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7.42 The following signal is to be sampled using a 12-bit, Æ5-V data-acquisition board
y t
ð Þ ¼ 4sin8pt þ 2sin20pt þ 3sin42pt
Select an appropriate sample rate and sample size that provide minimal spectral leakage.
7.43 A strain-gauge sensor is used with a bridge circuit and connected to a DAS as indicated in Figure
7.16. Estimate the range of offset nulling voltage available if the bridge excitation is 3.333 V, sensor
and bridge resistors are each at a nominal value of 120 V, and the adjustable trim potentiometer is
rated at 39 kV.
7.44 Design a low-pass Butterworth filter around a 10 Hz cutoff (À3 dB) frequency. The filter is to pass 95%
of signal magnitude at 5 Hz but no more than 10% at 20 Hz. Source and load impedances are 10 V.
7.45 A two-stage LC Butterworth filter with f c ¼ 100 Hz is used as an anti-alias filter for an analog signal.
Determine the signal attenuation experienced at 10, 50, 75, and 200 Hz.
The following problems make use of the accompanying software.
7.46 In the discussion of Figure 7.4, we point out the effects of sample rate and total sample period on the
reconstructed time signal and its amplitude spectrum. Use program Leakage.2 to duplicate Figure
7.4. Then develop a similar example (signal frequency, sample rate, and sample period) in which
fewer points and a slower sample rate lead to a better reconstruction in both time and frequency
domains. Incidentally, for a fixed sample rate, you can increment N and watch the acquired waveform
develop such that the leakage decreases to zero as the acquired signal reaches an exact integer period
of the waveform. For a fixed N, the same can be shown for changes in sample rate.
7.47 Using program Aliasing, solve Example 7.1 to find the alias frequency. Observe the plot of the
original and the acquired signal, as well as the amplitude spectrum. Decrement the signal frequency
1 Hz at a time until it is within the region where there no longer is aliasing. Based on these
observations, discuss how the acquired time signal changes and how this is related to aliasing.
7.48 Use program Aliasing to understand the folding diagram of Figure 7.3. For a sample rate of 20 Hz,
vary the signal frequency over its full range. Determine the frequencies corresponding to f N , 2f N , 3f N ,
and 4f N on Figure 7.3. Determine the alias frequencies corresponding to 1.6f N , 2.1f N , 2.6f N , and 3.2f N .
7.49 Using program Signal generation, examine the rule that when exact discrete representations are not
possible, a sample rate of at least five to ten times the maximum signal frequency gives adequate
approximation. Select a sine wave of 2 Hz and discuss the acquired waveform as the sample rate is
increased incrementally from a low to a high value. At what sample rate does the signal look like a
sine wave? Compare with the corresponding frequency and amplitude content from the amplitude
spectrum. Write up a short discussion of your observations and conclusions.
7.50 Program Leakage.2 samples a single frequency signal at a user-defined sample rate and period.
Describe how sample period corresponds to the length of the signal measured and how this affects
leakage in the amplitude spectrum. Does frequency resolution matter?
7.51 The image file with the companion software coins.jpg is the original color photograph of the coins
used in Figures 7.30 through 7.34. The image file graycoins.jpg is the corresponding grayscale
image. Using the Matlab commands IMREAD, IMSHOW, IM2BW, and EDGE reproduce the results
in Figures 7.30 through 7.34.
7.52 Using an image you download from the Internet or acquire with your own camera, create a grayscale
image and employ edge detection to process the image. Explore the effects of the gradient threshold
value on the quality of the edge detection. Create a binary image and repeat the process.
308 Chapter 7 Sampling, Digital Devices, and Data Acquisition
14:43:59 Page 308
7.42 The following signal is to be sampled using a 12-bit, Æ5-V data-acquisition board
y t
ð Þ ¼ 4sin8pt þ 2sin20pt þ 3sin42pt
Select an appropriate sample rate and sample size that provide minimal spectral leakage.
7.43 A strain-gauge sensor is used with a bridge circuit and connected to a DAS as indicated in Figure
7.16. Estimate the range of offset nulling voltage available if the bridge excitation is 3.333 V, sensor
and bridge resistors are each at a nominal value of 120 V, and the adjustable trim potentiometer is
rated at 39 kV.
7.44 Design a low-pass Butterworth filter around a 10 Hz cutoff (À3 dB) frequency. The filter is to pass 95%
of signal magnitude at 5 Hz but no more than 10% at 20 Hz. Source and load impedances are 10 V.
7.45 A two-stage LC Butterworth filter with f c ¼ 100 Hz is used as an anti-alias filter for an analog signal.
Determine the signal attenuation experienced at 10, 50, 75, and 200 Hz.
The following problems make use of the accompanying software.
7.46 In the discussion of Figure 7.4, we point out the effects of sample rate and total sample period on the
reconstructed time signal and its amplitude spectrum. Use program Leakage.2 to duplicate Figure
7.4. Then develop a similar example (signal frequency, sample rate, and sample period) in which
fewer points and a slower sample rate lead to a better reconstruction in both time and frequency
domains. Incidentally, for a fixed sample rate, you can increment N and watch the acquired waveform
develop such that the leakage decreases to zero as the acquired signal reaches an exact integer period
of the waveform. For a fixed N, the same can be shown for changes in sample rate.
7.47 Using program Aliasing, solve Example 7.1 to find the alias frequency. Observe the plot of the
original and the acquired signal, as well as the amplitude spectrum. Decrement the signal frequency
1 Hz at a time until it is within the region where there no longer is aliasing. Based on these
observations, discuss how the acquired time signal changes and how this is related to aliasing.
7.48 Use program Aliasing to understand the folding diagram of Figure 7.3. For a sample rate of 20 Hz,
vary the signal frequency over its full range. Determine the frequencies corresponding to f N , 2f N , 3f N ,
and 4f N on Figure 7.3. Determine the alias frequencies corresponding to 1.6f N , 2.1f N , 2.6f N , and 3.2f N .
7.49 Using program Signal generation, examine the rule that when exact discrete representations are not
possible, a sample rate of at least five to ten times the maximum signal frequency gives adequate
approximation. Select a sine wave of 2 Hz and discuss the acquired waveform as the sample rate is
increased incrementally from a low to a high value. At what sample rate does the signal look like a
sine wave? Compare with the corresponding frequency and amplitude content from the amplitude
spectrum. Write up a short discussion of your observations and conclusions.
7.50 Program Leakage.2 samples a single frequency signal at a user-defined sample rate and period.
Describe how sample period corresponds to the length of the signal measured and how this affects
leakage in the amplitude spectrum. Does frequency resolution matter?
7.51 The image file with the companion software coins.jpg is the original color photograph of the coins
used in Figures 7.30 through 7.34. The image file graycoins.jpg is the corresponding grayscale
image. Using the Matlab commands IMREAD, IMSHOW, IM2BW, and EDGE reproduce the results
in Figures 7.30 through 7.34.
7.52 Using an image you download from the Internet or acquire with your own camera, create a grayscale
image and employ edge detection to process the image. Explore the effects of the gradient threshold
value on the quality of the edge detection. Create a binary image and repeat the process.
308 Chapter 7 Sampling, Digital Devices, and Data Acquisition