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→Relation to Fourier analysis and similar methods
==Relation to Fourier analysis and similar methods==
==Relation to Fourier analysis and similar methods与傅里叶分析及类似方法的关系==
By writing a very general stimulus (in a linear system) as the superposition of stimuli of a specific and simple form, often the response becomes easier to compute.
By writing a very general stimulus (in a linear system) as the superposition of stimuli of a specific and simple form, often the response becomes easier to compute.
通过将一个非常普遍的刺激（在线性系统中）写成一个特定和简单形式的刺激的叠加，反应往往变得更容易计算。
By writing a very general stimulus (in a linear system) as the superposition of stimuli of a specific and simple form, often the response becomes easier to compute.
By writing a very general stimulus (in a linear system) as the superposition of stimuli of a specific and simple form, often the response becomes easier to compute.
For example, in [[Fourier analysis]], the stimulus is written as the superposition of infinitely many [[Sine wave|sinusoid]]s. Due to the superposition principle, each of these sinusoids can be analyzed separately, and its individual response can be computed. (The response is itself a sinusoid, with the same frequency as the stimulus, but generally a different [[amplitude]] and [[phase (waves)|phase]].) According to the superposition principle, the response to the original stimulus is the sum (or integral) of all the individual sinusoidal responses.
For example, in [[Fourier analysis]], the stimulus is written as the superposition of infinitely many [[Sine wave|sinusoid]]s. Due to the superposition principle, each of these sinusoids can be analyzed separately, and its individual response can be computed. (The response is itself a sinusoid, with the same frequency as the stimulus, but generally a different [[amplitude]] and [[phase (waves)|phase]].) According to the superposition principle, the response to the original stimulus is the sum (or integral) of all the individual sinusoidal responses.
例如，在[[Fourier analysis]]中，刺激被写为无穷多个正弦波[[sing wave | sinusoid]]的叠加。由于叠加原理，每个正弦波可以单独分析，并且可以计算其单独的响应。（反应本身是一个正弦波，与刺激频率相同，但通常是不同的[[振幅]]和[[相位（波）|相位]]）根据叠加原理，对原始刺激的反应是所有单个正弦波反应的总和（或积分）。
For example, in Fourier analysis, the stimulus is written as the superposition of infinitely many sinusoids. Due to the superposition principle, each of these sinusoids can be analyzed separately, and its individual response can be computed. (The response is itself a sinusoid, with the same frequency as the stimulus, but generally a different amplitude and phase.) According to the superposition principle, the response to the original stimulus is the sum (or integral) of all the individual sinusoidal responses.
For example, in Fourier analysis, the stimulus is written as the superposition of infinitely many sinusoids. Due to the superposition principle, each of these sinusoids can be analyzed separately, and its individual response can be computed. (The response is itself a sinusoid, with the same frequency as the stimulus, but generally a different amplitude and phase.) According to the superposition principle, the response to the original stimulus is the sum (or integral) of all the individual sinusoidal responses.
As another common example, in [[Green's function|Green's function analysis]], the stimulus is written as the superposition of infinitely many [[impulse function]]s, and the response is then a superposition of [[impulse response]]s.
As another common example, in [[Green's function|Green's function analysis]], the stimulus is written as the superposition of infinitely many [[impulse function]]s, and the response is then a superposition of [[impulse response]]s.
另一个常见的例子是，在格林函数分析[[Green's function | Green's function analysis]]中，刺激被写成无穷多个脉冲函数[[impulse function]]s的叠加，然后响应就是[[脉冲响应]]s的叠加。
As another common example, in Green's function analysis, the stimulus is written as the superposition of infinitely many impulse functions, and the response is then a superposition of impulse responses.
As another common example, in Green's function analysis, the stimulus is written as the superposition of infinitely many impulse functions, and the response is then a superposition of impulse responses.
Fourier analysis is particularly common for [[wave]]s. For example, in electromagnetic theory, ordinary [[light]] is described as a superposition of [[plane wave]]s (waves of fixed [[frequency]], [[Polarization (waves)|polarization]], and direction). As long as the superposition principle holds (which is often but not always; see [[nonlinear optics]]), the behavior of any light wave can be understood as a superposition of the behavior of these simpler [[plane wave]]s.
Fourier analysis is particularly common for [[wave]]s. For example, in electromagnetic theory, ordinary [[light]] is described as a superposition of [[plane wave]]s (waves of fixed [[frequency]], [[Polarization (waves)|polarization]], and direction). As long as the superposition principle holds (which is often but not always; see [[nonlinear optics]]), the behavior of any light wave can be understood as a superposition of the behavior of these simpler [[plane wave]]s.
傅里叶分析对于[[波]]s特别常见。例如，在电磁理论中，普通[[光]]被描述为[[平面波]]s（固定[[频率]]、[[偏振（波）|偏振]]和方向的波）的叠加。只要叠加原理成立（这通常是但并不总是；见[[非线性光学]]），任何光波的行为都可以理解为这些更简单的[[平面波]]行为的叠加。
Fourier analysis is particularly common for waves. For example, in electromagnetic theory, ordinary light is described as a superposition of plane waves (waves of fixed frequency, polarization, and direction). As long as the superposition principle holds (which is often but not always; see nonlinear optics), the behavior of any light wave can be understood as a superposition of the behavior of these simpler plane waves.
Fourier analysis is particularly common for waves. For example, in electromagnetic theory, ordinary light is described as a superposition of plane waves (waves of fixed frequency, polarization, and direction). As long as the superposition principle holds (which is often but not always; see nonlinear optics), the behavior of any light wave can be understood as a superposition of the behavior of these simpler plane waves.
傅立叶变换家族中的关系对于波浪来说尤其常见。例如，在电磁理论中，普通光被描述为平面波(具有固定频率、偏振和方向的波)的叠加。只要叠加原理能够持续(这种情况经常发生，但并不总是如此; 请参阅非线性光学) ，任何光波的行为都可以被理解为这些简单平面波行为的叠加。
傅立叶变换家族中的关系对于波浪来说尤其常见。例如，在电磁理论中，普通光被描述为平面波(具有固定频率、偏振和方向的波)的叠加。只要叠加原理能够持续(这种情况经常发生，但并不总是如此; 请参阅非线性光学) ，任何光波的行为都可以被理解为这些简单平面波行为的叠加。
==Wave superposition波叠加==
==Wave superposition波叠加==