Measurement and control technology and instruments - APS

1 .Singal

1.1 Type

• Deterministic signal
  • periodic signal
  • aperiodic signal [ continuous frequency spectrum ]
    • quasi-periodic signal : 2 and more frequency $cosw_0t+cos\sqrt2w_0t$
    • transient signal : $x(t)=x_0e^{-at}sin(w_0t+\varphi)$
• indeterministic [ random signal ]
  • stationary random signal
  • nonstationary

• continuous s

  

• discrete s

  

• analog s : 独变+幅值为连续

• digital s : 离散信号 , 幅值连续

• energy s : $\int^\infty_{-\infty}x^2(t)dt<\infty$

• power s : $\int^\infty_{-\infty}x^2(t)dt\rightarrow \infty$, $\dfrac{1}{t_2-t_1}\int^{t_2}_{t_1}x^2(t)dt<\infty$

1.2 Time-domain & frequency domain

• time domain : change with time
• frequency domain : frequency composition, amplitude, phase angle

1.3 Periodic square wave

1.4 Fourier series

use trigonometric function to approximate any signal

1.4.1 One side

$x(t)=a_0+\sum^\infty_{n=1}(a_ncosnw_0t+b_nsinw+0t)=a_0+\sum^\infty_1sin(nw_0t+\varphi_n)\quad n=1,2,3,\dots$

• $a_0=\dfrac{1}{T}\int^{\dfrac{T}{2}}_{-\dfrac{T}{2}}x(t)dt\a_n=\dfrac{2}{T}\int^{\dfrac{T}{2}}_{-\dfrac{T}{2}}x(t)cosnw_0tdt\b_n=\dfrac{2}{T}\int^{\dfrac{T}{2}}_{-\dfrac{T}{2}}x(t)sinnw_0tdt$

• $A_n=\sqrt{a^2_n+b^2_n}\tan\varphi_n=\dfrac{a_n}{b_n}$

1.4.2 Euler equation

$e^{\pm jwt}=coswt\pm jsinwt\coswt=\dfrac{1}{2}(e^{jwt}+e^{-jwt})\sinwt=\dfrac{1}{2j}(e^{jwt}-e^{-jwt})$

1.4.3 Both side

$x(t)=\sum^\infty_{n=-\infty}c_ne^{jnw_0t}=\sum^\infty_{-\infty}|c_n|e^{j(nw_0t+\varphi)}\quad n=0,\pm1,\pm2,\dots$

• $|c_n|=A_n=\sqrt{a^2_n+b^2_n}\\varphi_n=arctan\dfrac{a_n}{b_n}​$
• $c_n=\dfrac{1}{T}\int^{\dfrac{T}{2}}_{-\dfrac{T}{2}}x(t)e^{-jnw_0t}dt$
• $\int^a_af(x)dx=\left{\begin{array}{c,l}2\int^a_0f(x)dx,&偶\0,&奇\end{array}\right.$

1.5 Periodic Function

1.5.1 Feature

• discrete
• have a base frequency
• amplitude is less when frequency goes higher

1.5.2 Strength

• average : $\mu_x=\dfrac{1}{T_0}\int^{T_0}_0x(t)dt$
• root mean square value : $x_{rms}=\sqrt{\dfrac{1}{T_0}\int^{T_0}_0x^2(t)dt}$
• square value: $P_{aj}=x^2_{rms}=\dfrac{1}{T_0}\int^{T_0}_0x^2(t)dt​$

1.6 Aperiodic

$T_0\rightarrow\infty$ , frequency continus

1.7 Fourier transform

$X(f)=\int^\infty_{-\infty}x(t)e^{-j2\pi ft}dt=\dfrac{1}{2\pi}\int^\infty_{-\infty}x(t)e^{jwt}dt$

$x(t)=\int^\infty_{-\infty}X(f)e^{j2\pi ft}df=\int^\infty_{-\infty}X(w)e^{jwt}dw$

• $X(f)=|X(f)|e^{j\varphi(t)}$
• $|X(f)|$ : continuous amplitude spectrum
• $\varphi(f)$ continuous phase spectrum

1.7.1 Window function

$w(t)=\left{\begin{array}{cl}1,&|t|<\dfrac{T}{2}\0,&|t|>\dfrac{T}{2}\end{array}\right.\Leftrightarrow W(f)=T\dfrac{sin\pi fT}{\pi f T}=Tsinc(\pi fT)$

