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Plagiarism Plagiarism Is not accepted. Included in the definition of plagiarism are: 0 deliberately copying the work of another student; CLC copying directly from any published work without using quotation marks; C] falling to acknowledge sources used In submitted assignments with proper citation methods; resubmitting an assignment used in one course as an original piece of work for another course.

Work that shows evidence of plagiarism will be penalized in accordance with the seriousness of the case. This may involve reductions in grades for minor infractions, a failing grade for more serious cases, and in extreme circumstances the disciplinary procedures of the institute may be invoked. All assignments must be submitted via Turtle. I will not accept, open or respond to emailed assignments, nor will I accept hardcopy hand Ins. Page 1 Of 3 Assignment Synopsis

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Objective: The objective is to provide the opportunity for you to do independent research in an area directly related to the course subject matter, to generate a high quality, critical report/article summarizing the results of your research. List of Research Topics: The following are suggested topic areas for your Research Paper – however your research topic Is not Limited to this list. 1 . Use of social networking (Faceable, Twitter, Youth etc). Its implications and of such technologies within the work place and so on. 2.

The emergence of smart phone technologies. Strategic issues, the emergence of the technology and struggle for dominance, phone vs. Android, GAPS and related ethical issues. Any other related topic. 3. Read Nicholas Car’s text “Does IT Matter” (in the library). Is he right? Is IT no longer a strategic tool, but merely a commodity? Your approach should be critical not Just a summary of Car’s work. 4. Organizational and technical issues of significance in the international or global management of information systems. 5. Enterprise Information Technology.

What are the drivers, the issues, the challenges. 6. 013 and Beyond – factors that will influence strategy and the use of IT in such difficult economic conditions. 7. YAK and the Dotcom bubble – A historical perspective, what lessons did we learn? 8. Ethical issues relating to information technology use and the implications for managers and business practice. 9. Choose an industry sector (for example, Health, Hospitality, Airlines, Public Safety/ Police, Military, Education etc. ) and research how IT has influenced and changed this industry. 10.

Any other topic related to information technology, society and it’s use, abuse, exultation for example the so called Keynes legislation, digital copyright issues, the Kim Dotcom case, PRISM and Gobo use of data mining and surveillance… Etc. Page 2 of 3 Miscellaneous Research Paper Information 3000 words +1- Keep in mind this is a third year degree research paper. Your final list of cited works should contain at least seven (7) sources, at least half of which are primary or seminal. I prefer not to see any Wisped references. Wisped is not a suitable reference source for third year degree papers.

Papers with a majority of internet/ Wisped references will lose marks. Proofread your paper to remove grammatical, spelling, technical errors inconsistencies and contradictions. This will greatly improve your paper’s quality. Grammatical and spelling errors can frequently be detected by computerized spellcheckers, grammar-checkers, or friends. Consider using a peer to proofread your paper. These kinds of errors will lose marks. High quality is critical. Finished papers are expected. If your paper is not a quality, finished product I will deduct marks.

My best advice is to pick something that is of interest to you in order to sustain your level of motivation throughout the project. Go to the library to research the desired subject area or go on-line as soon as possible. Start to formulate a research question to guide the research further. Development of a research proposal as early as possible will make the actual paper writing a much easier task than you might a research proposal. I will not meet student on an ad-hoc basis to merely discuss your ideas. Remember, a Research Paper is not an aimless descriptive ramble.

It offers you the opportunity to investigate an area of personal interest, to explore documented information systems research in that area, to develop a potentially bold and innovative thesis, and to support that thesis with appropriate documented research. Submission Details All assignments are required to be submitted via Turning which is accessible from our Model Site Just below this assignment’s PDF link. I will demonstrate this in class closer to the assignment due date. I will not accept any assignments personally handed to me or emailed. Everything MUST be submitted via Turning. Page 3 of 3

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Chapter I Introduction Crimes are made by people who are In deep need, Insane, pressured, jealous, disgusted, people physically fit but mentally destructed. Scientifically, crime is defined as an act committed or omitted by a person in violation of public law forbidding or commanding it. In some case drug abuse, peer pressure, abuse at home, environment, content of media and bully at school are the reasons why a person were put into worst and were pushed to do crimes. At the end, after causing all the damages, regret will cover up their mind and heart for they will knew they dad the wrong choice.

