WorkshopsOn Noise, Cycle and Trend in Climate Data
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Ever since Fourier introduced the eponymous transform people tends to think everything in terms of simple harmonic waves. Powerful as it is, the Fourier analysis is a mathematical tool that decomposes any signal into components consisting of sinusoidal functions. In simple example, the Fourier analysis can consistently separate a signal into its constituent components, but for complex signal from physical phenomena whether those harmonic components represents any physical significance is a totally different question. As Fourier analysis is based on linear stationary assumption, but not all the phenomena are indeed linear and stationary. For a nonstationary, the trend in the signal is another important property of the process we want to define and quantify. Here, the Fourier analysis would be of limited use. Furthermore, data from all physical processes contain noise from all different sources covering natural processes to measuring devices. To separate the noise from the signal is a challenging problem where Fourier analysis could offer limited information. Take the climate change as an example, to find the cycle and trend is the goal of climate study. But climate data are full of noise from all kind of sources. Therefore, to find a method to apply to climate study is an urgent problem. Here we will introduce a new method, the Empirical Mode Decomposition (EMD), to separate noise form signal and also identify the cycles of change from the trend. A better way to define cycle is through frequency. With a proper frequency definition, the trend and noise could be easily identified. To define frequency, we have to decompose the data into the constituent component, each one would have to be a 'mono-component' function, or an Intrinsic Mode Function (IMF) through EMD.
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Norden Huang
2012-09-18
14:50:00 - 15:40:00
101 , Mathematics Research Center Building (ori. New Math. Bldg.)
Ever since Fourier introduced the eponymous transform people tends to think everything in terms of simple harmonic waves. Powerful as it is, the Fourier analysis is a mathematical tool that decomposes any signal into components consisting of sinusoidal functions. In simple example, the Fourier analysis can consistently separate a signal into its constituent components, but for complex signal from physical phenomena whether those harmonic components represents any physical significance is a totally different question. As Fourier analysis is based on linear stationary assumption, but not all the phenomena are indeed linear and stationary. For a nonstationary, the trend in the signal is another important property of the process we want to define and quantify. Here, the Fourier analysis would be of limited use. Furthermore, data from all physical processes contain noise from all different sources covering natural processes to measuring devices. To separate the noise from the signal is a challenging problem where Fourier analysis could offer limited information. Take the climate change as an example, to find the cycle and trend is the goal of climate study. But climate data are full of noise from all kind of sources. Therefore, to find a method to apply to climate study is an urgent problem. Here we will introduce a new method, the Empirical Mode Decomposition (EMD), to separate noise form signal and also identify the cycles of change from the trend. A better way to define cycle is through frequency. With a proper frequency definition, the trend and noise could be easily identified. To define frequency, we have to decompose the data into the constituent component, each one would have to be a 'mono-component' function, or an Intrinsic Mode Function (IMF) through EMD.
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