• frequency spectrum : $W(f)=\int^\infty_{-\infty}w(t)e^{-j2\pi ft}dt=\dfrac{1}{j2\pi f}(e^{j\pi fT}-e^{j\pi fT})\\Downarrow sin(\pi fT)=\dfrac{1}{2j}(e^{j\pi fT}-e^{-\pi fT})\=T\dfrac{sin\pi fT}{\pi fT}=Tsinc(\pi fT)$

  • $|W(f)|=T|sinc(\pi fT)|$
• only real part no virtual
• amplitude spectrum : $|W(f)|=T|sinc(2\pi fT)|$

1.7.2 F-transform princple

Superposition	$ax(t)+by(t)\leftrightarrow aX(f)+bY(f)$
scale change	$x(kt)\leftrightarrow\dfrac{1}{k}X(\dfrac{f}{k})$
time change	$x(t-t_0)\leftrightarrow X(f)e^{-j2\pi ft_0}$
frequency change	$x(t)e^{\mp j2\pi f_0t}\leftrightarrow X(f\pm f_0)$
time domain convolution	$x_1(t)*x_2(t)\leftrightarrow X_1(f)X_2(f)$
frequency domain convolution	$x_1(t)x_2(t)\leftrightarrow X_1(f)*X_2(f)$

• convolution : $\int^\infty_{-\infty}x_1(\tau)x_2(t-\tau)d\tau$

1.8 $\delta$ function

Window function : $\varepsilon\rightarrow 0\quad\Rightarrow\quad\delta (t)=\left{\begin{array}{cl}\infty,&t=0\0,&t\ne0\end{array}\right.​$

$\int^\infty_{-\infty}\delta(t)dt=\lim\limits_{\varepsilon\rightarrow0}\int^\infty_{-\infty}S_\varepsilon(t)dt=1​$

1.8.1 Princple

• sample:

  $\int^\infty_{-\infty}\delta(t-t_0)f(t)dt=\int^\infty_{-\infty}\delta(t-t_0)f(t_0)dt=f(t_0)\int^\infty_{-\infty}\delta(t-t_0)dt\=f(t_0)$

  

  convolution

  

  $x(t)*\delta(t)=\int^\infty_{-\infty}x(\tau)\delta(t-\tau)d\tau\\Downarrow {\rm even function}\=\int^\infty_{-\infty}x(\tau)\delta(t-\tau)d\tau=x(t)$

  $x(t)*\delta(t\pm t_0)=\int^\infty_{-\infty}x(\tau)\delta(t\pm t_0-\tau)d\tau=x(t\pm t_0)$

1.8.2 Frequency specturm

$\Delta (f)=\int^\infty_{-\infty}\delta(t)e^{-j2\pi ft}dt=e^0=1\\delta(t)=\int^\infty_{-\infty}1e^{j2\pi ft}df$

Time D	Frequency D
$\delta(t)$	1
1	$\delta(f)$
$\delta(t-t_0)$	$e^{-j2\pi f t_0}$
$e^{j2\pi f_0t}$	$\delta(f-f_0)$

1.9 Sine and cosine

$sin2\pi f_0t\leftrightarrow\dfrac{1}{2j}[\delta(f-f_0)-\delta(f+f_0)]\cos2\pi f_0t\leftrightarrow\dfrac{1}{2}[\delta(f-f_0)+\delta(f+f_0)]$

• $sin2\pi f_0t=\dfrac{1}{2j}(e^{j2\pi f_0t}-e^{-j2\pi f_0t})\cos2\pi f_0t=\dfrac{1}{2}(e^{j2\pi f_0t}+e^{-j2\pi f_0t})​$
• 

1.10 Comb function

$comb(t,T_s)=\sum^\infty_{-\infty}\delta(t-nt_s)\quad n=0,\pm1,\pm2\dots\\Updownarrow \comb(f,f_s)=\dfrac{1}{T_s}\sum^\infty_{-\infty}\delta(f-kf_s)=\dfrac{1}{T_s}\sum^\infty_{-\infty}\delta(f-\dfrac{k}{T_s})$

1.11 Random

${x(t)}={x_1(t),x_2(t).\dots x_i(t)\dots}$

• random progress

  • stationary : characteristic parameter dont change with time
  • nonstationary

• characteristic parameter

  • Constant - average

    $\mu_x=\lim\limits_{T\rightarrow\infty}\dfrac{1}{T}\int^T_0x(t)dt$

  • fluctuation - variance

    $\sigma^2_x=\lim\limits_{T\rightarrow \infty}\dfrac{1}{T}\int^T_0[x(t)-\mu_x]^2dt$

