8. Fourier Analysis, The goals of Fourier analyasis are To find the chief contributors, the relatively large constituent amplitudes, if any., Periodicity refers to waves that repeat themselves. Periodic motion makes regular rise-and-fall wave-like patterns on a time chart ???? The method uses concepts and definitions such as wavelengths, period frequency, phase, and harmonics, It reveals periodicity or lack thereof, in data. It is based on the idea that any time series can be decomposed into constituent sine waves. ???? Waves in a Fourier analysis usually differ in one way or another in wavelength, frequency, amplitude, and phase., Fourier analysis is a mathematical technique for uniquely describing a time-series in terms of periodic constituents. A chaotic time-series may or may not have periodicity. Consequently, a test for periodicity cannot by itself indicate chaos. However, a test for periodicity can reveal autocorrelation. One way of finding autocorrelation is by Fourier analysis., Fourier analysis uses only that subset of waves whose frequencies are an integer multiple of the fundamental frequency, two times the fundamental frequency, three times, etc. These constituent waves are called harmonics., Fourier analysis uses only that subset of waves whose frequencies are an integer multiple of the fundamental frequency, two times the fundamental frequency, three times, etc. ???? One of the key principles of Fourier analysis is that we can approximate virtually any wave or time series by selecting certain harmonics and adding enough of them together., The goals of Fourier analyasis are ???? Finding the coefficients is a major goal of Fourier analysis., Fourier analysis is a mathematical technique for uniquely describing a time-series in terms of periodic constituents. It reveals periodicity or lack thereof, in data. It is based on the idea that any time series can be decomposed into constituent sine waves., Summing waves of different wavelengths produces a composite wave. Fourier analysis decomposes composite waves, no matter how strange they look, into a series of sinusoidal constituent waves or time series. The coefficients for each wave reflect the magnitude of those amplitudes. Identifying the relatively large amplitudes in turn identifies the major periodicities in a time series., It reveals periodicity or lack thereof, in data. It is based on the idea that any time series can be decomposed into constituent sine waves. Phenomena made up of periodic constituents are common. A beam of sunlight contains many constituent colors, each characterized by its own unique wavelength. A musical tone consists of various constituent tones. A Fourier analysis gives special attention to the relative strengths of the periodic constituents., a8. Fourier Analysis is Fourier analysis is a mathematical technique for uniquely describing a time-series in terms of periodic constituents., The method uses concepts and definitions such as wavelengths, period frequency, phase, and harmonics b2. Harmonics, a8. Fourier Analysis is Fourier analysis is a standard step in time-series analysis, regardless of whether it is chaotic or not., A chaotic time-series may or may not have periodicity. Consequently, a test for periodicity cannot by itself indicate chaos. However, a test for periodicity can reveal autocorrelation. One way of finding autocorrelation is by Fourier analysis. It reveals periodicity or lack thereof, in data. It is based on the idea that any time series can be decomposed into constituent sine waves., One of the key principles of Fourier analysis is that we can approximate virtually any wave or time series by selecting certain harmonics and adding enough of them together. To determine which frequencies are present, and the relative importance of each as reflected in their coefficients (wave amplitudes)., The coefficients for each wave reflect the magnitude of those amplitudes. Identifying the relatively large amplitudes in turn identifies the major periodicities in a time series. Fourier coefficients reflect the relative contributions of the constituent waves., One of the key principles of Fourier analysis is that we can approximate virtually any wave or time series by selecting certain harmonics and adding enough of them together. b2. Harmonics, Phenomena made up of periodic constituents are common. A beam of sunlight contains many constituent colors, each characterized by its own unique wavelength. A musical tone consists of various constituent tones. A Fourier analysis gives special attention to the relative strengths of the periodic constituents. ???? The wavelength is the horizontal distance from any point on one wave to the equivalent point on the next wave. The wavelength is in distance units. If the horizontal axis is time, wave periods or cycle is used instead. A cycle is a complete wave and has no units., These constituent waves are called harmonics. b2. Harmonics, Summing waves of different wavelengths produces a composite wave. Fourier analysis decomposes composite waves, no matter how strange they look, into a series of sinusoidal constituent waves or time series. To determine which frequencies are present, and the relative importance of each as reflected in their coefficients (wave amplitudes).