3:30, SPTM-P2.1
EVENT BASED SAMPLING WITH APPLICATION TO VIBRATION ANALYSIS IN PNEUMATIC TIRES
N. PERSSON, F. GUSTAFSSON
Event based sampling occurs when the time instants are measured everytime the amplitude passes certain pre-defined levels. This is in contrast with classical signal processing where the amplitude is measured at regular time intervals. The signal processing problem is to separate the signal component from noise in both amplitude and time domains. Event based sampling occurs in a variety of applications. The purpose here is to explain the new types of signal processing problems that occur, and identify the need for processing in both the time and event domains. We focus on rotating axles, where amplitude disturbances are caused by vibrations and time disturbances from measurement equipment. As one application, we examine tire pressure monitoring in cars where suppression of time disturbance is of utmost importance.

3:30, SPTM-P2.2
A WINDOWING CONDITION FOR CHARACTERIZATION OF FINITE SIGNALS FROM SPECTRAL PHASE OR MAGNITUDE
S. SHETTY, J. MCDONALD, D. COCHRAN
Reconstruction of a signal from its spectral phase or magnitude is in general an ill-posed problem. Various conditions restricting the class of signals under consideration have been shown to be sufficient to regularize the problem so that a unique (or essentially unique) signal corresponds to any given spectral magnitude or spectral phase function. This paper shows that a finite discrete-time signal is characterized by its spectral magnitude (or phase) and the spectral magnitude (or phase) of an ancillary signal obtained by windowing the original signal.

3:30, SPTM-P2.3
A SAMPLING THEOREM FOR PERIODIC PIECEWISE POLYNOMIAL SIGNALS
M. VETTERLI, P. MARZILIANO, T. BLU
We consider the problem of sampling signals which are not bandlimited, but still have a finite number of degrees of freedom per unit of time, such as, for example, piecewise polynomials. We demonstrate that by using an adequate sampling kernel and a sampling rate greater or equal to the rate of innovation, one can uniquely reconstruct such signals. This proves a sampling theorem for a wide class of signals beyond bandlimited signals. Applications of this sampling theorem can be found in signal processing, communication systems and biological systems.

3:30, SPTM-P2.4
ON SAMPLING THEOREMS FOR NON BANDLIMITED SIGNALS
P. VAIDYANATHAN, B. VRCELJ
It is well-known that certain non bandlimited signals such as splines can be reconstructed from uniformly spaced samples similar to bandlimited signals. This usually requires noncausal IIR filters. We revisit this result and consider extensions such as derivative sampling theorems and pulse sampling theorems. It turns out that spline-like signals can often be reconstructed from joint sampling of amplitude and derivative using only FIR filters. We also briefly consider discrete time versions of these results.

3:30, SPTM-P2.5
EFFICIENT QUANTIZATION FOR OVERCOMPLETE EXPANSIONS IN R^N
B. BEFERULL-LOZANO, A. ORTEGA
The use of quantized redundant expansions is useful in applications where the cost of having oversampling in the representation is much lower than the use of a high resolution quantization (e.g. oversampled A/D). Most work to date has assumed that simple uniform quantization was used on the redundant expansion and then has dealt with methods to improve the reconstruction. Instead, in this paper we consider the design of quantizers for overcomplete expansions. Our goal is to design quantizers such that simple reconstruction algorithms (e.g. linear) provide as good reconstructions as with more complex algorithms. We achieve this goal by designing quantizers with different stepsizes for each coefficient of the expansion in such a way as to produce a quantizer with periodic structure.

3:30, SPTM-P2.6
JITTER EFFECTS IN A MULTIPATH ENVIRONMENT
C. MAILHES, B. LACAZE
This paper studies the effects of jitter in a multipath environment. The power spectral density of a process subjected to jitter and multipath is first derived. The problem of reconstruction of a time continuous process from observations subjected to jitter and multipath is then considered. Simulation and theoretical results are finally shown to be in good agreement.

3:30, SPTM-P2.7
A NOVEL HIGHLY STABLE HIGH-RESOLUTION OVERSAMPLED SIGMA-DELTA A/D CONVERTER CONFIGURATION
N. FRASER, B. NOWROUZIAN
Feedforward and multiple-feedback sigma-delta A/D converters offer high-resolution, but are susceptible to instability in the presence of capacitor tolerances in a corresponding switched-capacitor (SC) hardware implementation. The hitherto sigma-delta A/D converters are usually based on, a) complementary signal and noise transfer functions, and/or b) unit-circle noise transfer function zeros. This paper is concerned with the development of a novel sigma-delta A/D converter having, instead, magnitude-squared or magnitude complementary signal and noise transfer functions. The proposed A/D converter exhibits resolution and dynamic range properties similar to those of the existing feedforward and multiple-feedback A/D converters, but offers increased stability performance in the presence of capacitor tolerances in the SC hardware implementation. In addition, the SC hardware implementation of the resulting A/D converter leads to a capacitance spread which is comparable to that of hitherto sigma-delta A/D converters.

3:30, SPTM-P2.8
BLIND ESTIMATION OF TIMING ERRORS IN INTERLEAVED AD CONVERTERS
J. ELBORNSSON, J. EKLUND
Parallel AD converter structures is one way to increase the sampling rate. Instead of increasing the sample rate in one AD converter, several AD converters with lower sampling rate can be used instead. A problem in these structures is that the time between samples is usually not equal because there are errors in the delays between the AD converters. We will here present a method to estimate the timing offset errors. The estimation algorithm works without any special calibration signal, instead the normal input signal is used. The only assumption that we need on the input signal is that most of the energy is concentrated to a low pass band, below about 1/3 of the Nyquist frequency. Simulations of the time interleaved AD converter show that the method estimates the errors with high accuracy.