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Abstract Data acquisition and signal processing is of great
importance these days because it's utilized in a great amount
of
fields. Data acquisition (DAQ) is the process to measure with
a
computer an electric or physical phenomenon such as voltage,
current, temperature, pressure or sound. A data acquisition
system is made up of sensors, data acquisitioning hardware and
a
computer with its corresponding software. Compared with the
traditional data acquiring systems, DAQ systems based on
computers make use of the processing power, productivity,
visualization and connectivity, allowing a better solution of
the
data acquired. The main purpose of the data acquisitioning
systems is to capture and store information to be analyzed,
being
that a signal can contain much information about the qualities
of
the source.
I. OBJETIVE
The objective of this practice is to learn about the
fundamental
theory, practical theory about data acquisition and analog-
digital data conversion and their posterior processing.
II. INTRODUCTION
HE data acquisition systems are used by the majority of
engineers and researchers in research, industrial control,
measurements and tests to introduce and extract
information via PC. A DAQ system is made up of the
following [1]:
Sensors The sensors (also called transducers) convert a
physical phenomenon into a small electrical signal
that can be measured. Depending on the type of
sensor, the electrical output can be either current,
voltage, resistance or any other electrical attribute
that varies over time. Some sensors may need
additional components and circuits to produce a
signal that can be measured by a DAQ device.
Sensors can measure variables such as temperature,
strains, pressure, flow, forces and movement (this
one can be either displacement, velocity and
acceleration).
Signal Conditioning Some signals of the sensors tend to have a
lot of
interference or are too dangerous to be measured
directly. The signal conditioning circuit manipulates
a signal in a way that this one is appropriate to enter
an analog-digital converter (ADC). This circuit may
contain amplification, dampening, filtering and
insulation.
Analog-digital Converter (ADC)
The analog signals of the sensors have to be
converted into digital signals before being
manipulated by a digital device, such as a PC. An
ADC is a chip that provides a representation of a
digital signal in an instant of time. In real life, analog
signals vary continuously in time and a ADC realizes
periodical "samples" of the signal at a predefined
rate. These samples are then transferred to a
computer via USB, where the original signal is then
reconstructed in the software using the samples.
Computer
A computer with the proper software is necessary to
process and analyze information. This software also
needs to be able to provide a graphic representation
of the information.
III. BASIC THEORY
Sampling Frequency
During the sampling process the frequency of sound is
measured taking samples in intervals of equal time.
Sampling,
as it is known, is the basic process in the transformation
of
analog sound into digital sound. The amount of samples of a
wave is called sampling frequency. The higher the sampling
frequency is, the digitalized sound will be closer to the
original sound. The higher this one is, the capture of the
sound
will be more precise and thus, the sound will have a higher
quality.[2]
The resolution of sound is directly related with the
sampling frequency. This refers to the number of binary
digits,
1's and 0s, which make up each sample. Their measure of unit
is the bit and it makes reference to the size of each
sample.
The most common thing is to work with 16 bits, but 8 and 32
bits can also be used. If the audio resolution is of 8 bits
this
means that we've taken 256 values for the sample. If the
resolution and frequency are higher, so will be the quality
of
the sound.
#1 Fundamentals of Data Acquisition and Signal
Processing Haran Aguilar Reyes, 1607086
Structural Dynamics Laboratory, Dr. Diego Francisco Ledezma
16/02/2015
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Image 1. A signal at different resolutions. It can be
observed that at higher resolutions there's a better signal
quality.
Sampling Theorem of Shannon-Nyquist
The Shannon-Nyquist establishes that :
"A continuous signal can only be sampled correctly if it
doesn't contain frequency components higher than of the
sampling frequency."
This means that it is able to have an exact reconstruction
of
a signal from the samples of this one. In the case of the
human
hearing, the frequency is 20,000 Hz, so the correct sampling
frequency would be 40,000 Hz. Some studies increment this
value to 44,100 Hz, which is the value that tends to be
used.
If the sampling frequency is less than the double of the
maximum frequency of the signal, a phenomenon called
"Aliasing" occurs, where the sampled frequency differs from
the original signal.
Image 2. Example of the aliasing phenomenon.
Fourier Theorem
The analysis of harmonics present in sound that have a
determined timbre is determined by a Fourier analysis. The
Fourier theorem states something along the lines of:
"Any type of wave, with the condition that this one is
periodical (always repeats itlsef) can be broken down into a
shorter or longer (even infinite) series of pure
(sinusoidal)
waves called harmonics. These harmonics are so that their
combination gives way again to the original sound, and its
frequencies are the whole multiples of the fundamental
sound.
Image 3. Broken down signal.
The harmonics are sounds. A pure timbre (one sinusoidal
wave) is made up of only one sound, which is equal to
itself.
A complex timbre (a type of periodic wave different from a
sinusoidal one) is made up of a series of sinusoidal waves
mixed, summed or combined with each other. All of these
sounds come combined as one, in a way that we can't normally
distinguish one from another.
IV. PROCEDURE
Sampling Ideal Signals
The first part of the practice consisted in sampling a
signal
using the following equipment.
