Chirp  鸣叫

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A chirp is a signal in which the frequency increases (up-chirp) or decreases (down-chirp) with time. In some sources, the term chirp is used interchangeably with sweep signal.^[1] It is commonly applied to sonar, radar, and laser systems, and to other applications, such as in spread-spectrum communications (see chirp spread spectrum). This signal type is biologically inspired and occurs as a phenomenon due to dispersion (a non-linear dependence between frequency and the propagation speed of the wave components). It is usually compensated for by using a matched filter, which can be part of the propagation channel. Depending on the specific performance measure, however, there are better techniques both for radar and communication. Since it was used in radar and space, it has been adopted also for communication standards. For automotive radar applications, it is usually called linear frequency modulated waveform (LFMW).^[2]
“啁啾”是一种信号，在这种信号中，频率随着时间增加（上啁啾）或减少（下啁啾）。在一些来源中，啁啾一词与扫频信号可以互换使用。它通常应用于声纳、雷达和激光系统，以及其他应用，如扩频通信（参见啁啾扩频）。这种信号类型受到生物启发，由于频散（频率和波动传播速度之间的非线性关系）而作为现象发生。通常使用匹配滤波器来补偿这一点，匹配滤波器可以是传播通道的一部分。然而，根据特定的性能指标，对于雷达和通信都有更好的技术。由于它在雷达和空间应用中被使用，因此也被采用于通信标准。在汽车雷达应用中，它通常被称为线性调频波形（LFMW）。

In spread-spectrum usage, surface acoustic wave (SAW) devices are often used to generate and demodulate the chirped signals. In optics, ultrashort laser pulses also exhibit chirp, which, in optical transmission systems, interacts with the dispersion properties of the materials, increasing or decreasing total pulse dispersion as the signal propagates. The name is a reference to the chirping sound made by birds; see bird vocalization.
在扩频应用中，表面声波（SAW）设备通常用于生成和解调啁啾信号。在光学中，超短激光脉冲也表现出啁啾，这在光传输系统中与材料的色散特性相互作用，随着信号传播增加或减少总脉冲色散。这个名字是指鸟类发出的啁啾声；参见鸟类发声。

The basic definitions here translate as the common physics quantities location (phase), speed (angular velocity), acceleration (chirpyness). If a waveform is defined as: $${\displaystyle x(t)=\sin \left(\phi (t)\right)}$$
这里的基本定义翻译为常见的物理量：位置（相位）、速度（角速度）、加速度（鸣叫）。如果波形定义为： $${\displaystyle x(t)=\sin \left(\phi (t)\right)}$$

then the instantaneous angular frequency, ω, is defined as the phase rate as given by the first derivative of phase, with the instantaneous ordinary frequency, f, being its normalized version: $${\displaystyle \omega (t)={\frac {d\phi (t)}{dt}},\,f(t)={\frac {\omega (t)}{2\pi }}}$$
那么瞬时角频率ω定义为相位的变化率，它由相位的一阶导数给出，瞬时普通频率 f 是其归一化版本： $${\displaystyle \omega (t)={\frac {d\phi (t)}{dt}},\,f(t)={\frac {\omega (t)}{2\pi }}}$$

Finally, the instantaneous angular chirpyness (symbol γ) is defined to be the second derivative of instantaneous phase or the first derivative of instantaneous angular frequency, $${\displaystyle \gamma (t)={\frac {d^{2}\phi (t)}{dt^{2}}}={\frac {d\omega (t)}{dt}}}$$ Angular chirpyness has units of radians per square second (rad/s²); thus, it is analogous to angular acceleration.
最后，即时角度啁啾度（符号 γ）被定义为瞬时相位的二阶导数或瞬时角频率的一阶导数， $${\displaystyle \gamma (t)={\frac {d^{2}\phi (t)}{dt^{2}}}={\frac {d\omega (t)}{dt}}}$$ 角度啁啾度的单位是弧度每平方秒（rad/s ² ），因此，它类似于角加速度。