  • Strength - mean square value

    $\psi^2_x=\lim\limits_{T\rightarrow\infty}\dfrac{1}{T}\int^T_0x^2(t)dt$

    $\sigma^2_x=\psi^2_x-\mu^2_x$

  • Probability density function

    $p(x)=\lim\limits_{\Delta x\rightarrow0}\dfrac{P_r[x<x(t)\le x+\Delta x]}{\Delta x}\=\lim\limits_{\Delta x\rightarrow0}\dfrac{\lim\limits_{T\rightarrow\infty}\dfrac{T_x}{T}}{\Delta x}$

    • $T_x=\sum\limits_1^n\Delta t_i$
    • 正弦

  • autocorrelation function

  • power spectral density function

2. Testing device

2.1 Properities

• Statics

  

  

  • device error

  • contain stable featuure

• Dynamic
  • system parameter constant
  • linear
  • first=0，Laplace Transform H(s)，Fourier Transform H(jw)，$h(t)=L^{-1}[H(s)]$

2.2 Static Feature

2.2.1 Linearity

definition : the difference between output and ideal

$线性误差=\dfrac{\Delta max}{Y_{max}-Y_{min}}\times 100\%$

2.2.2 Sensitivity

Definition : unit input change cause the output change $\rightarrow$signal-to-noise ratio

$灵敏度=\dfrac{\Delta Y}{\Delta x}​$

2.2.3 hysterisis error

when increase and decrease the difference at same time

2.2.4 Resolution

smallest tangible change

$分辨力 =\dfrac{\Delta}{X_{max}-X_{min}}\times100\%$

2.3.5 Zero wander & sensitivity wander

2.3.6 Precision

• FS精度 : $\dfrac{\Delta 误差}{Max}$ Full Scale
• real precision : $\dfrac{\Delta 误差}{测量值}$

2.4 Dynamic performance

• Transfer function H(s) [ complex domain ] $\rightarrow$$t=0$sin function stimulate
• Frequency response function H(jw) [ frequency domain ] $\rightarrow$steady state output
• impulse response function h(t) [ time domain ]

2.4.1 Series and parallel

• Series : $$H(s)=H_1(s)H_2(s)\A(w)=\prod\limits^n A_i(w)\\varphi(s)=\sum\limits_1^n\varphi_i(s)$$
• parallel :$H(w)=\sum H_i(s)$

2.4.2 First-order system

• $H(s)=\dfrac{1}{\tau s+1}$
• $H(jw)=\dfrac{1}{j\tau w+1}\begin{cases}A(w)&=\dfrac{1}{\sqrt{1+(\tau w)^2}}\\varphi(w)&=-arctan(\tau w)\end{cases}$
• $h(t)=\dfrac{1}{\tau}e^{-\dfrac{t}{2}}$
  • $\tau ​$重要

2.4.3 Second-order system

• $H(s)=\dfrac{w^2_n}{s^2+2\zeta w_ns+w_n^2}$
• $H(jw)=\dfrac{1}{1-(\dfrac{w}{w_n})^2+2\zeta j\dfrac{w}{w_n}}\begin{cases}A(w)&=\dfrac{1}{\sqrt{[1-(\dfrac{w}{w_n})^2]^2+4\zeta^2(\dfrac{w}{w_n})^2}}\\varphi(w)&=-arctan\dfrac{2\zeta(\dfrac{w}{w_n})}{1-(\dfrac{w}{w_n})^2}\end{cases}$
• $h(t)=\dfrac{w_n}{\sqrt{1-\zeta^2}}e^{-\zeta w_nt}sin\sqrt{1-\zeta^2}w_nt\quad 0<\zeta<1$
  • $\zeta, w_n$

2.4.4 Distortionless condition

satisfy $y(t)=A_0x(t-t_0)$

$\downarrow F​$

$H(w)=A(w)e^{j\varphi(w)}=\dfrac{Y(w)}{X(w)}=A_0e^{-jt_0w}​$

Amplitude distortion$: A(w)=A_0=C$

Phase distortion : $\varphi(w)=-t_0w$

2.4.5 Dynamic measure

• the frequency response method : $x(t)=X_0sin2\pi ft$

  • 一阶 : $A(w)=\dfrac{1}{\sqrt{1+(\tau w)^2}}\\varphi(w)=-arctan(\tau w)$

• Step response method$u(t)$

3. Sensor

3.1 Type

• mechanical
• resistance, capacitance , inductance
• Magnetoelectricity , piezoelectricity, thermoelectricity
• laser

