Phase Response Of Filters Research Articles

Design of minimum-order allpass-based IIR multi-notch filters

The paper investigates the design methods for the minimum-order allpass-based infinite impulse response multi-notch filters. Monotonically decreasing nature of the stable allpass filter's phase response allows the formulation of the magnitude response specifications of the allpass-based multi-notch filter as the linear equality and inequality constraints in unknown allpass filter coefficients. As not all allpass filters satisfying mentioned constraints are of the same practical interest, several design methods minimizing various cost functions are proposed. One of these methods outperforms existing design methods in terms of stability margin, while utilization of other methods can result in higher area under the passbands squared magnitude response. Proposed methods are also compared with some of the existing infinite impulse response multi-notch filter design methods, whose lower complexity counterparts are derived by means of conclusions drawn and notations introduced while deriving the proposed design methods.

The least‐square design of minimum‐order allpass‐based infinite impulse response multi‐notch filters

SummaryThe paper investigates the least‐square design of minimum‐order infinite impulse response multi‐notch filters. Monotonically decreasing nature of the stable allpass filter's phase response, characterizing the allpass‐based multi‐notch filter, along with the simple relation between coefficients and the phase response of the allpass filter, allows the formulation of the multi‐notch filter's magnitude response specifications as the linear equality constraints regarding the positions of notch, left‐ and right‐hand cutoff frequencies. Since the number of such constraints equals triple the number of notch frequencies, while the number of unknown filter coefficients equals double the number of notch frequencies, variable elimination is first performed to ensure that specifications regarding the notch frequencies positions are strictly satisfied. The remaining overdetermined system of linear equations is then solved in the least‐square sense, leading to the approximate satisfaction of left‐ and right‐hand cutoff frequencies positions. Proposed design method is also compared with some of the existing infinite impulse response multi‐notch filter design methods.

Continuous Phase Estimation for Phase-Locked Neural Stimulation Using an Autoregressive Model for Signal Prediction.

Neural oscillations enable communication between brain regions. Closed-loop brain stimulation attempts to modify this activity by stimulation locked to the phase of concurrent neural oscillations. If successful, this may be a major step forward for clinical brain stimulation therapies. The challenge for effective phase-locked systems is accurately calculating the phase of a source oscillation in real time. The basic operations of filtering the source signal to a frequency band of interest and extracting its phase cannot be performed in real time without distortion. We present a method for continuously estimating phase that reduces this distortion by using an autoregressive model to predict the future of a filtered signal before passing it though the Hilbert transform. This method outperforms published approaches on real data and is available as a reusable open-source module. We also examine the challenge of compensating for the filter phase response and outline promising directions of future study.

The gammawarp filterbank: A frequency-warped implementation of the dynamic compressive gammachirp filter

This paper presents an alternative method for implementing a dynamic compressive gammachirp (dcGC) auditory filterbank. Instead of using a cascade of second-order sections, the new approach uses digital frequency warping to give the gammawarp filterbank. In the warped implementation, the unit delays in a conventional finite impulse-response (FIR) filter are replaced by first-order allpass filters. The set of warped FIR filter coefficients is constrained to be symmetrical, which results in a filter phase response that is identical for all filters in the filterbank. The dynamic variation in filter response is provided by interpolating the outputs of three linear filters adjusted for low-, medium-, and high-input signal levels. The gammawarp filterbank offers a substantial improvement in execution speed compared to previous dynamic gammachirp filter implementations. For a linear filterbank, the gammawarp execution time is comparable to that of a gammatone or linear second-order section gammachirp implementation for 32 bands, but there is a processing time advantage that increases as the number of bands is increased. For a dynamic compressive gammachirp filterbank, the gammawarp implementation is 27 to 47 times faster than the dcGC MATLAB code of Irino.