The instantaneous ordinary chirpyness (symbol c) is a normalized version, defined as the rate of change of the instantaneous frequency:^[3] $${\displaystyle c(t)={\frac {\gamma (t)}{2\pi }}={\frac {df(t)}{dt}}}$$ Ordinary chirpyness has units of square reciprocal seconds (s⁻²); thus, it is analogous to rotational acceleration.
瞬时普通啁啾度（符号 c）是一个标准化版本，定义为瞬时频率的变化率： ^[3] $${\displaystyle c(t)={\frac {\gamma (t)}{2\pi }}={\frac {df(t)}{dt}}}$$ 普通啁啾度的单位是平方倒秒（s ⁻² ）；因此，它类似于旋转加速度。

Linear chirp  线性啁啾

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Sound example for linear chirp (five repetitions)
线性啁啾的声音示例（五次重复）

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In a linear-frequency chirp or simply linear chirp, the instantaneous frequency ${\displaystyle f(t)}$ varies exactly linearly with time: $${\displaystyle f(t)=ct+f_{0},}$$ where ${\displaystyle f_{0}}$ is the starting frequency (at time ${\displaystyle t=0}$) and ${\displaystyle c}$ is the chirp rate, assumed constant: $${\displaystyle c={\frac {f_{1}-f_{0}}{T}}={\frac {\Delta f}{\Delta t}}.}$$
在线性频率啁啾或简单的线性啁啾中，瞬时频率 ${\displaystyle f(t)}$ 随时间线性变化： $${\displaystyle f(t)=ct+f_{0},}$$ 其中 ${\displaystyle f_{0}}$ 是起始频率（在时间 ${\displaystyle t=0}$ 时）并且 ${\displaystyle c}$ 是啁啾率，假设为常数： $${\displaystyle c={\frac {f_{1}-f_{0}}{T}}={\frac {\Delta f}{\Delta t}}.}$$

Here, ${\displaystyle f_{1}}$ is the final frequency and ${\displaystyle T}$ is the time it takes to sweep from ${\displaystyle f_{0}}$ to ${\displaystyle f_{1}}$.
这里， ${\displaystyle f_{1}}$ 是最终频率， ${\displaystyle T}$ 是从 ${\displaystyle f_{0}}$ 扫描到 ${\displaystyle f_{1}}$. 所需的时间

The corresponding time-domain function for the phase of any oscillating signal is the integral of the frequency function, as one expects the phase to grow like ${\displaystyle \phi (t+\Delta t)\simeq \phi (t)+2\pi f(t)\,\Delta t}$, i.e., that the derivative of the phase is the angular frequency ${\displaystyle \phi '(t)=2\pi \,f(t)}$.
任何振荡信号的相位对应的时域函数是频率函数的积分，因为人们期望相位像 ${\displaystyle \phi (t+\Delta t)\simeq \phi (t)+2\pi f(t)\,\Delta t}$ 增长，即相位的导数是角频率 ${\displaystyle \phi '(t)=2\pi \,f(t)}$ 。

For the linear chirp, this results in: $${\displaystyle {\begin{aligned}\phi (t)&=\phi _{0}+2\pi \int _{0}^{t}f(\tau )\,d\tau \\&=\phi _{0}+2\pi \int _{0}^{t}\left(c\tau +f_{0}\right)\,d\tau \\&=\phi _{0}+2\pi \left({\frac {c}{2}}t^{2}+f_{0}t\right),\end{aligned}}}$$
对于线性啁啾，这导致： $${\displaystyle {\begin{aligned}\phi (t)&=\phi _{0}+2\pi \int _{0}^{t}f(\tau )\,d\tau \\&=\phi _{0}+2\pi \int _{0}^{t}\left(c\tau +f_{0}\right)\,d\tau \\&=\phi _{0}+2\pi \left({\frac {c}{2}}t^{2}+f_{0}t\right),\end{aligned}}}$$

where ${\displaystyle \phi _{0}}$ is the initial phase (at time ${\displaystyle t=0}$). Thus this is also called a quadratic-phase signal.^[4]
其中 ${\displaystyle \phi _{0}}$ 是初始相位（在时间 ${\displaystyle t=0}$ 时）。因此，这也称为二次相位信号。 ^[4]

The corresponding time-domain function for a sinusoidal linear chirp is the sine of the phase in radians: $${\displaystyle x(t)=\sin \left[\phi _{0}+2\pi \left({\frac {c}{2}}t^{2}+f_{0}t\right)\right]}$$
线性频率调制的正弦波时域函数是相位的正弦值（弧度）： $${\displaystyle x(t)=\sin \left[\phi _{0}+2\pi \left({\frac {c}{2}}t^{2}+f_{0}t\right)\right]}$$