3.2 Resistance

measure

• strain, stress

• force, displacement, pressure, accerleration

3.2.1 Rheostat

$R=\rho\dfrac{c}{A}$

Precision : $S=\dfrac{dR}{dx}$

3.2.2 Resistance strain

3.2.2.1 Metal strain

deformation cause resistance valve change

material : constantan

$\dfrac{dR}{R}=\varepsilon(1+2\upsilon+\lambda E)\approx (1+2\upsilon)\varepsilon$

• $\upsilon$: Possion ratio

$S_g=\dfrac{dR/R}{dl/l}=1+2\upsilon$

3.2.2.2 Semi-conductor gauge

piezoresistance : when force the resistance valve change

$\dfrac{dR}{R}=\lambda E\varepsilon\S_g=\dfrac{dR/R}{dl/l}=\lambda E$

sensitive, but affected by temperature

3.3 Capacitance

$C=\dfrac{\varepsilon_0\varepsilon A}{\delta}$

• $\varepsilon$: relative dielectric constant，aps $\varepsilon=1$
• $\varepsilon_0​$: dielectric constant in vaccum，$\varepsilon_0=8.85\times10^{-12}F/m​$

3.3.1 distance change

$dC=-\varepsilon\varepsilon_0A\dfrac{1}{\delta^2}d\delta\S=\dfrac{dC}{d\delta}=-\varepsilon\varepsilon_0A\dfrac{1}{\delta^2}​$

unlinear

3.3.2 Area change

$A=\dfrac{\alpha r^2}{2}\C=\dfrac{\varepsilon\varepsilon_0 \alpha r^2}{2\delta}\S=\dfrac{dC}{d\alpha}=\dfrac{\varepsilon_0\varepsilon r^2}{2\delta}$

linear

3.4 Inductance

Variable Reluctance, self- inductance

$L=\dfrac{N^2}{R_m}=\dfrac{N^2\mu_0A_0}{2\delta}\S=\dfrac{N^2\mu_0A_0}{2\delta^2}​$

• $N$: number of turns
• $R_m=\dfrac{2\delta}{\mu_0A_0}$ : sum
  • $\mu_0$: magnetic permeability，$4\pi times 10^{-3}H/m$

3.5 Magnetoelectricity

Moving-coil

• speed : $e=NBlvsin\theta$
• angle speed : $e=kNBAw$

3.6 Piezoelectricity

Measure: pressure, stress, acceleration

Reversible : mechanical $\leftrightarrow$ electric

3.6.1 Principle

• piezoelectric effect : piezoelectric material generate electric field when pressed
• inverse piezoelectric effect : in electric field size change

3.6.2 Material

• piezoelectric monocrystal
• piezoceramics

3.6.3 Sensitive coefficient

$C=\dfrac{\varepsilon\varepsilon_0A}{\delta}$

• $\varepsilon=4.5F/m$，磺
• $\varepsilon=1200F/m$，钛酸铝

3.7 Thermoelectricity

• Thermocouple: temperature difference cause electromotive force

  

• thermal resistance : resistance value change with T

3.8 Photoelectricity

• Outside : light on , electronic out
• Inside : light , R change

3.9 Semiconductor

• Magneto-dependent sensor :

  Hall effect

  

• thermosensitive

3.10 Choose

4. Signal Conditioning

4.1 Bridge

4.1.1 Direct Current Brigde

$U_0=(\dfrac{R_1}{R_1+R_2}-\dfrac{R_4}{R_3+R_4})U_e$

• Signal arm : $R_1$

  $U_0=(\dfrac{R_1+\Delta R}{R_1+R_2+\Delta R}-\dfrac{R_4}{R_3+R_4})U_e\\downarrow 等阻\=\dfrac{\Delta R}{2(2R+\Delta R)}U_e\approx \dfrac{\Delta R}{4R}U_e$

• Half bridge : $R_1+R_2$

  $U_0=(\dfrac{R_1+\Delta R}{R_1+R_2}-\dfrac{R_4}{R_1+R_4})U_e\rightarrow等阻=\dfrac{\Delta R}{2R}U_e$