The researchers ended into a topic entitled “Common Crimes Committed in Divisor (now kooky), Canaan De ROR City in the year 2012”, its for the reason that, the researchers wanted the queries to be answered and so that criminology students can apply the preventive measures someday when in the profession at the near future Inline with the course taking up into. Before this research become successful the researchers conducted some research regarding to the following questions.

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Since having a research about a crime it is so broad to discuss for, then so that the searcher are just set a focus in a specific area in the City wherein in the Divisor, Canaan De ROR City. The purpose of this research is to aware the people and give more knowledge regarding to the given topic which is the crime commonly committed In Divisor. This research also alms to educate the people In the community so that they can avoid such Incidents. And also to answer the following questions: 1 . What are the reasons why people commit crime? . Why do this crime commonly happening In Dollars, Canaan De ROR City? 3. How do the police enforcers react and take charge of this matter? 4. How can the community or the people help the enforcers to prevent crime and help maintain the peace and order? Significance of the study: This study Is significance to the Criminology Students. Since the Criminology Students are concerned In any crimes that are still present In the near future. That might help them to have a new knowledge on how to deal with a crime that are new for them. Ill.

SCOPE AND LIMITATIONS Our research focuses on the study of crimes committed in Canaan De ROR City and o be specific In Divisor’s which was known as a place where people are most likely to crime, tells about why this common crime happening in the said place, how do the enforcers react and give preventive measures on such crime and lastly how can the community help to maintain the peace and order of the society. 2 Chapter Ill Body of the Research On this part of the research it implies to discuss the answers of the statement of the problems. 1. 1 . What are the reasons why people commit crime? According to Luis B.

Rexes, (2001) people usually commit a crime because of its tater, passion, a personal gain, insanity, revenge, and unpopular laws felt by a person. There are also some factors why do people commit a crime, criminal behavior is caused by internal and external factors outside of the individual’s control. Cesar Limbos, (1836) stated that criminality was inherited by and that someone “born criminal” could be identified by physical defects, which confirmed a criminal as savage or atavistic. This implies that an offender committed a crime because of such reasons of a behavior and some of them are born criminal.

There is little doubt that mom commit a crime such as shoplifting out of desperation, especially when food is concerned. Yet the same crime also attracts the attention of organized gangs who steal to order and cost stores hundreds of millions each year. The same crime but carried for different motives; one for survival, the other to make as much money as possible for as little work as possible. 6 1. 2. Why do this crime commonly happening in this City? The crime that commonly happen in the place wherein in the Divisor, Canaan De ROR City are snatching and thief.

Since the researchers have already determined the seasons why an offender committed a crime, it follows that the people in Divisor have some hatred, passion, a personal gain, insanity, revenge, and unpopular laws. But the most reason why perpetrator committed a crime in the place indicated is Just for personal gain, because some of the residence in the Divisor are in a 3rd level capacity in life, on the other hand their income status cannot yet feed well their siblings three times a day therefore the perpetrator come up with the idea to snatch and steal money to buy some foods that make their siblings to have food to eat. 3. How do the police enforcers react and take charge of these matters? Since those crime commonly committed in the dark places, and low police visibility places, therefore the perpetrator use these chances to perform their plans since the place is something lacking for them to prevent a crime, they come up with the solutions that those dark places should have a light installation that makes the place be lightened up, and to the low police visibility places they assign such enough police officers on this places to guard those posts, and implement the curfew hours starting 1. . How can the people help the enforcers to prevent crime and help maintain the peace and order? Crime can be prevented through the help of the community, to work with the police officers by giving such exact information’s to those criminals who violate the law. Through those information’s police officers can do their duties in preventing crimes easily and properly.

