Exercise Problems

Exercise 16.1 A vibration signal is measured with a sampling interval of 0.002 sec. What is maximum frequency of the signal, which will be measured without aliasing effects? If you would like to measure the signals with the maximum frequency three times what you obtained in the first step, what would be the sampling interval you would like to choose?                      
                                               
Exercise 16.2 In a particular measurement the following time domain data were measured: 0, 1, 1, 0, 1, 1, 0. The total time duration of the measurement was 0.06 sec. Obtain the DFT of the signal, and plot the real and imaginary parts of the same with respect to the frequency.          

Exercise 16.3 Choose a single correct answer from the following multiple choice questions

(i) During the numerical integration of a noisy signal

(A) the high frequency noise will get amplify  (B) the low frequency noise will get amplify
(C) no effect will be there on the noise                        (D) the noise will get removed

(ii) For a signal which contains 1 kHz, 3 kHz and 6 kHz frequency signals, if the signal is sampled with a frequency of 8 kHz, what are the frequency (in kHz) which all will be observed in the sampled signal

(A) 1, 2, 3                    (B) 1, 3, 6                    (C) 1, 3, 4                    (D) 1, 3

(iii) For a vibration signal the maximum frequency of interest is 1 kHz. What should be the sampling interval, Dt, to capture the correct signal?

(A)0.0005 sec                   (B) 0.0001 sec             (C) 0.005 sec             (D) 0.001 sec

(iv) Let the vibration frequency be w and the sampling frequency be ws. Then aliasing effect would not occur, when we have

(A)ws <  2w                       (B)ws>  2w                 (C) ws = w                  (D) ws < w                                          
(v) In signal processing Window Functions are used for

(A)To avoid the aliasing effect                      (B) to avoid the leakage error

 (C) to facilitate faster DFT                  (D) to facilitate noise removal

(vi) In signal processing of a time domain signal to frequency domain signal by DFT, the leakage error comes due to

1. perfect synchronization of captured signal sampling time with its actual time period
2. non-synchronization of captured signal sampling time with its actual time period
3. addition of external noise in the actual vibration signal
4. aliasing effect

(vii) The complex-DFT is used in rotating machinery signals to find additional information of

(A) amplitude                   (B) phase         (C) frequency           (D) direction of rotation

(viii) The basic assumption of the discrete Fourier transform (DFT) is that

1. The vibration signal must be periodic signal
2. The captured vibration signal length is the time period of the signal
3. The captured vibration signal length must be of the infinite time period
4. It cannot be applied to non-periodic vibration signals

(ix) The Fast Fourier Transform (FFT) is

1. An algorithm to help faster transformation of vibration signal to frequency domain
2. Theoretically it is same as DFT
3. Helps in visualing real time spectrum of an vibration signal
4. All the above cases (A), (B) & (C)

Answers: (i) B (ii) A  (iii) A   (iv) B   (v) B    (vi) B   (vii) D  (viii) B (ix) D