1、清華大學本科生考試試題專用紙（中文） 考試課程：測試與檢測技術基礎 2003年7月1日1. 回答下列問題。（每小題5分，總分40分）（1）DFT的主要步驟是什么？（2）什么是乃奎斯特頻率？如果使用的采樣頻率對信號進行采樣，在此采樣頻率下，可以精確分辨的最高信號頻率是多少？（3）是具有零均值的純隨機信號，求。（4）, 求。（5）對于一階低通RC濾波器（圖1），若截止頻率，求。RCFig. 1（6）將一個模擬信號數字化以進行譜分析。如果被分析的頻率范圍是，所需的頻率分辨率，請確定 （a）采樣頻率； （b）進行FFT所需的采樣點總數。（7）一個速度傳感器頻率響應的固有頻率，阻尼比，求其工作頻帶。（8

2、）為了消除通常在壓電傳感器中存在的雜散電容，應采取什么措施？2. （10分）如果是的傅里葉變換，確定下述兩信號的頻譜。（不用畫出頻譜圖）(a) (b) 3.（8分）求取下圖所示信號的頻譜。 2AA0T Fig. 24. （8分）用一應變片測量構件上某一點的應力。此應變片構成電阻電橋的一個臂，并用的直流電源對電橋進行激勵。如果應變片的電阻，應變片系數，電橋的輸出，確定該點應變片敏感方向上的應變和應力。（假定構件材料的彈性模量。）5. （8分）求時域信號的傅里葉變換，并畫出其頻譜圖。6. （8分） （a）信號，其中為其均值。計算該信號的自相關函數。 （b）如果信號自相關函數的形式為，計算信號的均方

3、值。7. （8分）一傳感器對一頻率為的信號作出響應，但同時也檢測到了60Hz噪聲，其輸出信號因此為為去除60Hz噪聲，采用了一個截止頻率為的高通濾波器。求經濾波后的輸出信號。8. （10分）一單自由度系統如圖（a）所示，它受到一鋸齒波力函數（圖（b）作用，求系統的穩態響應。 設系統的參數如下：，。 k m(a)AT2Tt0 (b)Fig. 3清華大學本科生考試試題專用紙 （A卷） 考試課程 測試與檢測技術基礎 2004 年 6 月 21日1. Answer the following questions (4 points for each question. Total points: 32

4、.)(1) Assuming a system has a frequency response, what is the output of the system when the input is a sine-wave signal?(2) A half-wave sinusoidal signal is (a) multiplied by two unit impulses, or(b) convoluted with the two unit impulses (see the figure below).Sketch the two result diagrams.T/20tx(t

5、)T/20tg(t)(3) What is the Nyquist frequency? If a sampling frequency is used to sample a signal, what is the highest frequency of the signal which can be accurately resolved at this sampling frequency?(4) For amplitude modulation, what operations are performed in time domain and in frequency domain

6、respectively?(5) For a first-order RC high-pass filter, what are its cut-off frequency and its frequency response?(6) If an auto-correlation function is of the form, determine the mean-square value of the signal.(7) A piezoelectric accelerometer has a frequency response with a natural frequency, and

7、 a damping ratio, what is its working frequency range?(8) An analog signal is digitized for spectrum analysis. If the analyzed frequency range is , and a frequency resolution (頻率分辨率) of is required, determine(a) the sampling frequency ; and(b) the number of the total sample points for an FFT procedu

8、re.2. (10 points) Determine the spectrum of the following signal. Plot the spectrum.where T/2 0Atx(t)3. (10 points) A filter has its frequency response function shown in Fig.(a) with its phase characteristic . For a saw-tooth input signal (see Fig.(b), determine the filters output. 02(a)1-1 0 1 2(b)

9、4. (7 points) Signal has its Fourier transform (Fig. (a). For the spectrum shown in Fig.(b), determine its time signal . (a)(b)5. (10 points) Find the Fourier series of the following signal and plot its spectrum.AT0T/2t6. (10 points) Find the frequency response function of the following filter. What

10、 kind of filter is it? Calculate its cut-off frequency and the damping ratio. A B 7. (7 points) A strain gage is used to measure the stress at a certain point of a structure. The strain gage forms one arm of a resistive bridge which is excited by a dc power supply. If the strain gage has a resistanc

11、e and a gage factor (應變片系數) , and the bridges output , determine the strain and the stress at the point in the sensing direction of the strain gage. (Assuming the Youngs modulus (彈性模量) of the structures material .)8. (14 points) An inertial vibration pick-up is shown in the figure below.a. If the pick-up is used as a displacement transducer, write its frequency response function. If the transducer has a natural frequency , and a damping ratio , for a sine-wave input of a frequency ,determine the relative amplitude error and the phase-shift (相位差) of the