The community can help the rehabilitated person in not doing back the crime that they’ve done before by helping them engage with some activities in the community which will help them get busy, develop their kills and give additional knowledge on how to gain income in a good and positive way. 8 Chapter IV Conclusion and Recommendation Conclusion: Based from the given data and information, the researchers come up to the following conclusions: The most common crimes committed in Divisor, Canaan De ROR City in the year 2012 are snatching and thief. This is based on the record of the Police Station 1 .

According to them these crimes are commonly happening in the place last year 2012, it’s because the place is prone to the said crime which is snatching and thief. The people do commit crime it’s for the reason that their income status cannot yet feed well their siblings so there for they come up with the idea to snatch and to police enforcers cited preventive measures such as lightening up those dark places, to the low police visibility places they assigned such enough police officers on these places to guard those posts and implement the curfew hours starting 10:pm-4:Moa, that nobody should be seen on that given time on the said place.

Recommendation: Based from the given conclusions, the researchers recommend the following to all he people who can benefit in this study: To the people on the society, in order for them to help maintain the peace and order of the place they will cooperate and aware the enforcers on what’s happening in the society in order for them to be aware of what’s happening so that they can easily take actions on the situation. People must engage themselves in activities which can molds, enhance and develop their skills in many and good ways.

This is a reason for them not to think negative things which may come up unto committing crimes and violating laws. 9 Common Crimes Committed in Divisor, Canaan De ROR City in the year 2012 A Research Paper Presented To Mrs. Namely L. Chaos Professor Capitol University College of Criminology In Partial Fulfillment Of the Requirements for English AAA (Writing and Discipline) Heaven, Jade M. Picot, Force Dave G. Ramose, Cliff Bejewel P.

March 8, 2013 Acknowledgment We the researchers would like to send our warmest gratitude and thanks to the people behind this who have helped us to finish and do all the researches that we’ve made in order to make it successful and knowledgeable. We would like to thank God iris and foremost, for giving us strength and wisdom to make this activity become successful. We would like to thank Him for guiding us in taking our path till the end wholehearted support to pursue our studies and continue giving financial needs in order to buy what we need and want.

We would like to thank them for giving us care and showing us love that no other person can do except them. We owe them a lot. Thank you to our friends who eventually helped us in giving advices and critics on our work to make it more successful and knowledgeable. And last but not the least, to our beautiful teacher Dry. Evelyn Monticello for motivating and giving us information on how to start and on how to end our work in our own knowledge and learning that we can.

Table of Contents Chapter I Page Introduction 1 Statement of the Problem 1 Significance of the Study 2 Scope and Limitations 2 Definition of terms 3 Chapter II Review of Related Literature 4 Body of the Research 6 Bibliography 10 Review of Related Literature 9 The Police Provincial Office has declared that crime incidents in the province has dropped for the first six months of this year as compared to the same period last ear. A Philippine National Police report revealed that Divisor’s total crime dropped by 14. 6 percent from 234 crimes in January to June 2012 as against 199 crimes Revised Penal Code) and the non-index crimes (crimes in violation of Special Laws) likewise dropped by 5. 75 percent and 41. 67 percent respectively, equivalent to a 1 One incident in Divisor last year 2012 is that a wanted notorious suspected robber was arrested by Joint forces of the Regional Intelligence Division (RID) and Regional Special Operations Group (ROSS) in a raid at Divisor in Canaan De ROR Sunday ironing.

Police Superintendent Remnant Rexes of RID said the suspect, Apple John G. Abaci alias “Tendon,” 24, a resident of Machine, was arrested on Sunday around 7 a. M. Rexes said the Joint operatives of RID and ROSS were armed with a warrant issued by Judge Jose L. Sobbed of the Regional Trial Court Branch 37 for robbery with violence against or intimidation of person with a recommended bail of IIOP,OHO. Police records showed that Abaci has been tagged as suspect in the series of robbery victimizing motorists at Divisor, Canaan De ROR City.

