THE AUDITORY MODELING TOOLBOX
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DEMO_HOHMANN2002 - Shows how to use the gammatone filterbank from Hohmann(2002)
Description
Part I: This example creates a 4th order gammatone filter with a center frequency of 1000Hz and a 3dB-bandwidth of 100Hz, suitable for input signals with a sampling frequency of 10kHz.
Part II: This example program demonstrates how to create and use the gammatone filterbank within the framework of Hohmann (2002).
Part III: This Example demonstrates how to create and how to use the combined analysis-synthesis Filterbank system.
Impulse response of the example gammatone filter
The frequency response function of this filter in dB over frequency in Hz
Figure 3 shows the frequency response of the individual filters
Figure 4 shows the impulse response of the analysis-synthesis system in the time domain
Figure 5 shows shows its frequency response
This code produces the following output:
The filter coefficient of this filter is: 0.97376 + 0.13968 Its normalization factor is : 1.4028e-07 Figure 1 shows the first 800 samples ofthe impulse response of a 4th order gammatone filter with a centerfrequency of Hz and a 3dB-bandwidth of dHz.Real part, imaginary part, and absolute value of the impulse response are plotted as lines 1, 2, and 3, respectively. Figure 2 shows the frequency response function of this filterin dB over frequency in Hz.Building a filterbank for 16276Hz sampling frequency. Lower cutoff frequency: 70Hz Upper cutoff frequency: 6700Hz Base frequency : 1000Hz filters per ERB : 1 filterbank contains 30 filters: # | f / Hz | normalization | coefficient 1| 73.223641 | 5.265982e-08 | 0.986867 + 0.027903i 2| 107.651956 | 8.085647e-08 | 0.984969 + 0.040957i 3| 146.004401 | 1.241101e-07 | 0.982654 + 0.055445i 4| 188.728245 | 1.904318e-07 | 0.979828 + 0.071514i 5| 236.321739 | 2.920749e-07 | 0.976374 + 0.089322i 6| 289.339925 | 4.477658e-07 | 0.972152 + 0.109040i 7| 348.401107 | 6.860992e-07 | 0.966986 + 0.130846i 8| 414.194064 | 1.050696e-06 | 0.960665 + 0.154929i 9| 487.486082 | 1.608029e-06 | 0.952929 + 0.181478i 10| 569.131901 | 2.459271e-06 | 0.943462 + 0.210687i 11| 660.083684 | 3.758199e-06 | 0.931880 + 0.242737i 12| 761.402124 | 5.738207e-06 | 0.917721 + 0.277794i 13| 874.268807 | 8.752923e-06 | 0.900427 + 0.315986i 14| 1000.000000 | 1.333716e-05 | 0.879330 + 0.357389i 15| 1140.061995 | 2.029808e-05 | 0.853641 + 0.401992i 16| 1296.088211 | 3.085102e-05 | 0.822431 + 0.449661i 17| 1469.898248 | 4.682124e-05 | 0.784622 + 0.500088i 18| 1663.519097 | 7.094204e-05 | 0.738989 + 0.552724i 19| 1879.208790 | 1.072934e-04 | 0.684168 + 0.606690i 20| 2119.482727 | 1.619433e-04 | 0.618693 + 0.660680i 21| 2387.143012 | 2.438807e-04 | 0.541066 + 0.712827i 22| 2685.311132 | 3.663608e-04 | 0.449888 + 0.760566i 23| 3017.464361 | 5.488321e-04 | 0.344054 + 0.800486i 24| 3387.476311 | 8.196695e-04 | 0.223067 + 0.828203i 25| 3799.662107 | 1.220009e-03 | 0.087477 + 0.838291i 26| 4258.828711 | 1.809067e-03 | -0.060519 + 0.824359i 27| 4770.330980 | 2.671403e-03 | -0.216318 + 0.779363i 28| 5340.134118 | 3.926697e-03 | -0.372053 + 0.696340i 29| 5974.883239 | 5.742619e-03 | -0.515783 + 0.569724i 30| 6681.980865 | 8.351410e-03 | -0.631053 + 0.397471i Figure 3 shows the frequency response of the individual filters. Building analysis filterbank Building synthesizer for an analysis-synthesis delay of 0.004 seconds The synthesizers parameters:---------------------------- # | delay | phase factor | gain / dB 1| 0 | 0.547900 + -0.836544i | 0.30 44 2| 0 | -0.477398 + -0.878687i | 1.56 44 3| 0 | -0.998794 + 0.049092i | 1.57 44 4| 0 | -0.325669 + 0.945484i | 1.15 44 5| 0 | 0.813638 + 0.581371i | 0.52 44 6| 0 | 0.713266 + -0.700893i | -0.21 44 7| 0 | -0.673924 + -0.738801i | -0.98 44 8| 0 | -0.652150 + 0.758090i | -1.74 44 9| 0 | 0.917335 + 0.398116i | -2.41 44 10| 0 | -0.094831 + -0.995493i | -2.93 44 11| 0 | -0.676236 + 0.736685i | -3.36 44 12| 0 | 0.969679 + -0.244383i | -3.60 44 13| 3 | -0.483470 + -0.875361i | -3.69 44 14| 9 | -0.931640 + -0.363382i | -3.64 44 15| 15 | -0.999885 + 0.015137i | -3.55 44 16| 21 | -0.999737 + 0.022920i | -3.67 44 17| 25 | -0.760047 + 0.649868i | -3.52 44 18| 30 | -0.885042 + 0.465511i | -3.69 44 19| 33 | -0.339377 + 0.940650i | -3.55 44 20| 37 | -0.607274 + 0.794492i | -3.70 44 21| 40 | -0.500187 + 0.865917i | -3.51 44 22| 43 | -0.686624 + 0.727012i | -3.60 44 23| 45 | -0.261163 + 0.965295i | -3.55 44 24| 47 | -0.022489 + 0.999747i | -3.69 44 25| 49 | -0.092279 + 0.995733i | -3.66 44 26| 51 | -0.518434 + 0.855117i | -3.47 44 27| 53 | -0.994152 + 0.107991i | -3.69 44 28| 54 | -0.775582 + 0.631247i | -3.63 44 29| 56 | -0.342105 + -0.939662i | -4.36 44 30| 57 | -0.229183 + -0.973383i | -1.22 44 Figure 4 shows the impulse response of the analysis-synthesis system in the time domain. Figure 5 shows its frequency response.
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