D. Sundararajan

A Practical Approach to Signals and Systems

Concisely covers all the important concepts in an easy-to-understand way Gaining a strong sense of signals and systems fundamentals is key for general proficiency in any electronic engineering discipline, and critical for specialists in signal processing, communication, and control. At the same time, there is a pressing need to gain mastery of these concepts quickly, and in a manner that will be immediately applicable in the real word. Simultaneous study of both continuous and discrete signals and systems presents a much easy path to understanding signals and systems analysis. In A Practical Approach to Signals and Systems, Sundararajan details the discrete version first followed by the corresponding continuous version for each topic, as discrete signals and systems are more often used in practice and their concepts are relatively easier to understand. In addition to examples of typical applications of analysis methods, the author gives comprehensive coverage of transform methods, emphasizing practical methods of analysis and physical interpretations of concepts. Gives equal emphasis to theory and practice Presents methods that can be immediately applied Complete treatment of transform methods Expanded coverage of Fourier analysis Self-contained: starts from the basics and discusses applications Visual aids and examples makes the subject easier to understand End-of-chapter exercises, with a extensive solutions manual for instructors MATLAB software for readers to download and practice on their own Presentation slides with book figures and slides with lecture notes A Practical Approach to Signals and Systems is an excellent resource for the electrical engineering student or professional to quickly gain an understanding of signal analysis concepts -concepts which all electrical engineers will eventually encounter no matter what their specialization. For aspiring engineers in signal processing, communication, and control, the topics presented will form a sound foundation to their future study, while allowing them to quickly move on to more advanced topics in the area. Scientists in chemical, mechanical, and biomedical areas will also benefit from this book, as increasing overlap with electrical engineering solutions and applications will require a working understanding of signals. Compact and self contained, A Practical Approach to Signals and Systems be used for courses or self-study, or as a reference book.

Digital signal processing : theory and practice

The discrete sinusoid time-domain analysis of discrete systems the discrete Fourier transform properties of the DFT the z-transform frequency-domain analysis of discrete systems digital filters - characterization and realization FIR filters IIR filters aliasing and other effects the continuous-time Fourier transform fundamentals of the PM DFT algorithms the u X 1 PM DFT algorithms DFT algorithms for real data.

Properties of the DFT

The following DFT properties are presented with examples: linearity, periodicity, time shifting, frequency shifting, time-reversal, duality, convolution, correlation, upsampling, zero padding, symmetry, and Parseval’s theorem.

Image Enhancement in the Frequency Domain

The frequency-domain representation of images is presented in the last chapter. Depending on the problem, either the spatial-domain or frequency-domain processing is advantageous. The interpretation of operations on images is often easier in the frequency domain. For longer filter lengths, frequency-domain processing provides faster processing. Linear filtering operations using a variety of filters are described in the frequency domain.

Morphological Image Processing

In processing the color and grayscale images, which occur mostly, their binary version is often used. In morphological processing of images, pixels are added or removed from the images. The structure and shape of the objects are analyzed so that they can be identified. The basic operations in this processing are binary convolution and correlation, that is based on logical operations rather than arithmetic operations. Dilation and erosion are the basic operations, and rest of the operations and algorithms are based on these operations. Morphological processing is also extended to gray-level images using the minimum and maximum operators.

The Continuous-Time Fourier Transform

Continuous Time Fourier Transform Chapter 4 in Oppenheim & Willsky Applicable to aperiodic signals (unlike Fourier series which is applicable only to periodic signals). Main idea: Treat aperiodic signal x(t) as the limit of a periodic signal x̃(t) as period T → ∞ (see figure below). As T increases, the fundamental frequency ω0 = 2π T decreases and the harmonic components become closer in frequency, forming a continuum in the limit T → ∞. Example:

Fast Computation of the DFT

The frequency-domain analysis of signals and systems is efficient, in practice, due to the availability of fast algorithms for the computation of the DFT. While the DFT is defined for any length, practically efficient algorithms are available only for fast computation of the N-point DFT with N an integral power of 2. The algorithms are based on the classical divide-and-conquer strategy of developing fast algorithms. A N-point DFT is recursively decomposed into half-length DFTs, until the DFT becomes trivial. The DFTs of the smaller transforms are combined to form the DFT of the input data. The decomposition can start from the time-domain end or the frequency-domain end. The first type is called decimation-in-time (DIT) algorithms. The second type is called decimation-in-frequency (DIF) algorithms. These algorithms are developed assuming that the data is complex-valued. They can be tailored to suit real-valued data. A set of algorithms are derived and examples of computing the DFT are given.

Two-Dimensional DFT

The 2-D DFT is presented as two sets of 1-D DFTs. Examples of the 2-D DFT are given. The formal definitions of 2-D DFT and IDFT are presented. The computation of the 2-D DFT by the row–column method is described with examples. Finally, a comprehensive coverage of the properties of the 2-D DFT is presented with examples.

Image Reconstruction from Projections

The Radon transform is presented, which is important in computerized tomography in medical and industrial applications. This transform enables to produce the image of an object, without intrusion, using its projections at various directions. As this transform uses the normal form of a line, it is presented first. Then, the Radon transform and its properties are described next. The Fourier-slice theorem and the filtered back-projection of the images are presented. Finally, line detection using the Hough transform is given. Examples are included to illustrate the various concepts.

Image Enhancement in the Spatial Domain

Although the transform domain processing is essential, as the images naturally occur in the spatial domain, image enhancement in the spatial domain is presented first. Point operations, histogram processing, and neighborhood operations are presented. The convolution operation, along with the Fourier analysis, is essential for any form of signal processing. Therefore, the 1-D and 2-D convolution operations are introduced. Linear and nonlinear filtering of images is described next.