英语翻译a.Fourier red noise spectrumMany geophysical time series can be modeled aseither white noise or red noise.A simple model for rednoise is the univariate lag-1 autoregressive [AR(1),orMarkov] process:(公式不用翻译)where a is the assumed lag-1 autocorrelation,x0 = 0,and zn is taken from Gaussian white noise.FollowingGilman et al.(1963),the discrete Fourier power spectrumof (15),after normalizing,is公式where k = 0 … N/2 is the frequency index.Thus,bychoosing
英语翻译
a.Fourier red noise spectrum
Many geophysical time series can be modeled as
either white noise or red noise.A simple model for red
noise is the univariate lag-1 autoregressive [AR(1),or
Markov] process:
(公式不用翻译)
where a is the assumed lag-1 autocorrelation,x0 = 0,
and zn is taken from Gaussian white noise.Following
Gilman et al.(1963),the discrete Fourier power spectrum
of (15),after normalizing,is
公式
where k = 0 … N/2 is the frequency index.Thus,by
choosing an appropriate lag-1 autocorrelation,one can
use (16) to model a red-noise spectrum.Note that a = 0
in (16) gives a white-noise spectrum.
The Fourier power spectrum for the Niño3 SST is
shown by the thin line in Fig.3.The spectrum has been
normalized by N/2s2,where N is the number of points,
and s2 is the variance of the time series.Using this
normalization,white noise would have an expectation
value of 1 at all frequencies.The red-noise background
spectrum for a = 0.72 is shown by the lower dashed
curve in Fig.3.This red-noise was estimated from (公式) where a1 and a2 are the lag-1 and lag-2
autocorrelations of the Niño3 SST.One can see the
broad set of ENSO peaks between 2 and 8 yr,well
above the background spectrum.
b.Wavelet red noise spectrum
The wavelet transform in (4) is a series of bandpass
filters of the time series.If this time series can be
modeled as a lag-1 AR process,then it seems reasonable
that the local wavelet power spectrum,defined
as a vertical slice through Fig.1b,is given by (16).To
test this hypothesis,100 000 Gaussian white-noise
time series and 100 000 AR(1) time series were constructed,
along with their corresponding wavelet power
spectra.Examples of these white- and red-noise wavelet
spectra are shown in Fig.4.The local wavelet spectra
were constructed by taking vertical slices at time
n = 256.The lower smooth curves in Figs.5a and 5b
show the theoretical spectra from (16).The dots show
the results from the Monte Carlo simulation.On average,
the local wavelet power spectrum is identical
to the Fourier power spectrum given by (16).
Therefore,the lower dashed curve in Fig.3 also
corresponds to the red-noise local wavelet spectrum.
A random vertical slice in Fig.1b would be expected
to have a spectrum given by (16).As will be shown in
section 5a,the average of all the local wavelet spectra
tends to approach the (smoothed) Fourier spectrum of
the time series.
答:傅立叶红噪声谱
许多地球物理时间序列,可以描述为
无论是白噪声或红色噪音。一个简单的模型为红色
噪音是指单滞后- 1自[的AR ( 1 ) ,或
马尔科夫]过程:
如果是假设滞后- 1自相关, x0 = 0 ,
锌是采取由高斯白噪声。以下
吉尔曼等人。 ( 1963 ) ,离散傅立叶功率谱
( 15 ) ,后规范,是 其中K = 0 … n / 2是频率指数。因此,通过
选择合适的滞后- 1自相关,可以
利用( 16 ) ,以示范红色噪声谱。注一= 0
在( 16 )给出了白噪声谱。
傅立叶功率谱为niño3 SST的是
所表现出的薄线图。 3 。频谱已
归由n/2s2 ,其中n是多少分,
和S2是方差的时间序列。使用本
正常化,白噪声,将有一个期望
价值1在所有频率。红噪声背景
频谱为= 0.72 ,是表现出较低的破灭
曲线图。 3 。这个红色噪声估计,从(公式)如A1和A2是滞后- 1和滞后- 2
自相关的niño3 SST的。人们可以看到
一整套广泛的ENSO的高峰期为2至8年,以及
上述背景光谱。
乙小波红色噪声谱
小波变换( 4 )是一系列的带
滤波器的时间序列。如果这个时间序列,可
仿照作为一个滞后- 1氩过程中,那似乎是合理的
了解到当地小波功率谱,其定义
作为一个垂直切片,通过图。 1 B款,是由( 16 ) 。至
检验这一假说, 10万高斯白噪声
时间序列和100000的AR ( 1 )时间序列建造,
随着其相应的小波功率
谱。的例子,这些白色和红色噪声小波
光谱示于图。 4 。当地小波能谱
分别采取垂直切片的时候
例256 。较低的平稳曲线图。 5A和五十亿
查看理论谱( 16 ) 。这些点查看
结果从蒙特卡洛模拟。平均来说,
当地小波功率谱是相同的
以傅立叶功率谱所给予的( 16 ) 。
因此,下冲向曲线图。 3还
对应于红噪音局部小波频谱。
随机垂直切片图。 1 B款预计将
有一个谱所给予的( 16 ) 。将显示在
第5A ,平均所有局部小波谱
趋于接近(平滑)傅立叶谱
该时间序列。
楼上的太浆糊了,机械翻译没意思的。建议楼主把问题关了吧,这个东西太专业了,你应该拿到理工科去问一下。
一.傅立叶红色的噪音光谱许多地球物理学的时间系列能被做模型当做白色噪音或红色的噪音.一个简单的模型为红色噪音是单变数落后-1 autoregressive[AR(1),或Markov] 程序:(公式不用翻译)哪里一是假装的落后-1 自相关...