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第1行： − 此词条暂由彩云小译翻译，未经人工整理和审校，带来阅读不便，请见谅。+ 第5行：
第5行： − 在数学动力学中，离散时间和连续时间是为随时间演化的变量建模的两种可供选择的框架。+ 第23行：
第23行： − 离散时间将变量的值视为发生在不同的、独立的”时间点” ，或者等同于在整个非零时间区域(”时间周期”)中没有变化——也就是说，时间被视为一个离散变量。因此，当时间从一个时间周期移动到下一个时间周期时，非时间变量从一个值跳到另一个值。这种时间观相当于一个数字时钟，在一段时间内给出10:37的固定读数，然后跳到新的10:38的固定读数，等等。在这个框架中，每个感兴趣的变量在每个时间段都被测量一次。任何两个时间周期之间的测量数量都是有限的。测量通常按照变量“时间”的连续整数值进行。+ 第65行：
第65行： − 相比之下，连续时间将变量视为具有一个特定值，可能只有无限短的时间量。在任何两个时间点之间还有无数其他时间点。变量“ time”的范围是整个实数行，或者取决于上下文，取决于它的某个子集，如非负雷亚尔。因此，时间被看作是一个连续变量。+ 第111行：
第111行： − 数学 f (t) sin (t) ，方 t in mathbb { r } / math+ 第119行：
第119行： − 上述信号的持续时间有限的副本可以是:+ 第127行：
第127行： − 数学 f (t) sin (t) ， quad t in [- pi， pi ] / math f (t)0 / math 否则。+ 第143行：
第143行： − 数学 f (t) frac {1} t } ， quad t in [0,1] / math f (t)0 / math 否则,+ 第151行：
第151行： − 是一个有限持续时间的信号，但是它的 math t0值是无限的 / math。+ 第167行：
第167行： − + 第175行：
第175行： − 任何模拟信号本质上都是连续的。用于数字信号处理的离散时间信号可以通过对连续信号的采样和量化得到。+ 第183行：
第183行： − 连续信号也可以定义在时间以外的独立变量上。另一个非常常见的独立变量是空间，它在图像处理中特别有用，因为它使用了两个空间维度。+ 第195行：
第195行： − 当涉及到经验测量时，通常采用离散时间，因为通常只能按顺序测量变量。例如，虽然经济活动实际上是连续发生的，但是没有经济完全处于停顿状态的时刻，只能对经济活动进行分散的测量。出于这个原因，例如，公布的国内生产总值(gdp)数据将显示一系列的季度价值。+ 第203行：
第203行： − + 第219行：
第219行： − 另一方面，在连续时间内建立理论模型在数学上更易于处理，而在物理学等领域，精确的描述往往需要使用连续时间。在连续时间上下文中，变量 y 在未指定的时间点上的值表示为 y (t) ，或者，当含义清楚时，简单地表示为 y。+ 第243行：
第243行： − 数学 x { t + 1} rx t (1-x t) ，/ math+ 第251行：
第251行： − + 第259行：
第259行： − 另一个例子模型的调整价格 p 响应非零过剩需求的产品如下+ 第267行：
第267行： − 数学 p { t + 1} p t + delta cdot f (p t，...) / 数学+ 第275行：
第275行： − + 第295行：
第295行： − 数学 frac { dP }{ dt } lambda cdot f (p，...) / math+ 第303行：
第303行： − 左边是价格对时间的一阶导数(也就是价格的变化率) math lambda / math 是调整速度参数，可以是任意正的有限数，math f / math 也是过剩需求函数。+ 第315行：
第315行： − 在离散时间中测量的一个变量可以绘制为一个阶跃函数，其中每个时间周期在水平轴上给定一个与每个其他时间周期相同长度的区域，测量的变量绘制为在整个时间周期区域内保持不变的高度。在这种图形技术中，图表显示为一系列水平步骤。或者，可以将每个时间段视为时间上的一个分离点，通常位于水平轴上的一个整数值处，测量变量绘制为高于该时间轴点的一个高度。在这种技术中，图表显示为一组点。+ 第363行：
第363行： − + 第369行：
第369行： − 作者链接+ 第381行：
第381行： − 出版商剑桥大学出版社+ 第393行：
第393行： − + 第399行：
第399行： − 页数+ 第405行：
第405行： − 我们会把你的名字写下来+ 第411行：
第411行： − 不会吧+ 第417行：
第417行： − 我会的+ 第423行：
第423行： − 会发生什么事+ 第433行：
第433行： − 作者: 托马斯 · 查尔斯 · 戈登+ 第439行：
第439行： − 作者链接+ 第445行：
第445行： − 瞬态分析+ 第451行：
第451行： − 出版商 Wiley+ 第463行：
第463行： − + 第469行：
第469行： − 页数+ 第475行：
第475行： − 我们会把你的名字写下来+ 第481行：
第481行： − 不会吧+ 第487行：
第487行： − 我会的+ 第493行：
第493行： − 会发生什么+
Moved page from wikipedia:en:Discrete time and continuous time (history)
此词条暂由彩云小译翻译，翻译字数共1367，未经人工整理和审校，带来阅读不便，请见谅。
In [[Dynamical system|mathematical dynamics]], '''discrete time''' and '''continuous time''' are two alternative frameworks within which to model [[Variable (mathematics)|variables]] that evolve over time.