Exponential chirp  指数啁啾

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Sound example for exponential chirp (five repetitions)
五次重复的指数啁啾声音示例

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In a geometric chirp, also called an exponential chirp, the frequency of the signal varies with a geometric relationship over time. In other words, if two points in the waveform are chosen, ${\displaystyle t_{1}}$ and ${\displaystyle t_{2}}$, and the time interval between them ${\displaystyle T=t_{2}-t_{1}}$ is kept constant, the frequency ratio ${\displaystyle f\left(t_{2}\right)/f\left(t_{1}\right)}$ will also be constant.^[5][6]
在几何调频信号中，也称为指数调频信号，信号的频率随时间以几何关系变化。换句话说，如果在波形中选择两个点， ${\displaystyle t_{1}}$ 和 ${\displaystyle t_{2}}$ ，并且它们之间的时间间隔 ${\displaystyle T=t_{2}-t_{1}}$ 保持不变，那么频率比 ${\displaystyle f\left(t_{2}\right)/f\left(t_{1}\right)}$ 也将保持不变。 ^{[5] [6]}

In an exponential chirp, the frequency of the signal varies exponentially as a function of time: $${\displaystyle f(t)=f_{0}k^{\frac {t}{T}}}$$ where ${\displaystyle f_{0}}$ is the starting frequency (at ${\displaystyle t=0}$), and ${\displaystyle k}$ is the rate of exponential change in frequency.
在指数扫频中，信号的频率作为时间的函数呈指数变化： $${\displaystyle f(t)=f_{0}k^{\frac {t}{T}}}$$ 其中 ${\displaystyle f_{0}}$ 是起始频率（在 ${\displaystyle t=0}$ ）， ${\displaystyle k}$ 是频率的指数变化率。

$${\displaystyle k={\frac {f_{1}}{f_{0}}}}$$

Where ${\displaystyle f_{1}}$ is the ending frequency of the chirp (at ${\displaystyle t=T}$).
其中 ${\displaystyle f_{1}}$ 是啁啾的结束频率（在 ${\displaystyle t=T}$ 时）。

Unlike the linear chirp, which has a constant chirpyness, an exponential chirp has an exponentially increasing frequency rate.
与具有恒定调频特性的线性啁啾不同，指数啁啾具有呈指数增长的频率变化率。

The corresponding time-domain function for the phase of an exponential chirp is the integral of the frequency: $${\displaystyle {\begin{aligned}\phi (t)&=\phi _{0}+2\pi \int _{0}^{t}f(\tau )\,d\tau \\&=\phi _{0}+2\pi f_{0}\int _{0}^{t}k^{\frac {\tau }{T}}d\tau \\&=\phi _{0}+2\pi f_{0}\left({\frac {Tk^{\frac {t}{T}}}{\ln(k)}}\right)\end{aligned}}}$$ where ${\displaystyle \phi _{0}}$ is the initial phase (at ${\displaystyle t=0}$).
指数啁啾的相位对应的时域函数是频率的积分： $${\displaystyle {\begin{aligned}\phi (t)&=\phi _{0}+2\pi \int _{0}^{t}f(\tau )\,d\tau \\&=\phi _{0}+2\pi f_{0}\int _{0}^{t}k^{\frac {\tau }{T}}d\tau \\&=\phi _{0}+2\pi f_{0}\left({\frac {Tk^{\frac {t}{T}}}{\ln(k)}}\right)\end{aligned}}}$$ 其中 ${\displaystyle \phi _{0}}$ 是初始相位（在 ${\displaystyle t=0}$ 时）。

The corresponding time-domain function for a sinusoidal exponential chirp is the sine of the phase in radians: $${\displaystyle x(t)=\sin \left[\phi _{0}+2\pi f_{0}\left({\frac {Tk^{\frac {t}{T}}}{\ln(k)}}\right)\right]}$$
正弦指数啁啾的相应时域函数是相位的正弦（以弧度表示）： $${\displaystyle x(t)=\sin \left[\phi _{0}+2\pi f_{0}\left({\frac {Tk^{\frac {t}{T}}}{\ln(k)}}\right)\right]}$$

