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Table 1. Command Frequencies f¢,m (Hz) of a Third-Octave Graphic Equalizer. 2. TARGET-RESPONSE INTERPOLATION

Table 1 Command Frequencies f¢,m (Hz) of a Third-Octave Graphic Equalizer. 2. TARGET-RESPONSE INTERPOLATION

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Fig. 1. (a) Target responses and (b) magnitude of the fre- quency responses obtained from command gains by using different interpolation methods: zeroth-order, linear, cubic Lagrange, and cu- bic Hermite interpolation.
Fig. 1. (a) Target responses and (b) magnitude of the fre- quency responses obtained from command gains by using different interpolation methods: zeroth-order, linear, cubic Lagrange, and cu- bic Hermite interpolation.
Table 3. Maximum Errors at Command Gain Points. Acceptable Errors Are Highlighted. points (f2, — f1,m) corresponds to the bands of a common third- octave graphic equalizer. However, this separation implies that there would exist overlapping bands (fom > fi,r form <r) and this would prevent proper interpolation between the command points.
Table 3. Maximum Errors at Command Gain Points. Acceptable Errors Are Highlighted. points (f2, — f1,m) corresponds to the bands of a common third- octave graphic equalizer. However, this separation implies that there would exist overlapping bands (fom > fi,r form <r) and this would prevent proper interpolation between the command points.
Fig. 2. In the LICS method, frequency points fi,m and f2,m limit the flat portion that surrounds the command gain value.
Fig. 2. In the LICS method, frequency points fi,m and f2,m limit the flat portion that surrounds the command gain value.
Table 2. Optimal and Fixed Values of a and the Resulting Error for the Three Test Cases.
Table 2. Optimal and Fixed Values of a and the Resulting Error for the Three Test Cases.
Fig. 3. Maximum error of the equalizer responses at the command points obtained by varying variable a in the three test cases. The maximum ripple in the magnitude frequency response betweer 300 Hz and 400 Hz is 0.7dB for both the cubic Hermite [in Fig 1(b)] and for the LICS method (in Fig. 4). Thus, the ripples car be seen to have been reduced between command points in compar. ison to linear interpolation, and the obtained magnitude frequency response connects the command gain values more accurately thar most methods in Fig. 1(b).
Fig. 3. Maximum error of the equalizer responses at the command points obtained by varying variable a in the three test cases. The maximum ripple in the magnitude frequency response betweer 300 Hz and 400 Hz is 0.7dB for both the cubic Hermite [in Fig 1(b)] and for the LICS method (in Fig. 4). Thus, the ripples car be seen to have been reduced between command points in compar. ison to linear interpolation, and the obtained magnitude frequency response connects the command gain values more accurately thar most methods in Fig. 1(b).
Fig. 4. Target response and magnitude of the frequency response obtained using the LICS method (a = 0.2), cf. Fig. 1(b). Table 4. Execution Time for the Hermite Cubic Interpolation and the LICS Method.
Fig. 4. Target response and magnitude of the frequency response obtained using the LICS method (a = 0.2), cf. Fig. 1(b). Table 4. Execution Time for the Hermite Cubic Interpolation and the LICS Method.
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