英语翻译In complex notation,the time and frequency domains each

英语翻译
In complex notation,the time and frequency domains each contain one signal made up of N complex points.Each of these complex points is composed of two numbers,the real part and the imaginary part.For example,when we talk
about complex sample
X[42] ,it refers to the combination of
Re X[42]
and
Im X[42] .In other words,each complex variable holds two numbers.When two complex variables are multiplied,the four individual components must be combined to form the two components of the product (such as in Eq.9-1).The following discussion on "How the FFT works" uses this jargon of complex notation.That is,the singular terms:signal,point,sample,and value,refer to the combination of the real part and the imaginary part.
The FFT operates by decomposing an N point time domain signal into N time domain signals each composed of a single point.The second step is to calculate the N frequency spectra corresponding to these N time domain signals.Lastly,the N spectra are synthesized into a single frequency spectrum.

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In complex notation,the time and frequency domains each contain one signal made up of N complex points.在复数记法中,时域和频域每一个都包含一个由N个复数点构成的信号.Each of these complex points is composed of two numbers,the real part and the imaginary part.这些复数点中的每一个都由两个数,即实部和虚部组成.For example,when we talk
about complex sample
X[42] ,it refers to the combination of
Re X[42]and Im X[42] .例如当我们谈论复数样本X[42]时,它指的是Re X[42]和 Im X[42]的组合.In other words,each complex variable holds two numbers.换句话说,每一个复数变量都具有两个数.When two complex variables are multiplied,the four individual components must be combined to form the two components of the product (such as in Eq.9-1).当两个复数变量相乘时,必须结合进四个独立的分量来形成两个积的分量（就如在公式9－1中）.The following discussion on "How the FFT works" uses this jargon of complex notation.下面对“FFT（快速傅立叶变换）如何发挥作用”的讨论采用了这一复数记法的专门术语.That is,the singular terms:signal,point,sample,and value,refer to the combination of the real part and the imaginary part.也就是说,单一的术语：信号、点、样本和数值指的是实部和虚部的组合.
The FFT operates by decomposing an N point time domain signal into N time domain signals each composed of a single point.FFT通过将一个N点时域信号分解成N个时域信号（每个都由一个点组成）而运算.The second step is to calculate the N frequency spectra corresponding to these N time domain signals.第二步是计算与这N个时域信号相应的N个频谱.Lastly,the N spectra are synthesized into a single frequency spectrum最后,该N个频谱被合成成一个单一的频谱.