Using MATLAB to Illustrate the \u27Phenomenon of Aliasing\u27

The phenomenon of aliasing is important when sampling analog signals. In cases where the signal is bandlimited, one can avoid aliasing by ensuring that the sampling rate is higher than the Nyquist rate . But in cases where the signal is not bandlimited , aliasing is unavoidable if the signal is not filtered before it is sampled. It is then crucial to understand the phenomenon in order to estimate the distortion generated when the signal is reconstructed from its samples. Using the software package MATLAB by MathWorks, Inc ., two examples are presented. The first is a pure sinusoid which is sampled at both higher and lower than the Nyquist rate , and the frequency spectrum of both sampled sinusoids are compared to illustrate the effect of aliasing. The second and more interesting case is a square wave which has an unlimited bandwidth. The square wave is a periodic wave that has Fourier expansion with odd harmonics only, the amplitudes of which drop as lin. A square wave is synthesized using MATLAB and its Fourier transform is presented graphically (The synthesized square wave inherently produces aliased components) . The odd harmonics and the aliased components seen on the graph are analyzed and compared to the predicted theoretical results. Graphs generated by MATLAB accompany the analysis for both signals

Arts, Computers and Artificial Intelligence

Science and art seem to belong to different cultures. Science and technology, mainly the products of the intellect, use terminology and vocabulary that are concise and well defined. In contrast, in artistic expression, ambiguity is a powerful component. Still the relationship between these two different categories of human activity is interesting and fascinating. In this paper, a general comparison of these two disciplines will be introduced. Then the possibility of mechanical creation of art using computers and artificial intelligence will be discussed. This will be followed by two techniques which are used to create poetry and music. First, a statistical approach for mechanical composition of music will be presented. This method uses parameters of existing music to create similar music. Second, a method of mechanical composition of poetry will be presented which combines linguistic models, a classification dictionary and semantic information

The Frequency Distribution of Quantization Error in Digitizers for Coherent Sampling

In this paper the frequency distribution of quantization error in coherent sampling of digitizers will be investigated. As the distribution of the quantization error affects the values of THD and SNR, it is relevant for a correct interpretation of THD and SNR of sine waves in coherent sampling. The distribution of the quantization error will be analyzed as a function of N, total number of samples and M, number of cycles in the sample set and it will be proved that for certain cases, the quantization error falls on odd harmonics only of the frequency of the sampled sine wave

Incorporating MATLAB\u27s Signal Processing Toolbox into a DSP course at an undergraduate E.E. program

This paper provides some suggestions for incorporating MATLAB\u27s Signal Processing Toolbox into a DSP course. Often, in a DSP course, students have difficulties understanding abstract and non-intuitive concepts and seeing their relevance to the practical part of their curriculum. The tools offered by MATLAB\u27s Signal Processing Toolbox, can help to make these concepts more tangible and provide a perspective for students. Some basic tools relevant to an undergraduate DSP course will be introduced, including examples of tool use and graphic results. The tools presented will be applied in the areas of synthesis and analysis of signals, FFT computation, impulse response and convolution, frequency response, the Z-transform, filter design and filter applications

Application of Wavelets and Principal Component Analysis in Image Query and Mammography

