频率特性的测量实验（频率特性概念及基本实验方法）

频率特性的定义

设系统传递函数为。定义系统输出信号的稳态响应相对其正弦输入信号的幅值之比为系统的幅频特性。

幅频特性描述系统在稳态下响应不同频率的正弦输入时在幅值上的增益特性（衰减或放大）。

定义系统输出信号的稳态响应相对其正弦输入信号的相移

为系统的相频特性。

相频特性描述系统在稳态下响应不同频率的正弦输入时在相位上产生的滞后或超前特性。

上述定义的幅频特性

和相频特性

统称为系统的频率特性，它描述了系统对正弦输入的稳态响应。当输入为非正弦的周期信号时，其输入可利用傅立叶级数展开成正弦波的叠加，其输出为相应的正弦波输出的叠加，例如下图所示。

当输入为非周期信号时，可将该非周期信号看做周期 T→∞的周期信号。

傅氏变换与拉氏变换

傅氏正变换式

拉氏正变换式

傅氏变换与拉氏变换是类似的。

除了积分下限不同外，只要将s换成jw,就可将已知的拉氏变换式变成相应的傅氏变换式。

翻译成英文：

The concept of frequency characteristics and basic experimental methods

Definition of frequency characteristics

Suppose the system transfer function is. Define the ratio of the steady-state response of the output signal of the system to the amplitude of its sinusoidal input signal as the amplitude-frequency characteristic of the system.

Amplitude-frequency characteristics describe the gain characteristics (attenuation or amplification) of the amplitude when the system responds to sinusoidal inputs of different frequencies in a steady state.

Define the phase shift of the steady-state response of the system output signal relative to its sinusoidal input signal

It is the phase frequency characteristic of the system.

The phase-frequency characteristic describes the lag or lead characteristic in the phase when the system responds to the sinusoidal input of different frequencies in the steady state.

Amplitude-frequency characteristics defined above

Sum phase frequency characteristics

Collectively referred to as the frequency characteristics of the system, it describes the steady-state response of the system to sinusoidal input.

When the input is a non-sinusoidal periodic signal, its input can be expanded into a superposition of sine waves using Fourier series, and its output is the superposition of corresponding sine wave outputs, as shown in the figure below.

When the input is an aperiodic signal, the aperiodic signal can be regarded as a periodic signal with period T→∞.

Fourier transform and Laplace transform

Fourier transform

Laplace transform

The Fourier transform is similar to the Laplace transform.

In addition to the difference in the lower limit of the integral, as long as s is replaced by jw, the known Laplace transform can be transformed into the corresponding Fourier transform.

资料来源：清华大学控制工程基础PPT

英文翻译：Google翻译

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