• Full bridge : $\sum R_i$

  $U_0=(\dfrac{R_1+\Delta R}{R_1+R_2}-\dfrac{R_4-\Delta R}{R_3+R_4})U_e\rightarrow等阻=\dfrac{\Delta R}{R}U_e$

sensitivity$S=\dfrac{U_0}{\Delta R/R}$

• signal arm : $\dfrac{U_e}{4}$
• half bridge : $\dfrac{U_e}{2}$
• Full bridge : $U_e$

4.1.2 AC bridge

4 arm can + L/R/C

$Z_{01}Z_{03}=Z_{02}Z_{04}\\varphi_1+\varphi_3=\varphi_2+\varphi_4$

4.2 Modulation & demodulation

• Modulation : use low frequency signal to control amplitude or frequency of oscillator signal

• demodulation : recover the original signal from the modulated signal

Utilize

• denoising
• long distance transmission

4.2.1 Amplitude modulation

$调幅=高频载波\cdot 被测信号\m(t)=x(t)\cdot cos2\pi f_0t\\downarrow F\\frac{1}{2}X(f+f_0)+\frac{1}{2}X(f-f_0)​$

• $f_0 muss >max(x(t))$，or 不重叠

4.2.2 Amplitude demodulation[Detection]

• synchronously demodulation

  $x(t)cos2\pi f_0tcos2\pi f_0 t=\frac{x(t)}{2}+\frac{1}{2}x(t)cos4\pi f_0t$

• Envelope detection

  

4.2.3 Frequency modulation

low amplitude change with the high frequency signal

LC oscillating circuit

$f_0=\dfrac{1}{2\pi \sqrt{LC_0}} \ x(t)=Acos[w_0t+k\int x(t)dt+\theta_0]$

Demodulation Frequency discrimination : high pass filter + envelope detection

4.3 Filter

• 低通Low-Pass
• 高通High-Pass
• 带通Band-Pass=H+L
• 陷波/带阻Band-Stop/Notch=H//L

4.3.1 Parameter

• Ideal

  

• Real

  

  • Cutoff frequency $f_{c1},f_{c2}​$ : half power point，$A=\dfrac{A_0}{\sqrt2}​$，[$-3dB=20\log(\dfrac{1}{\sqrt2})​$]
  • Bandwidth $B=f_{c2}-f_{c1}$ : [-3dB bandwidth]，B$\downarrow$，discrimination$\uparrow$
  • range$\pm \delta$ : small the best best
  • Quality coefficient : $Q=\dfrac{f_0}{B}$，Q$\uparrow$，choosing thebz best
  • 倍频程选择性 :
    • up : $|A(f_{c2})-A(2f_{c2})|$
    • down : $|A(f_{c1})-A(\dfrac{f_{c1}}{2})|$
    • fast the best
  • filter coeffecient : $\lambda=\dfrac{B_{-60dB}}{B_{-3dB}}$
    • ideal=1，normal 1-5

4.3.2 Real filter circuit

• low -pass

  $|H(f)|=\dfrac{1}{\sqrt{1+(f/f_c)^2}}\\phi (f)=-arctan(\dfrac{f}{f_c})$

  • $f_c=\dfrac{1}{2\pi RC}$

• high pass

  $|H(f)|=\dfrac{(f/f_c)}{\sqrt{1+(f/f_c)^2}}\\phi(f)=\dfrac{\pi}{2}-arctan(\dfrac{f}{f_c})​$

4.3.3 Band pass

• constant bandwidth ratio

  $\dfrac{B_i}{f_{oi}}=\dfrac{f_{c2i}-f_{c1i}}{f_{0i}}=C\f_{c2i}=2^nf_{c1i}$

  • n octave : n=1，octave，n=1/3，1/3 time octave
  • center : $f_{oi}=\sqrt{f_{c1i}f_{c2i}}$

• constant bandwidth

  $B=f_{c2i}-f_{c1i}=C$

  

5. Signal processing

5.1 Sampling theorem

sampling frequency is twice time of $f_h$

$f_s>2f_h\quad(3\sim 4)​$

no mix and overlap between the signal

5.2 Quantization $x(t)s(t)$

use one finite level to similarity the real

A/D transfer

5.3 Window function$x(t)s(t)w(t)$

• cut off : signal $\cdot$window function(time)
• give away : W(f) infinite bandwidth sinc function，$x(t)带限信号\rightarrow截断\rightarrow无限带宽$

