Most of the signal processing that we will study in this course involves local operations on a signal, namely transforming the signal by applying linear combinations of values in the neighborhood of each sample point. You are familiar with such operations from Calculus, namely, taking derivatives and you are also familiar with this from optics namely blurring a signal. We will be looking at sampled signals only. Let's start with a few basic examples. Local difference Suppose we have a 1D image and we take the local difference of intensities, DI(x) = 1 2 (I(x + 1) − I(x − 1)) which give a discrete approximation to a partial derivative. (We compute this for each x in the image.) What is the effect of such a transformation? One key idea is that such a derivative would be useful for marking positions where the intensity changes. Such a change is called an edge. It is important to detect edges in images because they often mark locations at which object properties change. These can include changes in illumination along a surface due to a shadow boundary, or a material (pigment) change, or a change in depth as when one object ends and another begins. The computational problem of finding intensity edges in images is called edge detection. We could look for positions at which DI(x) has a large negative or positive value. Large positive values indicate an edge that goes from low to high intensity, and large negative values indicate an edge that goes from high to low intensity. Example Suppose the image consists of a single (slightly sloped) edge:

http://ieeexplore.ieee.org/iel5/5/31307/01456462.pdf

Linear systems

dix A. Even if you don’t choose to memorize them this system aids in reference and retreival of important formulas. The book was compiled from notes developed during eight years of teaching a graduate course on the subject and was used as a text. Thus it has been student tested. Appendix F contains a number of problems, grouped to be used on a chapter by chapter basis The problems are designed to illustrate practical applications of the text material. The parts of this book of most interest and value to the EMC engineer will be the chapters on Thermal Noise, Antennas, Propagation and Transmission Lines, and  Reflection and Refraction. This is not  to downpade the chapters on Statistics and Its Applications, Signal Processing and Detection, and Some System Characteristics which also contain much potentially useful materials. Additional plus values for the book include a list of 40 references, a table of symbols used throughout the book, and a subject index. Some readers may find the condensed type and close line spacing hard to read. It was apparently set up by typewriter using an elite type face with single line spacing. When reduced down to a 6 by 9 5 inch size page it is too crowded for easy reading. In spite of this shortcoming your reviewer recommends this book as a worthwhile reference in this field of interest.

http://ieeexplore.ieee.org/iel5/5/31269/01455368.pdf

Signal analysis

The present invention relates to a method of transmitting and a method of receiving signals and corresponding apparatus. One aspect of the present invention relates to an efficient L1 signaling method for an efficient transmitter and an efficient receiver using the efficient L1 signaling method for an efficient cable broadcasting.

Apparatus for transmitting and receiving a signal and method of transmitting and receiving a signal

In this communication, necessary and sufficient conditions are presented for the unique blind identification of possibly nonminimum phase channels driven by cyclostationary processes. Using a frequencydomain formulation, it is first shown that a channel can be identified by the second-order statistics of the observation if and only if the channel transfer function does not have special uniformly spaced zeros. This condition leads to several necessary and sufficient conditions on the observation spectra and the channel impulse response. Based on the frequency-domain formulation, a new identification algorithm is proposed

Blind channel identification based on second-order statistics: a frequency-domain approach

The sampling theorem is one of the most basic and fascinating topics in engineering sciences. The most well-known form is Shannon's uniform-sampling theorem for bandlimited signals. Extensions of this to bandpass signals and multiband signals, and to nonuniform sampling are also well-known. The connection between such extensions and the theory of filter banks in DSP has been well established. This paper presents some of the less known aspects of sampling, with special emphasis on non bandlimited signals, pointwise stability of reconstruction, and reconstruction from nonuniform samples. Applications in multiresolution computation and in digital spline interpolation are also reviewed.

/pdf/generalizations-of-the-sampling-theorem-seven-decades-after-q7548wuqih.pdf

Generalizations of the sampling theorem: Seven decades after Nyquist

In an OFDM system, a transmitter (120) broadcasts a first TDM pilot on a first set of subbands followed by a second TDM pilot on a second set of subbands in each frame. The subbands in each set are selected from among N total subbands such that (1) an OFDM symbol for the first TDM pilot contains at least Sl identical pilot-1 sequences of length Ll and (2) an OFDM symbol for the second TDM pilot contains at least S2 identical pilot-2 sequences of length L2, where L2 > Ll, Sl x Ll = N, and S2 x L2 = N. The transmitter (120) may also broadcast an FDM pilot. A receiver ( 170) processes the first TDM pilot to obtain frame timing (e.g., by performing correlation between different pilot-1 sequences) and further processes the second TDM pilot to obtain symbol timing (e.g., by detecting for the start of a channel impulse response estimate derived from teh second TDM pilot).

Synchronization in a broadcast ofdm system using time division multiplexed pilots

Two digital filters H(z) and F(z) are said to be biorthogonal partners of each other if their cascade H(z)F(z) satisfies the Nyquist or zero-crossing property. Biorthogonal partners arise in many different contexts such as filterbank theory, exact and least squares digital interpolation, and multiresolution theory. They also play a central role in the theory of equalization, especially, fractionally spaced equalizers in digital communications. We first develop several theoretical properties of biorthogonal partners. We also develop conditions for the existence of biorthogonal partners and FIR biorthogonal pairs and establish the connections to the Riesz basis property. We then explain how these results play a role in many of the above-mentioned applications.

/pdf/biorthogonal-partners-and-applications-3kjs6k85hu.pdf

Biorthogonal partners and applications

A method for synchronizing timing of a receiver to a received orthogonal frequency division multiplexing (OFDM) signal is disclosed. A first timing acquisition is performed with a first received time division multiplexed (TDM) pilot to determine a course timing estimate of the received OFDM signal. A second timing acquisition is performed with a second TDM pilot to determine a fine timing estimate for a OFDM symbol of the received OFDM signal. In the second timing acquisition, the accumulated energy of channel taps over a detection window is determined and a trailing edge of the accumulated energy curve is detected. A Fourier transform (FT) collection window location for subsequent OFDM symbols is adjusted according to the trailing edge information.

Fine timing acquisition

A method for positioning a collection window for a Fourier transform function is disclosed. A first orthogonal frequency division multiplexing (OFDM) symbol and a second OFDM symbol are received. The first OFDM symbol comprises a plurality of frequency division multiplexed (FDM) symbols. The first OFDM symbol is characterized by at least two of the following: a delay spread, a first arriving path (FAP), or a last arriving path (LAP). A channel location is estimated from a channel impulse response. A point relative to the channel location is selected. A beginning of the collection window is positioned for the second OFDM symbol at the selected point. Alternatively, a point is selected at a first location relative to the channel location using a first algorithm if a delay spread is less than a predetermined length. The selected point is chosen at a second location relative to the channel location using a second algorithm if the delay spread is greater than the predetermined length.

Collection window positioning using time tracking information

The disclosure is directed to a receiver. The receiver includes an interference canceller configured to filter digital samples produced from a modulated signal transmitted over a wireless channel, and a digital variable gain amplifier (DVGA) configured to amplify the filtered digital samples.

Bojan Vrcelj

Papers

Synchronization in a broadcast ofdm system using time division multiplexed pilots

Biorthogonal partners and applications

Fine timing acquisition

Collection window positioning using time tracking information

Narrow-band interference canceller