Basics of Data Acquisition - Revision history

Oliver at 13:16, 9 July 2013

2013-07-09T13:16:41Z

Oliver: /* Filtering */

2013-07-09T13:15:36Z

‎Filtering

Oliver at 13:14, 9 July 2013

2013-07-09T13:14:39Z

Oliver at 13:13, 9 July 2013

2013-07-09T13:13:40Z

Oliver: /* Sampling Rate */

2013-07-09T13:12:31Z

‎Sampling Rate

Oliver: /* Display and Expectations */

2013-07-09T13:11:52Z

‎Display and Expectations

Oliver at 13:11, 9 July 2013

2013-07-09T13:11:12Z

Oliver: /* Noise */

2013-07-09T13:08:43Z

‎Noise

Oliver: /* Sampling Rate */

2013-07-09T13:06:33Z

‎Sampling Rate

Oliver: /* Sampling Rate */

2013-07-09T13:05:57Z

‎Sampling Rate

@@ Line 20: / Line 20: @@
 The highest frequencies in a signal can be formally determined by sampling the signal at the maximum rate, and looking at the spectrum of the signal (using the Spectrum window). High-frequency components in the spectrum with less than 2% or so of maximum amplitude usually contribute little to recording accuracy.
-[[File:Figure 4. The effects of filtering on a mixed-frequency signal.jpg|600px|thumb|left|Figure 4. The effects of filtering on a mixed-frequency signal: a high-pass filter removes low frequencies; a low-pass filter removes high frequencies.]]
+[[File:Figure 4. The effects of filtering on a mixed-frequency signal.jpg|600px|thumb|Figure 4. The effects of filtering on a mixed-frequency signal: a high-pass filter removes low frequencies; a low-pass filter removes high frequencies.]]
-[[File:Figure 5. A signal with various low-pass filter settings.jpg|300px|thumb|left|Figure 5. A signal with various low-pass filter settings: a small amount of filtering removes noise, but too much attenuates the high-frequency components of the signal.]]
+[[File:Figure 5. A signal with various low-pass filter settings.jpg|300px|thumb|Figure 5. A signal with various low-pass filter settings: a small amount of filtering removes noise, but too much attenuates the high-frequency components of the signal.]]
 == Filtering ==
 Any analog waveform can be described mathematically as the sum of a number of pure sine waves at various frequencies and amplitudes. Low frequencies characterize the slowly changing parts of a waveform; high frequencies, the quickly changing parts. A filter removes selected frequencies from a signal: for instance, a low-pass filter lets low frequencies pass and stops high frequencies. Low-pass filters are commonly used to help reduce noise and give a smoother signal. A high-pass filter removes any steady component of a signal; it also removes slow fluctuations; see Figure 4.

@@ Line 20: / Line 20: @@
 The highest frequencies in a signal can be formally determined by sampling the signal at the maximum rate, and looking at the spectrum of the signal (using the Spectrum window). High-frequency components in the spectrum with less than 2% or so of maximum amplitude usually contribute little to recording accuracy.
 [[File:Figure 4. The effects of filtering on a mixed-frequency signal.jpg|600px|thumb|left|Figure 4. The effects of filtering on a mixed-frequency signal: a high-pass filter removes low frequencies; a low-pass filter removes high frequencies.]]
 [[File:Figure 5. A signal with various low-pass filter settings.jpg|300px|thumb|left|Figure 5. A signal with various low-pass filter settings: a small amount of filtering removes noise, but too much attenuates the high-frequency components of the signal.]]
 Any analog waveform can be described mathematically as the sum of a number of pure sine waves at various frequencies and amplitudes. Low frequencies characterize the slowly changing parts of a waveform; high frequencies, the quickly changing parts. A filter removes selected frequencies from a signal: for instance, a low-pass filter lets low frequencies pass and stops high frequencies. Low-pass filters are commonly used to help reduce noise and give a smoother signal. A high-pass filter removes any steady component of a signal; it also removes slow fluctuations; see Figure 4.