5.4 Frequency Sampling$[x(t)s(t)w(t)]*d(t)$

pulse D(f)$\cdot$signal frequency spectrum$\rightarrow$时域窗内信号，窗外周期延拓

5.6 Correlation analysis

5.6.1 correlated coefficient

$\rho_{xy}=\dfrac{E[(x-\mu_x)(y-\mu_y)]}{\sigma_x\sigma_y}=E(XY)-E(X)E(Y)\=\pm \dfrac{1}{2}[D(X\pm Y)-D(X)-D(Y)]$

• $\sigma​$ : 标准差

5.6.2 Autocorrelation function

$R_x(\tau)=\lim\limits_{T\rightarrow\infty}\dfrac{1}{T}\int^T_0x(t)x(t+\tau)dt$

• Autocorrelation coefficient : $\rho_x(\tau)=\dfrac{R_x(\tau)-\mu_x^2}{\sigma_x^2}$
  • $\mu_x^2-\sigma_x^2\le R_x(\tau)\le \mu_x^2+\sigma_x^2​$
  • $R_x(\tau)_{max}=R_x(0)=\psi_x^2$
  • $\tau\rightarrow\infty,\rho_x(\tau)\rightarrow0/\mu_x^2$，x(t)和x(t+tau)无内部联系
  • $R_x(\tau)=R_x(-\tau)$， 偶函数
  • 周期函数的自相关函数仍为同频率周期函数，

[Exp]$x(t)=x_0sin(wt+\varphi)\rightarrow R_x(\tau)=\dfrac{x_0^2}{2}cosw\tau$

5.6.3 Cross-correlation function

$R_{xy}(\tau)=\lim\limits_{T\rightarrow\infty}\dfrac{1}{T}\int^T_0x(t)y(t+\tau)dt$

• $\tau\rightarrow\infty, \rho_{xy}\rightarrow0, R_{xy}(\tau)\rightarrow\mu_x\mu_y$，$x(t),y(t)$不相关
• $\mu_x\mu_y-\sigma_x\sigma_y\le R_{xy}(\tau)\le \mu_x\mu_y+\sigma_x\sigma_y$
• 非偶

[Exp]$\begin{array}{rl}x(t)&=x_0sin(wt+\varphi)\y(t)&=y_0sint(wt+\theta)\end{array}\rightarrow R_{xy}(\tau)=\dfrac{1}{2}x_0y_0cos(wt+\varphi-\theta)$

5.7 Power spectrum

5.7.1 Auto power spectrum density

$S_x(f)-=\int^\infty_\infty R_x(\tau)e^{-j2\pi f\tau}d\tau\R_x(\tau)=\int^\infty_\infty S_x(f)e^{j2\pi f\tau}df​$

5.7.2 Parseval theorem

Energy equation : $\int^\infty_\infty x^2(t)dt=\int^\infty_\infty|X(f)|^2df$

[Exp]

• $S_x(f)=\lim\limits_{T\rightarrow\infty}\dfrac{1}{T}|X(f)|^2df$
• $Y(f)=H(f)X(f)\S_y(f)=|H(f)|^2S_x(f)\S_{xy}(f)=H(f)S_x(f)$

5.7.3 Cross power spectrum

$S_{xy}(f)=\int^\infty_\infty R_{xy}(\tau) e^{-j2\pi f\tau}d\tau\\updownarrow\R_{xy}(\tau)=\int^\infty_\infty S_{xy}(f)e^{j2\pi f\tau}df$

$S_{xy}(f)=H(f)S_x(f)$

7. Vibration

7.1 Methode

• Light : 振动量to光信号
  • 光学读数显微镜测振
  • 激光干涉法测振
• Electric : 振动量to电量
  • 频率范围宽，动态范围广，测量灵敏

7.2 Excitation

• Sin: 广
• random : 带宽，白噪声
• transient : 宽频带
  • fast sin scan
  • impact hammer
  • step excitation

7.2.1 Exciter

excitation $\rightarrow$ object $\rightarrow$ forced vibration

• hammer
• electric exciter

7.2.2 Sensor

Vibration $\rightarrow$electric quantity

• 惯性式
• 相对式

• touch
• untouched

• 涡流位移
• 电容加速度
• 磁电加速度
• piezoelectric accelerometer
• impedance head

7.3 Signal analysis

• 振动仪
• frequency analyzer
• 频率特性分析仪
• digital signal processing system