In [[Dynamical system|mathematical dynamics]], '''discrete time''' and '''continuous time''' are two alternative frameworks within which to model [[Variable (mathematics)|variables]] that evolve over time.
In mathematical dynamics, discrete time and continuous time are two alternative frameworks within which to model variables that evolve over time.
In mathematical dynamics, discrete time and continuous time are two alternative frameworks within which to model variables that evolve over time.
在数学动力学中，离散时间和连续时间是两种可供选择的框架，在这两种框架内可以对随时间演化的变量建模。
Discrete time views values of variables as occurring at distinct, separate "points in time", or equivalently as being unchanged throughout each non-zero region of time ("time period")—that is, time is viewed as a discrete variable. Thus a non-time variable jumps from one value to another as time moves from one time period to the next. This view of time corresponds to a digital clock that gives a fixed reading of 10:37 for a while, and then jumps to a new fixed reading of 10:38, etc. In this framework, each variable of interest is measured once at each time period. The number of measurements between any two time periods is finite. Measurements are typically made at sequential integer values of the variable "time".
Discrete time views values of variables as occurring at distinct, separate "points in time", or equivalently as being unchanged throughout each non-zero region of time ("time period")—that is, time is viewed as a discrete variable. Thus a non-time variable jumps from one value to another as time moves from one time period to the next. This view of time corresponds to a digital clock that gives a fixed reading of 10:37 for a while, and then jumps to a new fixed reading of 10:38, etc. In this framework, each variable of interest is measured once at each time period. The number of measurements between any two time periods is finite. Measurements are typically made at sequential integer values of the variable "time".
离散时间将变量的值视为发生在不同的、分离的”时间点” ，或者等价于在整个非零时间区域(”时间周期”)中没有变化——也就是说，时间被视为一个离散变量。因此，当时间从一个时间周期移动到下一个时间周期时，非时间变量从一个值跳到另一个值。这种时间观相当于一个数字时钟，在一段时间内给出一个固定的读数10:37，然后跳到一个新的固定读数10:38，等等。在这个框架中，每个感兴趣的变量在每个时间段都被测量一次。任何两个时间周期之间的测量数量都是有限的。测量通常按照变量“时间”的连续整数值进行。
In contrast, continuous time views variables as having a particular value for potentially only an infinitesimally short amount of time. Between any two points in time there are an infinite number of other points in time. The variable "time" ranges over the entire real number line, or depending on the context, over some subset of it such as the non-negative reals. Thus time is viewed as a continuous variable.
In contrast, continuous time views variables as having a particular value for potentially only an infinitesimally short amount of time. Between any two points in time there are an infinite number of other points in time. The variable "time" ranges over the entire real number line, or depending on the context, over some subset of it such as the non-negative reals. Thus time is viewed as a continuous variable.
