Erratum: Digital-filter 2nd-order element with low quantising noise for poles and zeros at low frequencies

Colocated, output feedback is commonly used in the control of reverberant systems. More often than not, the system to be controlled displays high modal density at a moderate frequency, and thus the compliance of the out-of-bandwidth modes significantly influences the performance of the closed-loop system at low frequencies. In the assumed modes approach, the inclusion principle is used to demonstrate that the poles of the dynamic system converge from above when additional admissible functions are used to expand the solution. However, one can also interpret the convergence of the poles in terms of the zeros of the open-loop system. Since colocated inputs and outputs are known to have interlaced poles and zeros, the effect of a modification to the structural impedance locally serves to couple the modes of the system through feedback. The poles of the modified system follow loci defined by the relative location of the open-loop poles and zeros. Thus, as the number of admissible functions used in the series expansion is increased, the interlaced zeros of the colocated plant tend toward the open-loop poles, causing the closed-loop poles to converge from above as predicted by the inclusion principle. The analysis and results presented in this work indicate that the cumulative compliance of the out-of-bandwidth modes and not the modes themselves is required to converge the zeros of the open-loop system and the poles of the closed-loop system.

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Erratum: Relation between impulse response moments and locations of poles and zeros of digital filter

Electronics Letters ◽

10.1049/el:19910938 ◽

1991 ◽

Vol 27 (16) ◽

pp. 1496

Author(s):

A. Khare ◽

T. Yoshikawa

Keyword(s):

Impulse Response ◽

Digital Filter ◽

Poles And Zeros

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The S-SH Confusion Test and the Effects of Frequency Lowering

Journal of Speech Language and Hearing Research ◽

10.1044/2018_jslhr-h-18-0267 ◽

2019 ◽

Vol 62 (5) ◽

pp. 1486-1505

Author(s):

Joshua M. Alexander

Keyword(s):

Cognitive Processing ◽

Hearing Aids ◽

Response Times ◽

Nonlinear Frequency ◽

Low Frequencies ◽

Frequency Compression ◽

Negative Side ◽

Minimal Word ◽

Low Pass ◽

Negative Side Effects

PurposeFrequency lowering in hearing aids can cause listeners to perceive [s] as [ʃ]. The S-SH Confusion Test, which consists of 66 minimal word pairs spoken by 6 female talkers, was designed to help clinicians and researchers document these negative side effects. This study's purpose was to use this new test to evaluate the hypothesis that these confusions will increase to the extent that low frequencies are altered.MethodTwenty-one listeners with normal hearing were each tested on 7 conditions. Three were control conditions that were low-pass filtered at 3.3, 5.0, and 9.1 kHz. Four conditions were processed with nonlinear frequency compression (NFC): 2 had a 3.3-kHz maximum audible output frequency (MAOF), with a start frequency (SF) of 1.6 or 2.2 kHz; 2 had a 5.0-kHz MAOF, with an SF of 1.6 or 4.0 kHz. Listeners' responses were analyzed using concepts from signal detection theory. Response times were also collected as a measure of cognitive processing.ResultsOverall, [s] for [ʃ] confusions were minimal. As predicted, [ʃ] for [s] confusions increased for NFC conditions with a lower versus higher MAOF and with a lower versus higher SF. Response times for trials with correct [s] responses were shortest for the 9.1-kHz control and increased for the 5.0- and 3.3-kHz controls. NFC response times were also significantly longer as MAOF and SF decreased. The NFC condition with the highest MAOF and SF had statistically shorter response times than its control condition, indicating that, under some circumstances, NFC may ease cognitive processing.ConclusionsLarge differences in the S-SH Confusion Test across frequency-lowering conditions show that it can be used to document a major negative side effect associated with frequency lowering. Smaller but significant differences in response times for correct [s] trials indicate that NFC can help or hinder cognitive processing, depending on its settings.

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