Digital filter design with state space method for 1-bit signal processing based on delta-sigma modulation

2011 ◽  
Vol 175 (4) ◽  
pp. 48-56
Author(s):  
Yuji Ito ◽  
Shinji Doki ◽  
Sigeru Okuma
Keyword(s):  
Signal Processing ◽  
State Space ◽  
Digital Filter ◽  
Filter Design ◽  
State Space Method ◽  
Digital Filter Design ◽  
Delta Sigma ◽  
Delta Sigma Modulation ◽  
Space Method

ON THE POSITIVENESS OF A FUNCTIONAL SYMMETRIC MATRIX USED IN DIGITAL FILTER DESIGN

2004 ◽  
Vol 13 (05) ◽  
pp. 1105-1110 ◽  
Author(s):  
YAN WU
Keyword(s):  
Signal Processing ◽  
Generating Function ◽  
Digital Filter ◽  
Simple Proof ◽  
Filter Design ◽  
Symmetric Matrix ◽  
Toeplitz Matrices ◽  
Positive Definite ◽  
Real Numbers ◽  
Digital Filter Design

This paper gives a simple proof for the positiveness of two important symmetric Toeplitz matrices used in communication and signal processing. It utilizes the shifting property of a so-called Uniformly Band-Restricted (UBR) function, which is the generating function for a generic functional symmetric matrix. It is shown that the functional symmetric matrix is positive definite if the UBR function is evaluated at a sequence of distinct real numbers.

New Methodology for Smoothing Freeway Loop Detector Data: Introduction to Digital Filtering

1996 ◽  
Vol 1554 (1) ◽  
pp. 142-152 ◽  
Author(s):  
Benjamin A. Coifman
Keyword(s):  
Signal Processing ◽  
Digital Signal Processing ◽  
Digital Filter ◽  
Filter Design ◽  
Digital Signal ◽  
Data Set ◽  
Digital Filter Design ◽  
Loop Detector ◽  
Smoothing Process ◽  
Time Averages

A new methodology has been developed for smoothing loop detector data based on digital signal processing. After introducing basic signal processing theory, existing smoothing techniques like fixed-time averages, cumulative sums, and moving-time averages—all subsets of the larger digital signal processing methodology—are described. Nontraditional smoothing techniques based on custom digital filter design are then presented, specifically, low-pass filters that “pass” slowly changing features of the detector data unchanged while attenuating rapidly changing features. Custom digital filter design gives more control over the smoothing process than do traditional smoothing methods. In particular, the amount of amplification or attenuation at a given frequency (e.g., rapidly or slowly changing features) can be set. Whether a custom filter or a traditional smoothing process is used, an understanding of the frequency response can increase the usefulness of the resulting data by clarifying the limitations of the given smoothing process. To illustrate this, several smoothing processes are presented and contrasted using the same data set. The use of a custom digital filter is demonstrated in three practical applications: an examination of the bivariate flow-occupancy relationship and use of the filtering process to eliminate unstable disturbances from the data set, speed estimation from a single detector under congested conditions, and temporal issues relating to shock wave and fluctuation propagation specifically.

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