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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

T

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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.

.

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.