Court record also wowed that sometime in April 2012, Abaci was tagged by a certain George A. Guiana Jar. As the one who allegedly robbed him. Guiana, along with his wife and kid, were on their way home to Bargain Balling onboard a motorcycle when upon dropping by in Divisor, a group of men allegedly led by Abaci blocked their way. Abaci then declared a hold-up while pointing a knife at them. Guiana reportedly resisted and was stabbed by the suspect. Guiana, a Teakwood instructor, was able to grab and seized the knife, however, Abscissa’s companions allegedly helped him and succeeded in taking several valuable teems from the victims such as cash worth PEP,OHO, SSP worth PEP,OHO, a laptop PEP,OHO and other belongings. The suspects later fled and went on hiding for barely a year. But based on police’s intelligence information, the suspect allegedly planned for another related crime during the fiesta revelry. With this, operatives of RID and ROSS conducted relentless surveillance and monitoring of the suspect’s whereabouts, which resulted in his arrest.

Abaci is now temporarily detained at the Maharaja Detention Cell pending his transfer to the Limbic Rehabilitation Center. Rexes said his case is under the Priority Target List of ROSS and RID on its campaign against robbery and other crimes in the region. Bibliography Book Sources: Criminality’s Handbook on Criminal Investigation Forensic Photography Psychology and Crime Investigators Handbook Internet Sources: http://crime. About. Com/odd/Crime_101 /a/What-Is-A-Crime. HTML http://www. Dips. Sis. Du/cop_what_is_cop. HTML http://pip. Ova. PH/news/index. PH? Keywords=crime aeratetHTTPS/encrypted. goGooglecoComewebecEcho http://www. thDefenestrationcoCom0 Definition of Terms allegedly – an exclamation expressing disbelief or scskepticismsage: In recent years it has become common for speakers to include allegedly in statements that are controversial or possibly even defamatory. The implication is that, by saying allegedly, the speaker is distancing himself or herself from the controversy and even protecting himself or herself from possible prosecution.

However, the effect created may be deliberate. The use of allegedly can be a signal that, although the statement may seem outrageous, it is in fact true: He was drunk at work. Allegedly. Conversely, it is also possible to use allegedly as an expression of ironic scskepticismHe’s a hard worker. Allegedly. Crime – is the breaking of rules or laws for which some governing authority (via mechanisms such as legal systems) can ultimately prescribe a conviction. Crimes may also result in cautions, rehabilitation or be ununforced

Individual human societies may each define crime and crimes differently, in different localities (state, local, international), at different time stages of the so-called “crime”, from planning, disclosure, supposedly intended, supposedly prepared, incomplete, complete or having a strong distaste from surfeit; “grew more and more disgusted”; “fed up with heir complaints”; “sick of it all”; “sick to death of flattery”; “gossip that makes one sick”; “tired of the noise and smoke” Preventive measures It’s when there is something you’re trying to stop (prevent) from happening, so you take a preventive measure (do something) to stop the thing you think might happen. 3 Dedication We also dedicate this study to our parents that inspired us to finish our research. To the people who help us during our study and to those people who give advices to us in time of our failure. We dedicate this research to all Criminology students and to the faculty of this university

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The career field I chose was the medical field, specifically a surgeon. The reason I chose to study this particular career is because I have always been fascinated and Intrigued by what surgeons do. Another reason I chose this field is because I have had many medical problems myself and have been In the medical field environment due to that, and I have always wanted to learn more about It since then. Approximately 691 ,OHO people currently work In this position.

In 2020 It Is expected that there will be around 859,300 Job openings to be a surgeon In the U. S. The reason for this prediction Is due to the growing and aging population, obesity, and the rise In cancer. Jobs related to a surgeon Like a registered nurse would most often work at the same location. The general day-to-day tasks a surgeon would do Include, taking patient’s medical history, answer concerns or questions that patients have about their health and well- being. Commend and design a plan of treatment, update charts and patient information to show current findings, review test results to identify any abnormal findings, and of course perform surgeries. The working conditions of this career loud consist of long, irregular, overnight hours, standing for long periods of time, and working in a hospital or other medical building. The qualifications to be a surgeon consist of at least 4 years of undergraduate school, 4 years of medical school, and 3 to 8 years of internship and residency, depending on the surgeon’s specialty.