@@ Line 7: / Line 7: @@
 Most of the parameters that affect acquisition can be set by the user through the software. To make a good recording, the parameters must be appropriate for the signals being recorded. In some disciplines you may be able to find tables of suggested sampling rates, ranges, and filter settings, but these should not be applied blindly. You still need to know the science (what you are recording, why you are recording it, and what relation it bears to real phenomena) and the technique (how best to record, and what limitations or compromises are inherent in the process).
-[[File:Figure 2. Undersampling, recording a signal at 20.jpg|300px|thumb|left|Figure 2. Undersampling: recording a signal at 20 /s and 200 /s clearly shows that the former sampling rate is too low to depict the signal accurately.]]
+[[File:Figure 2. Undersampling, recording a signal at 20.jpg|300px|thumb|Figure 2. Undersampling: recording a signal at 20 /s and 200 /s clearly shows that the former sampling rate is too low to depict the signal accurately.]]
-[[File:Figure 3. Aliasing, sampling a 3.5 Hz signal at 4.jpg|300px|thumb|left|Figure 3. Aliasing: sampling a 3.5 Hz signal at 4 /s gives a misleading waveform, an apparent signal of 0.5 Hz.]]
+[[File:Figure 3. Aliasing, sampling a 3.5 Hz signal at 4.jpg|300px|thumb|Figure 3. Aliasing: sampling a 3.5 Hz signal at 4 /s gives a misleading waveform, an apparent signal of 0.5 Hz.]]
 == Sampling Rate ==
 Sampling replaces the original continuous analog signal by a series of discrete values (samples) taken at regular time intervals. The appropriate sampling rate depends on the signal to be measured. If the sampling rate is too low, information is irreversibly lost and the original signal will not be represented correctly; this is shown in Figure 2. If it is too high, there is no loss of information, but the excess data increases processing time and results in unnecessarily large disk files.
@@ Line 21: / Line 21: @@
 == Filtering ==
-[[File:Figure 4. The effects of filtering on a mixed-frequency signal.jpg|600px|thumb|Figure 4. The effects of filtering on a mixed-frequency signal: a high-pass filter removes low frequencies; a low-pass filter removes high frequencies.]]
+[[File:Figure 4. The effects of filtering on a mixed-frequency signal.jpg|600px|thumb|left|Figure 4. The effects of filtering on a mixed-frequency signal: a high-pass filter removes low frequencies; a low-pass filter removes high frequencies.]]
-[[File:Figure 5. A signal with various low-pass filter settings.jpg|300px|thumb|Figure 5. A signal with various low-pass filter settings: a small amount of filtering removes noise, but too much attenuates the high-frequency components of the signal.]]
+[[File:Figure 5. A signal with various low-pass filter settings.jpg|300px|thumb|left|Figure 5. A signal with various low-pass filter settings: a small amount of filtering removes noise, but too much attenuates the high-frequency components of the signal.]]
 Any analog waveform can be described mathematically as the sum of a number of pure sine waves at various frequencies and amplitudes. Low frequencies characterize the slowly changing parts of a waveform; high frequencies, the quickly changing parts. A filter removes selected frequencies from a signal: for instance, a low-pass filter lets low frequencies pass and stops high frequencies. Low-pass filters are commonly used to help reduce noise and give a smoother signal. A high-pass filter removes any steady component of a signal; it also removes slow fluctuations; see Figure 4.

