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Signal Processing

Efficient target-response interpolation for a graphic equalizer

Profile image of Vesa VälimäkiVesa Välimäki

2016, 2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

https://doi.org/10.1109/ICASSP.2016.7471738
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Abstract

A graphic equalizer is an adjustable filter in which the command gain of each frequency band is practically independent of the gains of other bands. Designing a graphic equalizer with a high precision requires evaluating a target response that interpolates the magnitude response at several frequency points between the command gains. Good accuracy has been previously achieved by using polynomial interpolation methods such as cubic Hermite or spline interpolation. However, these methods require large computational resources, which is a limitation in real-time applications. This paper proposes an efficient way of computing the target response without sacrificing the approximation accuracy. This new approach called Linear Interpolation with Constant Segments (LICS) reduces the computing time of the target response by 55% and has an intrinsic parallel structure. Performance of the LICS method is assessed on an ARM Cortex-A7 core, which is commonly used in embedded systems.

Figures (7)
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
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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