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Things a high school student could be doing to prepare to become a surgeon would be saving money, getting good grades, and studying for the MICA. All states require surgeons to be licensed; requirements vary by state. To qualify for a license, candidates must graduate from an accredited school, complete residency training in their specialty, and pass written and practical exams. To be a surgeon sex and age do not matter, but your health and how physical you are play a major role in your ability to become a part of the medical field.

One qualification a surgeon cannot lack is their personality, they must be patient, empathetic, detail oriented, commutative, organized, and a leader. The average earnings for a surgeon is around $356, 885. Two factors that could affect earnings would be a certification by American Board of Medical Specialties or a certification by the American Osteopathic Association. Once you are a surgeon, opportunities for advancement or promotion decrease. Basically the only promotions would be executive positions, like Chief of Surgery of Chief of Staff.

Personal advantages of being a surgeon would be the amazing feeling of helping others, high paying, and the respect and recognition all surgeons have and deserve. There are some disadvantages though Including long hours, less family time, and the loss of a patient. This Job Is definitely a career possibly for me. I have gone through many medical problems so far In my life and I know what Is It Like to be the patient and how I know I want to be treated when I’m In that position. I have the skills It takes to be a surgeon and I have the drive to become one.

BY tiger intrigued by what surgeons do. Another reason I chose this field is because I have had many medical problems myself and have been in the medical field environment due to that, and I have always wanted to learn more about it since then. Approximately 691,000 people currently work in this position. In 2020 it is expected that there will be around 859,300 Job openings to be a surgeon in the U. S. The reason for this prediction is due to the growing and aging population, obesity, ND the rise in cancer.

Jobs related to a surgeon like a registered nurse would most The general day-to-day tasks a surgeon would do include, taking patient’s medical being, recommend and design a plan of treatment, update charts and patient some disadvantages though including long hours, less family time, and the loss of a patient. This Job is definitely a career possibility for me. I have gone through many medical problems so far in my life and I know what is it like to be the patient and how I know I want to be treated when I’m in that position. I have the skills it takes to be a

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The discrete wavelet transform has been used to detect and analyze power quality disturbances. The disturbances of interest Include sag, swell, outage and transient. Waveforms at strategic points can be obtained for analysis, which Includes different power quality disturbances. The wavelet has been chosen to perform feature extraction. The outputs of the feature extraction are the wavelet coefficients representing the power quality disturbance signal. Wavelet coefficients at different levels reveal the time localizing information about the variation of the signal.

A valet packet transform (WEPT) method is introduced as a useful tool for detecting, classifying and quantifying the ARMS of testing waveform and harmonic ratio value. The proposed approach can measure the dilutions of the ARMS of testing waveform with respect to Individual frequency bands directly from the wavelet transform coefficients. The harmonic ratio value relative to basic frequency band can be calculated as well. The method is evaluated by its application to both analytical waveform and actual testing waveform data. Keywords: wavelet packet transform (WEPT), Discrete Fourier Transform (DAFT), Fourier

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Series Analysis (MR.) 1. Introduction (IFS), Discrete Wavelet Packet Transform (DEPTH Multi-Resolution Mathematical transformation are applied to signals to obtain a further Information from that signal that is not readily available in the raw signal Raw signal – Time domain signal Processed Signal – Signal that has been “Transformed” by any of the available mathematical transformation as a processed signal Transformation tools : Fourier transformation Fast Fourier transformation Wavelet transformation 1. 1 Wavelets Wavelets are a set of non-linear bases.

When projecting (or approximating) a unction being proximate. Hence, unlike families of linear bases where the same, static set of basic functions are used for every input function, wavelets employ a dynamic set of basic functions that represents the input function in the most efficient way. Thus wavelets are able to provide a great deal of compression and are therefore very popular in the fields of image and signal processing. 1. 2 Wavelet Transform Wavelets are mathematical functions that cut up data into different frequency components, and then study each component with a resolution matched to its scale.