Effects of signal processing on the measurement of maximum sound pressure levels

Maximum sound pressure levels are commonly used for environmental noise and building acoustics measurements. This paper investigates the signal processing errors due to Fast or Slow time-weighting detectors when combined with octave band filters, one-third octave band filters or an A-weighting filter. For 6th order Butterworth CPB filters the inherent time delay caused by the phase response of filters is quantified using three different approaches to establish the following rules-of-thumb: (1) time-to-gradient/amplitude matching occurs when Bt≈1, (2) time-to-peak matching occurs when Bt≈2 and (3) time-to-settle matching occurs when Bt≈4 for octave band filters, and when Bt≈3 for one-third octave band filters. Four different commercially-available sound level meters are used to quantify the variation in measured maximum levels using tone bursts, half-sine pulses, ramped noise and recorded transients. Tone bursts indicate that Slow time-weighting is inappropriate for maximum level measurements due to the large bias error. The results also show that there is more variation between sound level meters when considering Fast time-weighted maximum levels in octave bands or one-third octave bands than with A-weighted levels. To reduce the variation between measurements with different sound level meters, it is proposed that limits could be prescribed on the phase response for CPB filters and A-weighting filters.

Estimates of auditory filter phase response at and below characteristic frequency (L)

Animal studies in basal cochlear regions have shown that basilar-membrane phase curvature (or rate of change of group delay with frequency) is negative around characteristic frequency (CF), but near zero well below CF. This study examined whether psychophysical masking experiments in humans show the same difference between on- and off-CF phase curvature. Masked thresholds were measured for a 2-kHz signal in the presence of harmonic tone complex maskers with a fundamental frequency of 100 Hz, band-limited between 200 and 1400 Hz (off-frequency masker) or between 1400 and 2600 Hz (on-frequency masker). The results from four normal-hearing listeners are consistent with predictions from animal physiological data: negative phase curvature is found for the on-frequency masker, whereas the phase curvature for the off-frequency masker is near zero. The method and results provide a strong test for the temporal response of computational models of human cochlear filtering.

Design protocols for time-dependent finite impulse response digital filters based on regression analysis of Fourier transform infrared interferograms

A protocol for the design of time-dependent finite impulse response (FIR) digital filters is described for use in extraction of frequency information from Fourier transform infrared (FT-IR) interferogram data. Building upon previous work that devised a multiple linear regression (MLR) approach to the filter design, the current work develops a design protocol that produces filters with narrow frequency responses, high attenuation, and better performance than conventional FIR filters with a similar number of coefficients. The five variables that influence the frequency response characteristics of filters designed with this method are: (1) entrance criterion that determines the number of significant filter coefficients in the stepwise MLR analysis, (2) the offset values that represent which interferogram points before and after the point that is to be filtered are included in the convolution sum, (3) the target width of the filter passband, (4) the filter position, and (5) the number of interferograms used in the regression. A full factorial experimental design is used to study the main and interaction effects of these factors and their contribution to determining the frequency response function of the computed filter. It is found that an interaction exists between the offset range and the target width of the passband, necessitating a joint study of these parameters. However, the entrance criterion, the number of interferograms, and the filter position can be studied independently. The effect of each of these variables on the performance of the computed filters is explored in detail. The results of this study provide a set of guidelines for choosing values of the five variables that allow the desired tradeoffs to be achieved between the number of filter coefficients, passband width, stopband attenuation, and filter phase response.

Phase effects in masking in normal-hearing and hearing-impaired listeners

Changes in the phase relationships between components in a harmonic tone complex masker can lead to large changes in masked threshold for long-duration sinusoids in normal-hearing listeners. The effect is reduced or absent in hearing-impaired listeners. This reduction could be due to a loss of peripheral compression, a change in the auditory filters’ phase response, or both. Signal thresholds were measured as a function of masker phase curvature, signal frequency, and masker fundamental frequency (F0). In contrast to previous studies, more than just two phase relationships were considered, allowing us to compare the overall phase response of impaired and normal ears. Peripheral compression was estimated in a separate experiment using a notched-noise masking technique. If changes in filter phase response can account for the differences between normal-hearing and hearing-impaired listeners, then certain phase relationships should produce large threshold differences even in hearing-impaired listeners. If peripheral compression is important, threshold differences in hearing-impaired listeners should emerge at very low F0s, due to the predicted interaction between peripheral compression and temporal processing at higher stages. Preliminary results suggest that the difference between normal-hearing and hearing-impaired listeners can be explained primarily in terms of peripheral compression. [Work supported by DFG and NIDCD.]