Mechanical Engineering - Measurement

Multiple choice test

1 1. Describe the spectral leakage using the convolution theorem, in less than 10 lines. The leakage is a result of not having the precise frequency of the signal in our discrete frequencies, multiple of 1/T. It is caused by the convolution in frequency from the window spectra and the signal spectrum. Since in time we have to simply multiply them, the discrete frequencies are instead result of the multiplication in frequency of the circular convolution spectrum and one of the signal, since to periodicize the signal we have to make the convolution in time between those two functions. The windowing affects leakage in represented in the spectrum, since once the window spectrum is centered on the signal bin, the discrete frequencies has to be taken until they reac h the window spectrum. The leakage can be reduced using a hanning window, which almost cancels the side lobes due to higher attenuation than the rectangular one. 2. The Fourier Transform of a rectangular window: o is periodic  is complex ✕ o none of the others o is real 3. The 99th percentile of a Gaussian distribution with mean= 0 and variance= 1 is: o -1.475 o -0.034 o 0.134  None of the other ✔ 2 4. A purely harmonic signal has a frequency of 10.51 Hz with amplitude 4 V, the signal is acquired with an accelerometer with full -scale range of ± 10 V. The ADC used for the acquisition has a f samp of 20 Hz. A configuration that allows to correctly reconstruct the amplitude of the spectral component is: o Number of samples = 200 . Hanning window o Number of samples = 40. Hanning window  None of the other ✔ o Number of samples = 40 . Rectangular w indow 5. If an operator is linear: o the coherence is always 1, independently from the frequency o cannot accept multiple inputs  it is always additive ✔ o none of the other 6. About the Fourier transform we can say that: o the Fourier transform of a real even function is an imaginary odd function  the Fourier transform of a real odd function is an imaginary odd function ✔ o the Fourier transform of a real even function is a real odd function o the Fourier transform of a real odd function is a real odd function 7. A linear system, characterized by multiple inputs with coherence smaller than 1 in specific frequency ranges, describe by: o the real component of the transfer function o the imaginary component of the transfer function o the imaginary component of the impulse response  none of the other ✔ 3 8. The asymptotic attenuation of the rectangular window is: o 40 dB/decade o 10 dB/decade  20 dB/decade ✔ o none of the others 9. The LSB of a converter with Vmax= 2.5 V and Vmin= -2.5 V and B= 12 is:  1.22 mV ✔ o 2440uV (u = micro) o None of the others o 4.88 mV 10. The modulus of a double -sided spectrum:  none of the other ✔ o depends on the signal cross correlation o depends on the signal covariance o decreases with the signal sampling frequency 11. Which of the following tools could be useful in case I would like to remove non -periodic noise from a single signal? o cross -correlation o none of the others o trigger acquisition  autocorrelation ✔ 4 12. The phase of a double -sided spectrum of a real signal: o is zero for odd signals o is symmetrical with respect to f=0 o is defined only for positive frequencies  is odd ✔ 13. In a Short Time Fourier Transform, the x and y axes show respectively: o amplitude and frequency o none of the other  time and frequency ✔ o time and amplitude 14. The CPDF curve of a Gaussian distribution: o none of the other o is larger than the signal RMS o is always increasing  is not decreasing ✔ 15. The skewness of a sine wave with RMS = 1 m/s 2, standard deviation of 1 m/s 2 and a frequency of 10 Hz is: o None of the other  0 ✔ o 1 o 2 5 16. Which is the method providi ng the largest excitations force (load) in the study of frequency response function? o none of the other o the impact hammer o the piezoelectric patch or shaker  the hydraulic actuator ✔ 17. The synchronous sampling is: o common in monitoring impulse phenomena o achieved acquiring a signal with a sampling rate independent by the observed phenomenon o common in monitoring high frequency signals  none of the other ✔ 18. Which is the method providing the lowest excitation frequency in the study of frequency response funct ion? o the impact hammer o none of the other  the hydraulic actuator ✔ o the piezoelectric patch or shaker 19. The average of spectra with a deterministic phase and random modulus tends to: o the real sampling frequency  none of the other ✔ o the phase is correctly detected, but the modulus tends to zero o the cross -spectral average 6 20. If an operator is linear: o the coherence is always 1, indepedently from the frequency o cannot accept multiple inputs o none of the other  it is always casual ✔ 21. The probability density function p(x) of a signal at level x indicates: o the probability that the instantenous value of the signal in between x and x + delta, where delta is 1  the probability that the instantenous value of the signal in between x and x + delta, where delta infinitesimal ✔ o the cumulative probability at x + delta o the cumulative probability at x