1. A Gaussian (normal) random variable X has the following probability
density function.
2. Before sampling (digitizing) the signal from a pressure transmitter installed in a
water pipe, the signal was conditioned by passing it through a band-pass
filter with a high-pass setting of 0.05 Hz and a low-pass setting of 20 Hz.
A. The filter eliminates (or removes) signal frequencies in the range XXXXXXXXXXHz
B. The filter passes (or retains) signal frequencies in the range XXXXXXXXXXHz
C. The filter passes signal frequencies greater than 20 Hz
D. The filter passes signal frequencies less than 0.05 Hz
3. The autocorrelation function, Rxx(t), of a stationary signal X(t) always
satisfies the following.
A. Minimum at lag t = 0
B. Maximum at lag t = 0
C. Both A and B
D. None of the above
4. A set of N data points of a signal is defined by {X(1), X(2), … , X(N)}. Ifmis the
mean value of this signal, the mathematical expression for calculating the
standard deviation of this signal is
5. In the computation of fast Fourier transform (FFT) of digitized signal using data
decimation in time, one of the following is a valid integer for the number of
points per block, N.
6. The RMS value of a certain signal is 2.5 V, and a peak in the signal has a value of
X = 7.5 V. The crest factor corresponding to X = 7.5 V is
A. 7.5 x 2.5 V2
B. 7.5/2.5
C. 2.5/7.5
D XXXXXXXXXXV
E XXXXXXXXXXV
7. The cross-correlation function between two stationary signals X(t) and Y(t) is
given by Rxy(t) = 10 exp(-2t). For what value oft(t= 0), Rxy(t) is a maximum?
A. 0.0 B. 1.0 C. 1/10 D. 10.0
8. If the maximum frequency content of a signal from an accelerometer (signal is
conditioned using a low-pass filter) is 2500 Hz, the minimum frequency with which the signal must be digitized without creating error in the digitized (or sampled) signal is
A. 1250 Hz B. 2500 Hz C. 5000 Hz D. 4000 Hz
9. A signal from an accelerometer mounted on a pump shaft bearing was sampled
at 1024 Hz. The maximum information frequency (Nyquist folding frequency) in the digitized signal is equal to
A. 2048 Hz. B. 1024 Hz. C. 512 Hz. D XXXXXXXXXXHz.
10. The rotational speed of a pump shaft is approximately equal to 1200 RPM. The
frequency corresponding to [5 x order] is
A. 20 Hz. B. 40 Hz. C. 60 Hz. D. 80 Hz. E. 100 Hz
11. X(t) and Y(t) are two stationary signals. If Sxx(f), Syy(f), and Sxy(f) are the auto- spectrum of X(t), auto-spectrum of Y(t), and the cross-spectrum between X(t)
and Y(t) at frequency f respectively, then the coherence function ?2(f) at frequency f between X and Y is given by
12. The coherence function between two temperature detector signals (in the
frequency domain) is close to 1.0 in the range 0.1 Hz and 2 Hz. This indicates that
A. The two signals are linearly related in this frequency band
B. The signal-to-noise ratios of both signals are high in this frequency band
C. The signal-to-noise ratios of both signals are low in this frequency band
D. A and B
E. A and C
13. Angular misalignment between two shafts is best detected by
A. Accelerometers placed vertically on the bearings
B. Accelerometers placed on the rotating shaft
C. Accelerometers placed on the bearings in the direction axial to the shaft
D. Accelerometers placed on the coupling between the two shafts
14. Parallel misalignment between two shafts is best detected by
A. Accelerometers placed vertically on the bearings
B. Accelerometers placed on the rotating shaft
C. Accelerometers placed on the bearings in the direction axial to the shaft
D. Accelerometers placed on the coupling between the two shafts
15. The rotational speed of a pump shaft is 19.5 Hz. The frequency spectrum of accelerometers placed on inboard and outboard bearings in the vertical direction generally indicate parallel misalignment at a frequency of
A. 19.5 Hz. B. 39 Hz. C. 9.75 Hz. D. Always a non-synchronous value of shaft speed.