相比之下，连续时间将变量视为具有特定值的变量，其时间可能只有无限短的时间。在任意两个时间点之间，还有无数其他时间点。变量“时间”的范围是整个实数行，或者取决于上下文，取决于它的某个子集，如非负雷亚尔。因此，时间被看作是一个连续变量。
<math>f(t) = \sin(t), \quad t \in \mathbb{R}</math>
<math>f(t) = \sin(t), \quad t \in \mathbb{R}</math>
数学中的四个 t = sin (t)
A finite duration counterpart of the above signal could be:
A finite duration counterpart of the above signal could be:
上述信号的一个有限持续时间的副本可以是:
<math>f(t) = \sin(t), \quad t \in [-\pi,\pi]</math> and <math>f(t) = 0</math> otherwise.
<math>f(t) = \sin(t), \quad t \in [-\pi,\pi]</math> and <math>f(t) = 0</math> otherwise.
[-pi，pi ] </math > 和 < math > f (t) = 0 </math > 否则。
<math>f(t) = \frac{1}{t}, \quad t \in [0,1]</math> and <math>f(t) = 0</math> otherwise,
<math>f(t) = \frac{1}{t}, \quad t \in [0,1]</math> and <math>f(t) = 0</math> otherwise,
[0,1] </math > 和 < math > f (t) = 0 </math > 否则,
is a finite duration signal but it takes an infinite value for <math>t = 0\,</math>.
is a finite duration signal but it takes an infinite value for <math>t = 0\,</math>.
是一个有限持续时间的信号，但是对于 < math > t = 0，</math > 它取一个无限值。
For some purposes, infinite singularities are acceptable as long as the signal is integrable over any finite interval (for example, the <math>t^{-1}</math> signal is not integrable at infinity, but <math>t^{-2}</math> is).
For some purposes, infinite singularities are acceptable as long as the signal is integrable over any finite interval (for example, the <math>t^{-1}</math> signal is not integrable at infinity, but <math>t^{-2}</math> is).
在某些情况下，只要信号在任何有限区间上可积，无限奇点是可以接受的(例如，math t ^ {-1} / math 信号在无穷远处不可积，但 math t ^ {-2} / math 可积)。
在某些情况下，只要信号在任何有限区间上可积，无限奇点是可以接受的(例如，< math > t ^ {-1} </math > 信号在无穷远处不可积，但 < math > t ^ {-2} </math > 可积)。
Any analog signal is continuous by nature. Discrete-time signals, used in digital signal processing, can be obtained by sampling and quantization of continuous signals.
Any analog signal is continuous by nature. Discrete-time signals, used in digital signal processing, can be obtained by sampling and quantization of continuous signals.
任何模拟信号本质上都是连续的。数字信号处理中使用的离散时间信号，可以通过对连续信号的采样和量化来获得。
Continuous signal may also be defined over an independent variable other than time. Another very common independent variable is space and is particularly useful in image processing, where two space dimensions are used.
Continuous signal may also be defined over an independent variable other than time. Another very common independent variable is space and is particularly useful in image processing, where two space dimensions are used.
连续信号也可以定义在时间以外的独立变量上。另一个非常常见的独立变量是空间，它在图像处理中特别有用，在图像处理中使用两个空间维度。
Discrete time is often employed when empirical measurements are involved, because normally it is only possible to measure variables sequentially. For example, while economic activity actually occurs continuously, there being no moment when the economy is totally in a pause, it is only possible to measure economic activity discretely. For this reason, published data on, for example, gross domestic product will show a sequence of quarterly values.
Discrete time is often employed when empirical measurements are involved, because normally it is only possible to measure variables sequentially. For example, while economic activity actually occurs continuously, there being no moment when the economy is totally in a pause, it is only possible to measure economic activity discretely. For this reason, published data on, for example, gross domestic product will show a sequence of quarterly values.
当涉及到经验测量时，通常采用离散时间，因为通常只能按顺序测量变量。例如，虽然经济活动实际上是连续发生的，但是没有经济完全停顿的时刻，只能对经济活动进行分散的测量。出于这个原因，例如，公布的国内生产总值(gdp)数据将显示一系列的季度价值。
When one attempts to empirically explain such variables in terms of other variables and/or their own prior values, one uses time series or regression methods in which variables are indexed with a subscript indicating the time period in which the observation occurred. For example, y<sub>t</sub> might refer to the value of income observed in unspecified time period t, y<sub>3</sub> to the value of income observed in the third time period, etc.
