Structural Analysis

LABORATORY #1 |
STRUCTURAL ANALYSIS
|
FUNDAMENTALS OF SIGNAL AQCUISITION AND ANALYSIS |

JORGE SAUCEDO TERREROS 1462003JOSÉ ALEJANDRO TORRES BECERRIL 1535170BRUNO GUILLERMO GÓMEZ MACÍAS 1432063 12/02/2013 |

SUMMARY
IN THIS PRACTICE WE ARE GOING TO ANALYZE AND PROVE THE VERACITY OF THE NYQUIST THEOREM WITH THE HELP OF MATLAB AND ADOBE AUDITION, WE WILL ANALYZE DIFFERENT TYPES OF SIGNALSLIKE SINUSOIDAL, SAWTOOTH AND SQUARE. THESE ONES GENERATED BY A SIGNAL GENERATOR WITH DIFFERENT FREQUENCIES AT DIFFERENT SAMPLING RATES.
AT LAST WE WILL TEST TWO MOTORS SIGNALS OUTPUTS, THESE ONES OWN THE CHARACTERISTIC OF ONE PRODUCING MORE NOISE AND VIBRATION THAN THE OTHER.

INTRODUCTION
THIS PRACTICE OF SIGNAL PROCESSING IS A VERY SIMPLE EXAMPLE OF WHERE THE FOURIER ANALYSIS IS DEVELOPED. ITIS OF GREATLY IMPORTANCE BECAUSE ALL THE KNOWLEDGE APPLIED IN THIS PRACTICE ARE THE BASES OF THE FUNCTION OF TELECOMMUNICATIONS, AUDIO, VIDEO, IMAGES, ETC. TWO ARE THE BASIC INSTRUMENTS: THE FOURIER SERIES FOR SUPERPOSITION OF BASIC WAVES OR ARMONICS AND THE NYQUIST THEOREM. BASICALLY WE ARE TRANSFORMING A PERIODIC FUNCTION IN TIME DOMAIN, TO A SIGNAL IN FREQUENCY DOMAIN.

THEORY
WINDOWSIN SIGNAL PROCESSING, A WINDOW FUNCTION IS A MATHEMATICAL FUNCTION THAT IS ZERO-VALUED OUTSIDE OF SOME CHOSEN INTERVAL. FOR INSTANCE, A FUNCTION THAT IS CONSTANT INSIDE THE INTERVAL AND ZERO ELSEWHERE IS CALLED A RECTANGULAR WINDOW, WHICH DESCRIBES THE SHAPE OF ITS GRAPHICAL REPRESENTATION. THE APPLICATIONS OF WINDOW FUNCTIONS INCLUDE SPECTRAL ANALYSIS AND THE DESIGN OF FINITE IMPULSERESPONSE FILTERS. 
FAST FOURIER TRANSFORMER (FFT)
IS AN ALGORITHM TO COMPUTE THE DISCRETE FOURIER TRANSFORM AND ITS INVERSE. THERE ARE MANY DIFFERENT FFT ALGORITHMS INVOLVING A WIDE RANGE OF MATHEMATICS, FROM SIMPLE COMPLEX-NUMBER ARITHMETIC TO GROUP THEORY AND NUMBER THEORY.


NYQUISTS THEOREM
AN ANALOG SIGNAL WAVE FORM CAN BE RECONSTRUCTED, WITHOUT ERROR, FROM SAMPLES TAKEN AT EQUAL TIME INTERVALS.  THESAMPLING RATE MUST BE GREATER THAN TWICE THE VALUE OF THE HIGHEST FREQUENCY COMPONENT OF THE ANALOG SIGNAL.  IF 20 KHZ PERFORMANCES IS SOUGHT, YOU WOULD NEED MORE THAN A 40 KHZ SAMPLING RATE. (FS ≥ 2F)
IN SIGNAL PROCESSING, THE NYQUIST RATE, NAMED AFTER HARRY NYQUIST, IS TWO TIMES THE BANDWIDTH OF A BANDLIMITED SIGNAL OR A BANDLIMITED CHANNEL. THIS TERM IS USED TO MEAN TWO DIFFERENT THINGS UNDER TWODIFFERENT CIRCUMSTANCES:

1. AS A LOWER BOUND FOR THE SAMPLE RATE FOR ALIAS-FREE SIGNAL SAMPLING (NOT TO BE CONFUSED WITH THE NYQUIST FREQUENCY, WHICH IS HALF THE SAMPLING RATE OF A DISCRETE-TIME SYSTEM) AND
2. AS AN UPPER BOUND FOR THE SYMBOL RATE ACROSS A BANDWIDTH-LIMITED BASEBAND CHANNEL SUCH AS A TELEGRAPH LINE OR PASSBAND CHANNEL SUCH AS A LIMITED RADIO FREQUENCY BAND OR AFREQUENCY DIVISION MULTIPLEX CHANNEL.

FILTER
 IS A DEVICE OR PROCESS THAT REMOVES FROM A SIGNAL SOME UNWANTED COMPONENT OR FEATURE. FILTERING IS A CLASS OF SIGNAL PROCESSING, THE DEFINING FEATURE OF FILTERS BEING THE COMPLETE OR PARTIAL SUPPRESSION OF SOME ASPECT OF THE SIGNAL. MOST OFTEN, THIS MEANS REMOVING SOME FREQUENCIES AND NOT OTHERS IN ORDER TO SUPPRESS INTERFERING SIGNALS AND REDUCEBACKGROUND NOISE. HOWEVER, FILTERS DO NOT EXCLUSIVELY ACT IN THE FREQUENCY DOMAIN; ESPECIALLY IN THE FIELD OF IMAGE PROCESSING MANY OTHER TARGETS FOR FILTERING EXIST.
THE DRAWBACK OF FILTERING IS THE LOSS OF INFORMATION ASSOCIATED WITH IT. SIGNAL COMBINATION IN FOURIER SPACE IS AN ALTERNATIVE APPROACH FOR REMOVAL OF CERTAIN FREQUENCIES FROM THE RECORDED SIGNAL.
FILTERS MAY BE:
* ANALOG OR DIGITAL
*DISCRETE-TIME (SAMPLED) OR CONTINUOUS-TIME
* LINEAR OR NON-LINEAR
* TIME-INVARIANT OR TIME-VARIANT, ALSO KNOWN AS SHIFT INVARIANCE. IF THE FILTER OPERATES IN A SPATIAL DOMAIN THEN THE CHARACTERIZATION IS SPACE INVARIANCE.
* PASSIVE OR ACTIVE TYPE OF CONTINUOUS-TIME FILTER
* INFINITE IMPULSE RESPONSE (IIR) OR FINITE IMPULSE RESPONSE (FIR) TYPE OF DISCRETE-TIME OR DIGITAL FILTER....