Breast cancer is currently one of the major causes of death for women in the U.S. Mammography is currently the most effective method for detection of breast cancer and early detection has proven to be an efficient tool to reduce the number of deaths. Mammography is the most demanding of all clinical imaging applications as it requires high contrast, high signal to noise ratio and resolution with minimal x-radiation. According to studies [36], 10% to 30% of women having breast cancer and undergoing mammography, have negative mammograms, i.e. are misdiagnosed. Furthermore, only 20%-40% of the women who undergo biopsy, have cancer. Biopsies are expensive, invasive and traumatic to the patient. The high rate of false positives is partly because of the difficulties in the diagnosis process and partly due to the fear of missing a cancer. These facts motivate research aimed to enhance the mammogram images (e.g. by enhancement of features such as clustered calcification regions which were found to be associated with breast cancer) , to provide CAD (Computer Aided Diagnostics) tools that can alert the radiologist to potentially malignant regions in the mammograms and to develope tools for automated classification of mammograms into benign and malignant classes. In this paper we apply wavelet and Principal Component analysis, including the approximate Karhunen Loeve aransform to mammographic images, to derive feature vectors used for classification of mammographic images from an early stage of malignancy. Another area where wavelet analysis was found useful, is the area of image query. Image query of large data bases must provide a fast and efficient search of the query image. Lately, a group of researchers developed an algorithm based on wavelet analysis that was found to provide fast and efficient search in large data bases. Their method overcomes some of the difficulties associated with previous approaches, but the search algorithm is sensitive to displacement and rotation of the query image due to the fact that wavelet analysis is not invariant under displacement and rotation. In this study we propose the integration of the Hotelling transform to improve on this sensitivity and provide some experimental results in the context of the standard alphabetic characters

Order and Disorder, Entropy in Math, Science, Nature and the Arts

Often, science and engineering students have difficult time in viewing certain concepts in their holistic form. An example for such a concept is the concept of Entropy. Although it originated from the field of thermodynamics, the relation between order and disorder is a profound one and manifests itself in various fields, sometimes unrelated, such as math and science, nature and the arts. In the discipline of physics, the amount of disorder in a system has been quantified by the concept of Entropy. In the area of information theory it provides a quantitative measure of the amount of compression that may be achieved in a coding scheme and in nature it poses an intriguing question when we consider biological systems. In the arts, which is an unrelated field to the previously mentioned, entropy can be seen in the balance and the tension between the regular and irregular, the expected and the unexpected themes, which make a piece of art valuable. In this paper we provide some interesting insights into the concept of Entropy and its implications in the fields of physics, information theory, decision making, nature and the arts

Combining Wavelets and Hotelling Transforms in Image Query

In the content based image query, also referred to as query by example, similarity retrieval or sketch retrieval, the query image is provided by the user either as a sketch of the object, as the output of a scanner or a video camera. Some of the difficulties associated with content based image query are described in [1], e.g. significant difference between the query image and the target image, artifacts and poor resolution of the query image make a straightforward comparison of images using L1 and l2 metrics not effective. In [2] a new strategy is suggested based on wavelet decomposition of the query image and the database images combined with a metric which is designed to be insensitive to small differences in the query process. This approach is found to be fast and overcomes the above mentioned problems. Wavelet coefficients of an image may be very strongly when the image is displaced or rotated (unlike color histogram of an image which is invariant under displacement and rotation). Although the metric suggested in [2] is more robust to these errors when compared to the L1 and L2 metric (but worse when compared to the metric based on color histograms), still the error is significant. In this paper we provide some experimental data on the sensitivity of the wavelet coefficients to displacement and rotation in the context of the standard characters and suggest an integration of the Hotelling transform to improve on this sensitivity. We also provide some experimental data on the distribution of the largest wavelet coefficients at different levels of the wavelet decomposition and discuss some questions relevant to the approach of using a set of the largest wavelet coefficients for image query

Introduction To Wavelets and Principal Components Analysis

Wavelet analysis found to have a variety of applications. While other transforms such as the DCT may achieve a better compression ratio, their rule of zeroing small coefficients is applied evenly and globally while in wavelet analysis, the rule of zeroing can be applied locally, preserving small coefficients that account for important minute features (such as in fingerprints). Starting with an introduction to wavelet analysis and some related concepts useful for classification the book provides a coverage of the theory and mathematical foundations of wavelets, the Best Basis, the Joint Best Basis, Principal Component Analysis and the Approximate PCA as well as the application of these tools to derive feature vectors for the classification of mammographic images. This book will be useful as a reference text and will benefit both the audience whose interest is at the conceptual level, as it provides a qualitative description of the underlying ideas of wavelet theory and the audience who is interested also in the theory and mathematical foundations of wavelet analysis and its applications