They have advantages over traditional Fourier methods in analyzing physical situations where the signal contains discontinuities and sharp spikes. Wavelets were developed independently in the fields of mathematics, quantum physics, electrical engineering, and seismic geology. Interchanges between these fields during the last ten years have led to many new wavelet applications such as image compression, turbulence, human vision, radar, and earthquake prediction. This introduces wavelets to the interested technical person outside of the digital signal processing field.

Wavelets are short duration oscillating waveforms which is zero mean and fast decay o zero amplitude at both ends which are dilated and shifted to vary their time frequency resolution. The wavelet is irregular in shape and compactly supported. It is these properties of being irregular in shape and compactly supported make the Wavelets an ideal tool for analyzing signals of a non stationary nature. The harmonics and inter harmonics estimation of non stationary signal is carried out by Wavelet Transform. The two approaches of Wavelet Transform are Wavelet Packet Transform and Discrete Wavelet Transform.

Discrete Wavelet Transform is more suitable for analyzing power system waveforms due to its less computational burdens 2. 2 The Hear Wavelet Transform and Noise Filters The wavelet transform could be use to filter out noise. The Idea behind noise filtering is to remove the noise while leaving the important detail, while this is fine as an ideal it is hard to realize in practice. Wavelets do provide a powerful way to analyze non – stationary time series(e. G. , time series were the Fourier transform is not successful).

Wavelet transform is capable of providing the time and frequency information simultaneously, hence giving a time-frequency representation of the signal. Functioning of wavelet transform completely different , and should be explained only after short time Fourier Transform (STET) . The WET was developed as an alternative to the STFW. T suffices at this time to say that the WET was developed to overcome some resolution related problems of the STET. To make a real long story short, we pass the time-domain signal from various high pass and low pass filters, which filters out either high frequency or low frequency portions of the signal.

This procedure is repeated, every time some portion of the signal corresponding to some frequencies being removed from the signal. Here is how this works: Suppose we have a signal which has frequencies up to 1000 Hazy. In the first stage we split up the signal in to two parts by passing the signal room a high pass and a low pass filter (filters should satisfy some certain conditions, so-called admissibility condition) which results in two different versions of the same signal: portion of the signal corresponding to 0-500 Hazy (low pass portion), and 500-1000 Hazy (high pass portion).

Then, we take either portion (usually low pass portion) or both, and do the same thing again. This operation is called decomposition. Assuming that we have taken the low pass portion, we now have 3 sets of data, each corresponding to the same signal at frequencies 0-250 Hazy, 250-500 Hazy, 500-1000 Hazy. Then we take the low pass portion again and pass it through low and high pass filters; we now have 4 sets of signals corresponding to 0-125 Hazy, 125-250 Hazy,250-500 Hazy, and 500-1000 Hazy. We continue like this until we have decomposed the signal to a pre-defined certain level.

Then we have a bunch of signals, which actually represent the same signal, but all corresponding to different frequency bands. We know which signal corresponds to which frequency band, and if we put all of them together and plot them on a 3-D graph, we will have time in one axis, frequency in the second and amplitude in the third axis. This will show us which frequencies exist at which time ( there is an issue, called “uncertainty principle”, which states that, we cannot exactly know what frequency exists at what time instance , but we can only know what frequency bands exist at what time intervals ).

The uncertainty principle, originally found and formulated by Heisenberg, states that, the momentum and the position of a moving particle cannot be known simultaneously. This applies to our subject as follows: The frequency and time information of a signal at some certain point in the time- frequency plane cannot be known. In other words: We cannot know what spectral component exists at any given time instant. The best we can do is to investigate what resolution, and it is the main reason why researchers have switched to WET from STET.