When one attempts to empirically explain such variables in terms of other variables and/or their own prior values, one uses time series or regression methods in which variables are indexed with a subscript indicating the time period in which the observation occurred. For example, y<sub>t</sub> might refer to the value of income observed in unspecified time period t, y<sub>3</sub> to the value of income observed in the third time period, etc.
当人们试图根据其他变量和 / 或他们自己先前的值对这些变量进行实证解释时，他们使用时间序列或回归方法，在这些方法中，变量被索引，下标表示观测发生的时间周期。例如，y 子 t / sub 可能是指在未指定时期内观察到的收入值，y 子3 / sub 是指在第三个时期内观察到的收入值，等等。
当人们试图根据其他变量和/或他们自己先前的值对这些变量进行实证解释时，他们使用时间序列或回归方法，在这些方法中，变量被索引，下标表示观测发生的时间周期。例如，y < sub > t </sub > 可能是指在非特定时间段 t 观察到的收入值，y < sub > 3 </sub > 是指在第三时间段观察到的收入值，等等。
On the other hand, it is often more mathematically tractable to construct theoretical models in continuous time, and often in areas such as physics an exact description requires the use of continuous time. In a continuous time context, the value of a variable y at an unspecified point in time is denoted as y(t) or, when the meaning is clear, simply as y.
On the other hand, it is often more mathematically tractable to construct theoretical models in continuous time, and often in areas such as physics an exact description requires the use of continuous time. In a continuous time context, the value of a variable y at an unspecified point in time is denoted as y(t) or, when the meaning is clear, simply as y.
另一方面，在连续时间内建立理论模型在数学上更易于处理，而在物理学等领域，精确的描述往往需要使用连续时间。在连续时间上下文中，未指定时间点上变量 y 的值通常表示为 y (t) ，或者，如果含义清楚，则简单地表示为 y。
<math> x_{t+1} = rx_t(1-x_t),</math>
<math> x_{t+1} = rx_t(1-x_t),</math>
< math > x _ { t + 1} = rx _ t (1-x _ t) ，</math >
in which r is a parameter in the range from 2 to 4 inclusive, and x is a variable in the range from 0 to 1 inclusive whose value in period t nonlinearly affects its value in the next period, t+1. For example, if <math>r=4</math> and <math>x_1 = 1/3</math>, then for t=1 we have <math>x_2=4(1/3)(2/3)=8/9</math>, and for t=2 we have <math>x_3=4(8/9)(1/9)=32/81</math>.
in which r is a parameter in the range from 2 to 4 inclusive, and x is a variable in the range from 0 to 1 inclusive whose value in period t nonlinearly affects its value in the next period, t+1. For example, if <math>r=4</math> and <math>x_1 = 1/3</math>, then for t=1 we have <math>x_2=4(1/3)(2/3)=8/9</math>, and for t=2 we have <math>x_3=4(8/9)(1/9)=32/81</math>.
其中 r 是2到4包含范围内的参数，x 是0到1包含范围内的变量，其周期 t 的值对下一周期 t + 1的值产生非线性影响。例如，如果数学 r 4 / math 和 math x 11 / 3 / math，那么对于 t 1，我们有 math x24(1 / 3)(2 / 3)8 / 9 / math，对于 t 2，我们有 math x34(8 / 9)(1 / 9)32 / 81 / math。
其中 r 是2到4包含的参数，x 是0到1包含的变量，其周期 t 的值对下一周期 t + 1的值产生非线性影响。例如，如果 < math > r = 4 </math > 和 < math > x1 = 1/3 </math > ，那么对于 t = 1，我们有 < math > x2 = 4(1/3)(2/3) = 8/9 </math > ，对于 t = 2，我们有 < math > x3 = 4(8/9)(1/9) = 32/81 </math > 。
Another example models the adjustment of a price P in response to non-zero excess demand for a product as
Another example models the adjustment of a price P in response to non-zero excess demand for a product as
另一个例子模型的价格 p 的调整，以响应非零过剩需求的产品如下
<math>P_{t+1} = P_t + \delta \cdot f(P_t,...)</math>
<math>P_{t+1} = P_t + \delta \cdot f(P_t,...)</math>
< math > p _ { t + 1} = p _ t + delta cdot f (p _ t，...) </math >
where <math>\delta</math> is the positive speed-of-adjustment parameter which is less than or equal to 1, and where <math>f</math> is the excess demand function.
where <math>\delta</math> is the positive speed-of-adjustment parameter which is less than or equal to 1, and where <math>f</math> is the excess demand function.