@@ Line 11: / Line 11: @@
 == Sampling Rate ==
 Sampling replaces the original continuous analog signal by a series of discrete values (samples) taken at regular time intervals. The appropriate sampling rate depends on the signal to be measured. If the sampling rate is too low, information is irreversibly lost and the original signal will not be represented correctly; this is shown in Figure 2. If it is too high, there is no loss of information, but the excess data increases processing time and results in unnecessarily large disk files.
 Recordings of periodic waveforms that have been sampled too slowly may be misleading as well as inaccurate because of aliasing, as shown in Figure 3. An analogy to aliasing can be seen in old films: spoked wagon wheels may appear to stop or even go backwards when their rate of rotation matches the film frame speed — obviously not an accurate record.
 To prevent aliasing, the sampling rate must be at least twice the rate of the highest expected frequency of the incoming waveform. This sampling rate is known as the Nyquist frequency, the minimum rate at which digital sampling can accurately record an analog signal. For example, if a signal has maximum frequency components of 100 Hz, the sampling rate needs to be at least 200 Hz to record it accurately. To provide a safety factor to guard against information loss, it is usual to sample at five to ten times the highest expected frequency rather than the minimum two times.
 In most cases, the highest expected frequency will be known. It may well be limited by the transducer used: a bridge transducer to measure mechanical force will not produce high frequencies, for instance. If you are unsure of the frequency range (bandwidth) of your signal, a useful rule of thumb is to choose a sampling rate high enough to allow at least 5 to 20 samples for any transient peaks or recurring waves in the signal.
 The highest frequencies in a signal can be formally determined by sampling the signal at the maximum rate, and looking at the spectrum of the signal (using the Spectrum window). High-frequency components in the spectrum with less than 2% or so of maximum amplitude usually contribute little to recording accuracy.
@@ Line 28: / Line 24: @@
 [[File:Figure 5. A signal with various low-pass filter settings.jpg|300px|thumb|Figure 5. A signal with various low-pass filter settings: a small amount of filtering removes noise, but too much attenuates the high-frequency components of the signal.]]
 Any analog waveform can be described mathematically as the sum of a number of pure sine waves at various frequencies and amplitudes. Low frequencies characterize the slowly changing parts of a waveform; high frequencies, the quickly changing parts. A filter removes selected frequencies from a signal: for instance, a low-pass filter lets low frequencies pass and stops high frequencies. Low-pass filters are commonly used to help reduce noise and give a smoother signal. A high-pass filter removes any steady component of a signal; it also removes slow fluctuations; see Figure 4.
 Filters are imperfect. A 200 Hz low-pass analog filter, say, might leave frequencies up to 150 Hz untouched, reduce a 200 Hz signal to 0.7 of its original amplitude (this is its cut-off frequency), and reduce higher frequencies more and more. If you were expecting useful frequencies of up to 100 Hz, you could sample at 400 samples per second and filter out any higher frequencies using a 200 Hz filter. If higher frequencies are left unfiltered, then they could possibly be aliased, resulting in the false appearance of lower frequencies.
 Filtering can change the signal to some extent: its use must be balanced against the distortions it can remove, such as noise, baseline drift, and aliasing. If the filter settings overlap the bandwidth of a signal, then the signal will have components removed. If you were interested in a waveform with components down to 5 Hz and used a 20 Hz high-pass filter (filtering out 0 to 20 Hz signals), then vital information would be lost from the signal. This is shown in Figure 5.

@@ Line 11: / Line 11: @@
 == Sampling Rate ==
 Sampling replaces the original continuous analog signal by a series of discrete values (samples) taken at regular time intervals. The appropriate sampling rate depends on the signal to be measured. If the sampling rate is too low, information is irreversibly lost and the original signal will not be represented correctly; this is shown in Figure 2. If it is too high, there is no loss of information, but the excess data increases processing time and results in unnecessarily large disk files.
 Recordings of periodic waveforms that have been sampled too slowly may be misleading as well as inaccurate because of aliasing, as shown in Figure 3. An analogy to aliasing can be seen in old films: spoked wagon wheels may appear to stop or even go backwards when their rate of rotation matches the film frame speed — obviously not an accurate record.
 To prevent aliasing, the sampling rate must be at least twice the rate of the highest expected frequency of the incoming waveform. This sampling rate is known as the Nyquist frequency, the minimum rate at which digital sampling can accurately record an analog signal. For example, if a signal has maximum frequency components of 100 Hz, the sampling rate needs to be at least 200 Hz to record it accurately. To provide a safety factor to guard against information loss, it is usual to sample at five to ten times the highest expected frequency rather than the minimum two times.
 In most cases, the highest expected frequency will be known. It may well be limited by the transducer used: a bridge transducer to measure mechanical force will not produce high frequencies, for instance. If you are unsure of the frequency range (bandwidth) of your signal, a useful rule of thumb is to choose a sampling rate high enough to allow at least 5 to 20 samples for any transient peaks or recurring waves in the signal.
 The highest frequencies in a signal can be formally determined by sampling the signal at the maximum rate, and looking at the spectrum of the signal (using the Spectrum window). High-frequency components in the spectrum with less than 2% or so of maximum amplitude usually contribute little to recording accuracy.

