# THE AUDITORY MODELING TOOLBOX

Applies to version: 1.1.0

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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 ofthe impulse response of a 4th order gammatone filter with a centerfrequency 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 filterin 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.