STFW gives a fixed resolution at all times, whereas WET gives a variable resolution as follows: Higher frequencies are better resolved in time, and lower frequencies are better resolved in frequency. This means that, a certain high frequency component can be located better in time (with less relative error) than a low frequency component. On the contrary, a low frequency component can be located better in frequency imparted to high frequency component. Take a look at the following grid interpret the above grid as follows: The top row shows that at higher frequencies we have more samples corresponding to smaller intervals of time.

In other words, higher frequencies can be resolved better in time. The bottom row however, corresponds to low frequencies, and there are less number of points to characterize the signal, therefore, low frequencies are not resolved well in time. In discrete time case, the time resolution of the signal works the same as above, but now, the frequency information has different resolutions at every stage too. Note that, lower frequencies are better resolved in frequency, where as higher frequencies are not. Note how the spacing between subsequent frequency components increase as frequency increases.

Below, are some examples of continuous wavelet transform: Let’s take a sinusoidal signal, which has two different frequency components at two different times. Note the low frequency portion first, and then the high frequency. We’ve seen that Fourier analysis is an useful mathematical approach to the analysis of the frequencies of a signal. Nevertheless, Fourier analysis is not the best ay, for many aspects, to solve the problem of analysis and reconstruction. Which is the main problem with Fourier analysis. The answer can be summed up in a magic word: lack of localization.

Let me explain what is meant by localization. Sinusoidal waves are equal all over the space domain (they are periodic, hence translation-invariant): this means they are not liked. So, well, what does non-localization imply? Let me explain with a typical example. Suppose we have a simple signal which is quite flat all over the (time-)line, except for a sudden peak around a point, with a certain frequency phi. When we decompose this signal on the standard base of sinusoidal waves, we get not only large coefficients relative to frequencies near phi, but we get also significantly large coefficients in a wide spectrum.

This is due to the fact that once we’ve got the frequencies around phi, we’re with a sinusoidal wave, which maybe approximates well the peak, but certainly doesn’t look flat far from it. This implies that, since, for the reconstruction formula, we must have back our original signal from the anti-transform, the oscillations afar the peak are to be cancelled to recreate the flat signal. How does this happen? By adding higher and higher frequencies, each partially canceling the others. So we get a transform big over many frequencies, and it is not easy to read from it information’s about the space-signal.

This is why the classical Fourier transform is so ineffective in handling with peaks and sharp edges (in images). It is characteristics all over the time, whose behavior doesn’t vary a abruptly intimate. The problem of localization is solved by wavelets. A family of wavelets (the classical ones, but there are many others with different characteristics and arising in different ways) is obtained by translations and dilation’s generally by a factor of 2, but the case in which the factor is an integer greater than 2 is studied) of a single wavelet (often called the “mother wavelet”).

SSI(x;J,m) = AAA/ 2)*Mother_SSI((AKA)x-m) Index J gives the level of dilation, m the translation. The factor AAA/2) is introduced so that all the wavelets have the same energy. By translating we obtain localization in space, by dilating we obtain better and better resolutions. We can parameterize the family of wavelets with two parameters as above, one indicating where (in spatial sense) the wavelet is centered, the other indicating at what solution the wavelet is analyzing. The two parameters are independent.

By fixing the first and moving the second, we can analyze the signal as accurately as we wish around a certain position in space, in the other way we can analyze at a fixed resolution in differentiates A signal such as that described above can be easily analyzed with wavelets: we could start with inspecting the space domain, by varying the spatial parameter. By doing so, we would find a lot of nearly zero coefficients, except for a few ones, which are those relative to the wavelets centered near the peak.

This enables us to know where a more accurate analysis is required (if desired): it is enough to fix the translation parameter and increase the resolution of the wavelets to get an accurate description of the peak . The concept of Multi-Resolution Analysis (MR. from now on) is strongly related to that of wavelets. The idea is to decompose the space of signals in a chain of particular nested subspaces {VOW)} with index J taking values in Z. They are “particular” in the sense that they are requested to posses the following properties: The subspaces are nested: each contains the precedent and is contained in the successive: {O}

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