@@ Line 53: / Line 53: @@
 == Display and Expectations ==
-[[File:Figure 7. A signal viewed with various display settings changed.jpg|500px|thumb|Figure 7. A signal viewed with various display settings changed — this is the same waveform in each case.]]
+[[File:Figure 7. A signal viewed with various display settings changed.jpg|400px|thumb|Figure 7. A signal viewed with various display settings changed — this is the same waveform in each case.]]
 The two most important settings for data recording are the input range and recording speed. Provided these are set correctly, then your signals will be recorded which high precision. However, the actual appearance of the data on the computer monitor can be affected by the vertical magnification and time base compression used in the Chart display settings, and screen resolution of your monitor, as shown in Figure 7.

@@ Line 21: / Line 21: @@
 == Filtering ==
-[[File:Figure 4. The effects of filtering on a mixed-frequency signal.jpg|300px|thumb|Figure 4. The effects of filtering on a mixed-frequency signal: a high-pass filter removes low frequencies; a low-pass filter removes high frequencies.]]
+[[File:Figure 4. The effects of filtering on a mixed-frequency signal.jpg|600px|thumb|Figure 4. The effects of filtering on a mixed-frequency signal: a high-pass filter removes low frequencies; a low-pass filter removes high frequencies.]]
 [[File:Figure 5. A signal with various low-pass filter settings.jpg|300px|thumb|Figure 5. A signal with various low-pass filter settings: a small amount of filtering removes noise, but too much attenuates the high-frequency components of the signal.]]
 Any analog waveform can be described mathematically as the sum of a number of pure sine waves at various frequencies and amplitudes. Low frequencies characterize the slowly changing parts of a waveform; high frequencies, the quickly changing parts. A filter removes selected frequencies from a signal: for instance, a low-pass filter lets low frequencies pass and stops high frequencies. Low-pass filters are commonly used to help reduce noise and give a smoother signal. A high-pass filter removes any steady component of a signal; it also removes slow fluctuations; see Figure 4.
@@ Line 46: / Line 46: @@
 == Noise ==
 [[File:Figure 6. Noise in a signal (left) can mar the original signal (right), unless filtered out.jpg|300px|thumb|Figure 6. Noise in a signal (left) can mar the original signal (right), unless filtered out.]]
 Noise is defined as ‘unwanted signal’. It is likely to be a problem at lower range settings, when you are trying to measure very small signals. Random noise, such as thermal noise, is inherent in all electronic circuits, including those of the e-corder recording unit, and generally must be filtered to minimize it. The trick is to choose a low-pass filter setting that removes most of the background noise without unduly changing the signal of interest. See Figure 6.
@@ Line 54: / Line 53: @@
 == Display and Expectations ==
-The two most important settings for data recording are the input range and recording speed. Provided these are set correctly, then your signals will be recorded which high precision. However, the actual appearance of the data on the computer monitor can be affected by the vertical magnification and time base compression used in the Chart display settings, and screen resolution of your monitor.
+[[File:Figure 7. A signal viewed with various display settings changed.jpg|500px|thumb|Figure 7. A signal viewed with various display settings changed — this is the same waveform in each case.]]
 The screen display on a monitor is generally about 72 dots per inch (dpi), so the apparent resolution may be poor if the display is kept small. However, the resolution of the underlying recorded data is independent of the resolution of the display: even if the channel is very thin or not visible on screen, sampled data are recorded at full fidelity, as can be seen by expanding the channel display or examining the signal in the Zoom window.