As was the case for the Linear Chirp, the instantaneous frequency of the Exponential Chirp consists of the fundamental frequency ${\displaystyle f(t)=f_{0}k^{\frac {t}{T}}}$ accompanied by additional harmonics.^{[citation needed]}
与线性啁啾的情况一样，指数啁啾的瞬时频率由基频 ${\displaystyle f(t)=f_{0}k^{\frac {t}{T}}}$ 及其附加谐波组成。 ^{[citation needed]}

Hyperbolic chirps are used in radar applications, as they show maximum matched filter response after being distorted by the Doppler effect.^[7]
双曲线啁啾在雷达应用中被使用，因为它们在经历多普勒效应的失真后显示出最大的匹配滤波器响应。 ^[7]

In a hyperbolic chirp, the frequency of the signal varies hyperbolically as a function of time: $${\displaystyle f(t)={\frac {f_{0}f_{1}T}{(f_{0}-f_{1})t+f_{1}T}}}$$
在双曲线啁啾中，信号的频率随时间呈双曲线变化： $${\displaystyle f(t)={\frac {f_{0}f_{1}T}{(f_{0}-f_{1})t+f_{1}T}}}$$

The corresponding time-domain function for the phase of an hyperbolic chirp is the integral of the frequency: $${\displaystyle {\begin{aligned}\phi (t)&=\phi _{0}+2\pi \int _{0}^{t}f(\tau )\,d\tau \\&=\phi _{0}+2\pi {\frac {-f_{0}f_{1}T}{f_{1}-f_{0}}}\ln \left(1-{\frac {f_{1}-f_{0}}{f_{1}T}}t\right)\end{aligned}}}$$ where ${\displaystyle \phi _{0}}$ is the initial phase (at ${\displaystyle t=0}$).
超幅线性啁啾的相位对应的时域函数是频率的积分： $${\displaystyle {\begin{aligned}\phi (t)&=\phi _{0}+2\pi \int _{0}^{t}f(\tau )\,d\tau \\&=\phi _{0}+2\pi {\frac {-f_{0}f_{1}T}{f_{1}-f_{0}}}\ln \left(1-{\frac {f_{1}-f_{0}}{f_{1}T}}t\right)\end{aligned}}}$$ ，其中 ${\displaystyle \phi _{0}}$ 是初始相位（在 ${\displaystyle t=0}$ 时）。

The corresponding time-domain function for a sinusoidal hyperbolic chirp is the sine of the phase in radians: $${\displaystyle x(t)=\sin \left[\phi _{0}+2\pi {\frac {-f_{0}f_{1}T}{f_{1}-f_{0}}}\ln \left(1-{\frac {f_{1}-f_{0}}{f_{1}T}}t\right)\right]}$$
正弦超双曲线啁啾的相应时域函数是相位（以弧度为单位）的正弦： $${\displaystyle x(t)=\sin \left[\phi _{0}+2\pi {\frac {-f_{0}f_{1}T}{f_{1}-f_{0}}}\ln \left(1-{\frac {f_{1}-f_{0}}{f_{1}T}}t\right)\right]}$$

A chirp signal can be generated with analog circuitry via a voltage-controlled oscillator (VCO), and a linearly or exponentially ramping control voltage.^[8] It can also be generated digitally by a digital signal processor (DSP) and digital-to-analog converter (DAC), using a direct digital synthesizer (DDS) and by varying the step in the numerically controlled oscillator.^[9] It can also be generated by a YIG oscillator.^{[clarification needed]}
可以通过电压控制振荡器（VCO）和线性或指数逐渐增加的控制电压，使用模拟电路生成一个啁啾信号。 ^[8] 也可以通过数字信号处理器（DSP）和数模转换器（DAC）数字生成，使用直接数字合成器（DDS）并通过变更数控振荡器中的步幅。 ^[9] 还可以通过 YIG 振荡器生成。 ^{[clarification needed]}

