where As and An denote the signal a

其中，As和An分别表示信号幅度和噪声幅度（以相同单位表示）。当SNR低时，感兴趣的信号可能变得无法区分。因此，必须采用适当的数据采集策略以最小化不可避免地影响测量的噪声水平（第3章）。<br>复数信号可能会分解为基本信号。基本信号的例子是脉冲和正弦波。当信号分解成按比例缩放和偏移的脉冲时，便会进行时域分析。相反，如果将信号分解为不同频率的缩放正弦曲线，则在频域中进行分析。始终可以将信号从一个域转换到另一个域，因此最终的选择通常取决于对计算效率，数据解释的简便性和降噪技术的考虑。<br>通常通过定义理想的恒定参数线性系统（也称为线性时不变LTI系统，图1.1）来描述物理系统的动态行为。如果系统的所有基本属性都相对于时间不变，则其特征为常数。此外，如果响应特性是加性和均质的，则它显示了输入和输出之间的线性映射。结果，系统对给定输入的线性组合的响应等于系统对各个单独分析的输入的响应的相同线性组合。常数参数假设对于实践中遇到的几个物理系统是合理有效的。但是，其有效性取决于所考虑的时间间隔的延长。

where As and An denote the signal amplitude and the noise amplitude (expressed in the same units), respectively. When the SNR is low, the signal of interest can become indistinguishable. Thus, appropriate data acquisition strategies must be adopted to minimize the level of noise that inevitably affects measurements (Chap. 3).<br>Complex signals may be decomposed into elemental signals. Examples of elemental signals are the impulse and the sinusoid. When the signal is decomposed into scaled and shifted impulses, a time domain analysis takes place; if, instead, the signal is decomposed into scaled sinusoids of different frequency, analysis is carried out in the frequency domain. It is always possible to convert a signal from one domain to the other, so the final choice is usually dictated by considerations about computational efficiency, ease of data interpretation, and noise reduction techniques.<br>The dynamic behavior of physical systems is often described by defining an ideal constant-parameter linear system (also known as linear time-invariant— LTI—system, Fig. 1.1). A system is characterized by constant parameters if all its fundamental properties are invariant with respect to time. Moreover, it shows a linear mapping between input and output if the response characteristics are additive and homogeneous. As a result, the response of the system to a linear combination of given inputs equals the same linear combination of the system responses to the individual, separately analyzed inputs. The constant-parameter assumption is reasonably valid for several physical systems encountered in the practice. However, its validity depends on the extension of the considered time interval.

其中，As和An分别表示信号幅度和噪声幅度（以相同的单位表示）。当信噪比较低时，感兴趣的信号可能变得难以区分。因此，必须采取适当的数据采集策略，以尽量减少不可避免地影响测量的噪声水平（第3章）。<br>复杂信号可以分解为基本信号。基本信号的例子是脉冲和正弦波。当信号被分解成标度和位移脉冲时，进行时域分析；如果信号被分解成不同频率的标度正弦，则在频域进行分析。将信号从一个域转换到另一个域总是可能的，因此最终的选择通常取决于对计算效率、数据解释的易用性和降噪技术的考虑。<br>物理系统的动态行为通常通过定义一个理想的常参数线性系统（也称为线性时不变LTI系统，图1.1）来描述。如果一个系统的所有基本性质都是关于时间不变的，那么它就具有常数参数的特征。此外，如果响应特性是可加的和齐次的，则表示输入和输出之间的线性映射。结果，系统对给定输入的线性组合的响应等于系统对单独分析的输入的响应的相同线性组合。常数参数假设对于实际中遇到的几个物理系统是合理有效的。然而，它的有效性取决于所考虑的时间间隔的延长。<br>