其中 math delta / math 是小于或等于1的正调整速度参数，其中 math f / math 是超额需求函数。
其中 < math > delta </math > 是小于或等于1的正调整速度参数，< math > f </math > 是超额需求函数。
<math>\frac{dP}{dt}=\lambda \cdot f(P,...)</math>
<math>\frac{dP}{dt}=\lambda \cdot f(P,...)</math>
(p，...) </math >
where the left side is the first derivative of the price with respect to time (that is, the rate of change of the price), <math>\lambda</math> is the speed-of-adjustment parameter which can be any positive finite number, and <math>f</math> is again the excess demand function.
where the left side is the first derivative of the price with respect to time (that is, the rate of change of the price), <math>\lambda</math> is the speed-of-adjustment parameter which can be any positive finite number, and <math>f</math> is again the excess demand function.
其中左边是价格对时间的一阶导数(即价格变化率) ，< math > lambda </math > 是调整速度参数，可以是任意正的有限数字，< math > f </math > 又是超额需求函数。
A variable measured in discrete time can be plotted as a step function, in which each time period is given a region on the horizontal axis of the same length as every other time period, and the measured variable is plotted as a height that stays constant throughout the region of the time period. In this graphical technique, the graph appears as a sequence of horizontal steps. Alternatively, each time period can be viewed as a detached point in time, usually at an integer value on the horizontal axis, and the measured variable is plotted as a height above that time-axis point. In this technique, the graph appears as a set of dots.
A variable measured in discrete time can be plotted as a step function, in which each time period is given a region on the horizontal axis of the same length as every other time period, and the measured variable is plotted as a height that stays constant throughout the region of the time period. In this graphical technique, the graph appears as a sequence of horizontal steps. Alternatively, each time period can be viewed as a detached point in time, usually at an integer value on the horizontal axis, and the measured variable is plotted as a height above that time-axis point. In this technique, the graph appears as a set of dots.
在离散时间中测量的一个变量可以绘制为一个阶跃函数，其中每个时间周期在水平轴上给定一个与每个其他时间周期相同长度的区域，测量的变量绘制为在整个时间周期区域内保持不变的高度。在这种图形技术中，图表显示为一系列水平步骤。或者，可以将每个时间段视为时间上的一个分离点，通常位于水平轴上的一个整数值处，测量变量绘制为该时间轴点之上的一个高度。在这种技术中，图表显示为一组点。
| author1 = Gershenfeld, Neil A.
| author1 = Gershenfeld, Neil A.
1 Gershenfeld，Neil a.
1 = Gershenfeld，Neil a.
| authorlink =
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| title = The Nature of mathematical Modeling
| title = The Nature of mathematical Modeling
| publisher = Cambridge University Press
| publisher = Cambridge University Press
剑桥大学出版社
| year = 1999
| year = 1999
| location =
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| 位置
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2012年10月11日
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2012年10月15日
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2012年10月22日
| isbn = 0-521-57095-6}}
| isbn = 0-521-57095-6}}
| isbn = 0-521-57095-6}}
| isbn = 0-521-57095-6}}
| isbn = 0-521-57095-6}}
| author1 = Wagner, Thomas Charles Gordon
| author1 = Wagner, Thomas Charles Gordon
1 = Wagner，Thomas Charles Gordon
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| title = Analytical transients
| title = Analytical transients
| title = Analytical transients
| title = Analytical transients
| title = 分析瞬态
| publisher = Wiley
| publisher = Wiley
| publisher = Wiley
| publisher = Wiley
| publisher = Wiley
| year = 1959
| year = 1959
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2012年10月11日
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2012年10月15日
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2012年10月22日
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我不知道你会怎么做