A chirp signal shares the same spectral content with an impulse signal. However, unlike in the impulse signal, spectral components of the chirp signal have different phases,^{[10][11][12][13]} i.e., their power spectra are alike but the phase spectra are distinct. Dispersion of a signal propagation medium may result in unintentional conversion of impulse signals into chirps (Whistler). On the other hand, many practical applications, such as chirped pulse amplifiers or echolocation systems,^[12] use chirp signals instead of impulses because of their inherently lower peak-to-average power ratio (PAPR).^[13]
啁啾信号与脉冲信号具有相同的频谱内容。然而，与脉冲信号不同，啁啾信号的频谱成分具有不同的相位，即它们的功率谱相似，但相位谱各不相同。信号传播介质的色散可能导致脉冲信号意外地转化为啁啾信号（Whistler）。另一方面，许多实际应用，如啁啾脉冲放大器或回声定位系统，使用啁啾信号而不是脉冲，因为它们具有固有的较低峰值与平均功率比（PAPR）。

Chirp modulation, or linear frequency modulation for digital communication, was patented by Sidney Darlington in 1954 with significant later work performed by Winkler in 1962. This type of modulation employs sinusoidal waveforms whose instantaneous frequency increases or decreases linearly over time. These waveforms are commonly referred to as linear chirps or simply chirps.
啾啾调制，或用于数字通信的线性频率调制，是在 1954 年由 Sidney Darlington 获得专利，1962 年 Winkler 进行了重要的后续工作。这种调制类型采用正弦波形，其瞬时频率随时间线性增加或减少。这些波形通常被称为线性啾啾或简单的啾啾。

Hence the rate at which their frequency changes is called the chirp rate. In binary chirp modulation, binary data is transmitted by mapping the bits into chirps of opposite chirp rates. For instance, over one bit period "1" is assigned a chirp with positive rate a and "0" a chirp with negative rate −a. Chirps have been heavily used in radar applications and as a result advanced sources for transmission and matched filters for reception of linear chirps are available.
因此，它们频率变化的速率称为啁啾速率。在二进制啁啾调制中，通过将比特映射到相反啁啾速率的啁啾中来传输二进制数据。例如，在一个比特周期内，“1”分配一个正速率 a 的啁啾，而“0”分配一个负速率 −a 的啁啾。啁啾在雷达应用中被广泛使用，因此可用于线性啁啾传输的先进源和用于接收的匹配滤波器已经可用。

Another kind of chirp is the projective chirp, of the form: $${\displaystyle g=f\left[{\frac {a\cdot x+b}{c\cdot x+1}}\right],}$$ having the three parameters a (scale), b (translation), and c (chirpiness). The projective chirp is ideally suited to image processing, and forms the basis for the projective chirplet transform.^[3]
另一种啁啾是投影啁啾，形式为： $${\displaystyle g=f\left[{\frac {a\cdot x+b}{c\cdot x+1}}\right],}$$ ，具有三个参数 a（比例）、b（平移）和 c（啁啾性）。投影啁啾非常适合图像处理，并构成了投影啁啾变换的基础。 ^[3]

A change in frequency of Morse code from the desired frequency, due to poor stability in the RF oscillator, is known as chirp,^[14] and in the R-S-T system is given an appended letter 'C'.
由于射频振荡器稳定性差，摩尔斯代码频率从期望频率的变化称为 chirp，在 R-S-T 系统中会附加一个字母 'C'。

• Chirp spectrum - Analysis of the frequency spectrum of chirp signals
  啁啾频谱 - 啁啾信号频谱的分析
• Chirp compression - Further information on compression techniques
  Chirp 压缩 - 有关压缩技术的更多信息
• Chirp spread spectrum - A part of the wireless telecommunications standard IEEE 802.15.4a CSS
  啁啾扩频 - 无线电信标准 IEEE 802.15.4a CSS 的一部分
• Chirped mirror  啁啾镜
• Chirped pulse amplification
  啁啾脉冲放大
• Chirplet transform - A signal representation based on a family of localized chirp functions.
  Chirplet 变换 - 一种基于局部啁啾函数族的信号表示。
• Continuous-wave radar  连续波雷达
• Dispersion (optics)  色散（光学）
• Pulse compression  脉冲压缩
• Radio propagation § Measuring HF propagation
  无线电传播 § 测量高频传播

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Look up chirp in Wiktionary, the free dictionary.
在维基词典中查找 chirp，这本免费词典。

• Online Chirp Tone Generator (WAV file output)
  在线鸣叫音调生成器（WAV 文件输出）
• CHIRP Sonar on FishFinder
  CHIRP 声纳在鱼探测器上
• CHIRP Sonar on FishFinder
  CHIRP 声纳在鱼探测器上