The sampling theorem and linear prediction in signal analysis
type: Item
instance of: scholarly article
title: The sampling theorem and linear prediction in signal analysis
zbMATH Open document ID: 0633.94002
author: Paul L. Butzer
author: W. Splettstoesser
author: Rudolf L. Stens
published in: Jahresbericht der Deutschen Mathematiker-Vereinigung (DMV)
publication date: 1988-01-01T00:00:00Z
review text: In 1979, a standard for the digital storage and the reproduction of audio signals, known as the CD-ROM system, has been defined. The CD-ROM system which forms one of the most remarkable achievements of modern High Tech has become the world standard for achieving fidelity of sound reproduction that far surpasses any other available technique. A metallic disc 120 mm in diameter is used to store the digitized audio waveform. The waveform is sampled at 44.1 kilosamples/s to provide a recorded bandwidth of 20 kHz; each audio sample is uniformly quantized to one of \(2^{16}\) levels (16 bits/sample). Operating a CIRC encoder, the recording equipment stores on a single DM-ROM about \(10^{10}\) bits in the form of a sequence of minute pits that are optically scanned by a laser beam. The link between an analog waveform and its sampled version is provided by the sampling procedure. This procedure can be implemented in several ways, the most popular being the sample-and-hold operation. The output of the sampling process is called pulse amplitude modulation (PAM) because the successive output intervals can be described as a sequence of pulses with amplitudes derived from the input waveform samples. The analog waveform can be approximately retrieved from a PAM waveform by low-pass filtering. Now the basic question of D/A conversion reads: How closely can a filtered PAM waveform approximate the original input waveform? The question can be answered by reviewing the sampling theorem, which roughly states: A bandlimited signal having no spectral components above \(f_ m\) hertz can be determined uniquely by values sampled at uniform intervals of \(T_ s\) seconds, where \(T_ s\leq 1/(2f_ m).\) This particular statement is also known as the Whittaker-Shannon-Kotel'nikov uniform sampling theorem. Stated another way, the upper limit on \(T_ s\) can be expressed in terms of the sampling rate, denoted \(f_ s=1/T_ s\). The restriction \(f_ s\geq 2f_ m\) is known as the Nyquist criterion. It…
Mathematics Subject Classification ID: 94A05
Mathematics Subject Classification ID: 94A15
Mathematics Subject Classification ID: 94A12
Mathematics Subject Classification ID: 60G25
Mathematics Subject Classification ID: 62M20
Mathematics Subject Classification ID: 93E10
Mathematics Subject Classification ID: 41A45
Mathematics Subject Classification ID: 41A15
zbMATH DE Number: 4031560
zbMATH Keywords: audio signals
zbMATH Keywords: CD-ROM system
zbMATH Keywords: analog waveform
zbMATH Keywords: sampling procedure
zbMATH Keywords: sample-and-hold operation
zbMATH Keywords: pulse amplitude modulation
zbMATH Keywords: low-pass filtering
zbMATH Keywords: Whittaker-Shannon-Kotel'nikov uniform sampling theorem
zbMATH Keywords: linear prediction of signals
zbMATH Keywords: perfect low-pass filter sinc
zbMATH Keywords: error estimates
zbMATH Keywords: digital communication
zbMATH Keywords: truncation error
zbMATH Keywords: amplitude error
zbMATH Keywords: noise error
zbMATH Keywords: time-jitter error
zbMATH Keywords: optical signal processing
zbMATH Keywords: hologram
zbMATH Keywords: holographic transform
reviewed by: Walter Schempp
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4031560