Analysis and design of gammatone signal models
In the upper row the waveforms of two gammatone filters are plotted. The lower row shows the magnitude frequency response of gammatone filters that are equally distributed along the ERB scale from .
Discrete signal processing system used to analyze the overcomplete gammatone signal models.
The frame-bound ratios of non-decimated gammatone signal models with the number of filters analyzed over the frequency intervals and . For the frequency interval of , the frame-bound ratio converges toward a tight frame for higher filter numbers.
Best possible frame-bound ratios for a fixed bandwidth factor and filter number (upper plot) or filter order and filter number (lower plot). The gammatone signal model parameters were , , and analyzed over the frequency interval from .
The frame-bound ratios of decimated gammatone signal models with the number of filters and decimation factors analyzed over the frequency interval of .
(a) Bifrequency map for a gammatone signal model with the number of filters and the decimation factor of in every subband. The axes show the normalized frequency domains associated with the input and output signals. The center line represents the time-invariant part that maps the input to the output signal and is independent of any decimation. All other lines are due to aliasing terms introduced by a decimation of the subband coefficients. The zoom-in (b) shows that in this example in-band aliasing occurs in the last three filters, in which aliasing components fall into the passband of these filters. The filter’s passbands are indicated by a grid of thin white lines.
The SAR achieved by optimized decimation factors for a given degree of overcompleteness and different bandwidth factors of gammatone filters.
Signal reconstruction experiment using non-decimated overcomplete gammatone signal models for the svega.wav test signal. The upper plot shows the results for a signal model without subband processing (GTFB) and the lower plot shows the achieved SNR for a sparse gammatone signal model based on the MP algorithm.
Perceptual reconstruction quality for svega.wav encoded without quantization with a linear quantization and a linear quantization including a PAM.
Signal reconstruction experiment using decimated overcomplete gammatone signal models being optimized to maximize the SAR of the test signal (svega.wav), as described in Sec. IV B, compared to commonly chosen decimation factors that are inverse-proportional to the bandwidth of the filters while fulfilling Condition I.
The eigenvalues of an overcomplete gammatone signal model with filters being equally spaced on the ERB scale compared to an optimized frequency scale with frequency shifts applied to the ERB scale as shown in the lower row.
Frame-bound ratios analyzed for different bandlimited signals and number of gammatone filters .
The SAR for svega.wav and a gammatone signal model with filters achieved with optimized decimation factors compared to commonly chosen decimation factors that are inverse-proportional to the bandwidth of the filters while fulfilling Condition I.
Examples for gammatone signal model parameters found in the literature. The frame-bound analysis was performed on a limited frequency interval to exclude distortion effects from the first and last filters.
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