Respective cables and connections
Signal generator
Osciloscope
Sound Card
Computer
From the output of the generator, the signal was divided
into the osciloscope and the sound card, which was connected
to the PC via USB.
Image 3. Signal generator used for this practice.
Three types of signals were generated, varying their
frequencies and the sampling frequencies. The olny thing
kept
constant was the peak to peak amplitude, which was set to
1000 mV.
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Signal Generator Audio Software
Signal Frequency
(Hz)
Sampling
Frequency (Hz)
Sinusoidal 2000 6000
4000 6000
Saw tooth 2000 6000
2000 48000
Cuadrada 2000 48000
4000 48000
The results obtained where the following:
Image 4. Sinusoidal signal with a frequency of 2000 Hz and
a sampling frequency of 6000 Hz.
Image5. Sinusoidal signal with a frequency of 4000 Hz and
a sampling frequency of 6000 Hz.
Image 6. Saw tooth signal with a frequency of 2000 Hz and
a sampling frequency of 6000 Hz.
Image 7. Saw tooth signal with a frequency of 2000 and a
sampling frequency of 48,000 Hz.
Imagen 8. Square signal with a frequency of 2000 Hz and a
sampling frequency of 48,000Hz.
Adobe Audition was the software used to sample the
signals. In the software the sampling frequency desired to
work with was selected.
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Capturing Signals From a Real Source
The second part of this practice consisted in capturing
signals from a real source.
The equipment used for this section was the following.
Cables and adapters
2 Motors
Accelerometer
Signal conditioner
Sound card
Computer with Matlab
Image 9. Motors used for the second part of the practice.
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The vibration emitted with the motors was measured with
an accelerometer and the information was analyzed in Matlab
at different sampling frequencies.
Motor Sampling Frequency (Hz)
A 8,000
16,000
B 8,000
16,000
The results obtained where the following:
Image 9. Motor A. Sampling frequency of 8000 Hz
Image 10. Motor A. Sampling frequency of 16000 Hz
Image 10. Motor B. Sampling frequency of 16000 Hz.
Image 11. Motor B. Sampling frequency of 16000 Hz.
Spectral Frequency
We obtained the spectral frequency for the data we
acquired.
Image 12. Commands used to obtain the spectral
frequency
The command above was used to obtain the spectral
frequencies, and the results obtain were plotted.
Image 13. Frequency spectrum for motor A, with a sampling
frequency of 8000 Hz.
Frequency (Hz)
Am
pli
tude
Frequency (Hz)
Frequency (Hz)
Frequency (Hz)
Am
pli
tude
Am
pli
tude
Am
pli
tude
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Imagen 14. Frequency spectrum for motor A, with a
sampling frequency of 16000 Hz
Imagen 15. Frequency spectrum for motor B, with a
sampling frequency of 8000 Hz.
Imagen 16. Frequency spectrum for motor B, with a
sampling frequency of 16,000Hz
V. DISCUSSION
Analyzing the results from the first part of the practice,
which are the ones that correspond to the sampling of ideal
signals, it can be seen that when the sampling frequency is
incremented, in all of the cases, the signal obtained in the
software is closer to that one which is displayed on the
oscilloscope (ideal signal). The case where this could be
seen
the most was for the square signal, in which when the
sampling frequency was incremented to 48,000 Hz, this one
became more like an ideal square signal. It can be seen in
Image 8, that having a high sampling frequency it is able to
reconstruct the original signal.
For the second part of the practice, the data obtained was
from a real source. In the results graphed, we can clearly
see
that motor A has much less noise than motor B, comparing
Images 9 &10 vs 11&12. This was seen during the
practice,
because motor B emitted more noise compared to motor A.
This could have been caused by some unbalanced or failing
component.
VI. CONCLUSIONES
More knowledge was obtained about the fundamental
theory of data acquisition. Both acquisition from an ideal
source and a real source was done, the ideal signals came
from
a signal generator while the real signals were obtained from
an
accelerometer.
Using a PC it was able to analyze the signal coming from
the source. In the case of the real source was seen that
data
acquisition can be utilized in a great number of
applications.
VII. REFERENCES
[1] Np. Que es la adquisicin de datos?, National Instruments.
Web, Febrero 2015.
http://www.ni.com/data-acquisition/what-is/esa/
[2] Np, Muestreo y resolucin de audio, Foto y Diseo Digital,
Fotonostra. Web, Febrero 2015
http://www.fotonostra.com/digital/muestreoaudio.ht
VIII. BIOGRAPHYS
Harry Nyquist(7 February 1889 - 4 April 1976) was
an important contributor to the theory of
information.
Worked in the development and research of
AT&T from 1917 to 1934, and continued when the company
changed its name to Bell Telephone
Laboratories that year, and continued until his
retirement in 1954. Nyquist received the Medal of Honor IEEE in
1960 for "Fundamental knowledge
about thermal noise, data transmission, and negative
retro alimentation". His early theory work in determination of a
broadband to transmit information set the fundamentals for later
advances Claude Elwood
Shannon, who developed the theory of information.