This paper proposes to speed up the design of a third-order graphic equalizer by training a neural network to imitate its gain optimization. Instead of using the neural network to learn to design the graphic equalizer by optimizing its magnitude response, we present the network only with example command gains and the corresponding optimized gains, which are obtained with a previously proposed least-squares-based method. We presented this idea recently for the octave graphic equalizer with 10 band filters and extend it here to the third-octave case. Instead of a network with a single hidden layer, which we previously used, this task appears to require two hidden layers. This paper shows that good results can be reached with a neural network having 62 and 31 units in the first and the second hidden layer, respectively. After the training, the resulting network can quickly and accurately design a third-order graphic equalizer with a maximum error of 1.2 dB. The computing of the filter gains is over 350 times faster with the neural network than with the original optimization method. The method is easy to apply, and may thus lead to widespread use of accurate digital graphic equalizers.

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A virtual bass system creates an impression of bass perception in sound systems with weak low-frequency reproduction, which is typical of small loudspeakers. Virtual bass systems extend the bandwidth of the low-frequency audio content using either a nonlinear function or a phase vocoder, and add the processed signal to the reproduced sound. Hybrid systems separate transients and steady-state sounds, which are processed separately. It is still challenging to reach a good sound quality using a virtual bass system. This paper proposes a novel method, which separates the tonal, transient, and noisy parts of the audio signal in a fuzzy way, and then processes only the transients and tones. Those upper harmonics, which can be detected above the cutoff frequency, are boosted using timbre-matched weights, but missing upper harmonics are generated to assist the missing fundamental phenomenon. Listening test results show that the proposed algorithm outperforms selected previous methods in terms of perceived bass sound quality. The proposed method can enhance the bass sound perception of small loudspeakers, such as those used in laptop computers and mobile devices.

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