Application Cases

Experiment Name: Research on Orthogonal Compensation for Parametric Array Loudspeakers Based on Power Series

Research Direction:
This paper proposes a distortion compensation method based on orthogonal amplitude modulation, where the compensation component and the original audio signal are modulated onto mutually orthogonal carrier waves. The compensation component is expressed in a power series form, and the distortion compensation effect is improved by adjusting the coefficients of the power series. Additionally, a one-dimensional Volterra filter model is established to characterize the distortion behavior of the parametric array loudspeaker system. This model is utilized to offline adjust the compensation coefficients of the compensation component, achieving effective distortion compensation with relatively low computational complexity.

Experimental Content:
The Berktay far-field solution serves as the foundation for most signal processing algorithms in parametric array loudspeakers, providing a certain level of characterization for their distortion. However, due to approximations and assumptions during its derivation, it is only applicable to calculating the axial sound pressure in the far field and cannot accurately account for non-far-field conditions or distortions beyond the second order. To more precisely represent the distortion of the parametric array loudspeaker system, the Orthogonal Diagonalized Volterra Filter (ODVF) can be used as a nonlinear model for system identification. The ODVF filter is a simplified version of the Volterra filter model. Dr. Mu Yongsheng and colleagues have demonstrated that the ODVF model can effectively simulate the distortion of parametric array loudspeaker systems. Compared to the Volterra filter model, the ODVF model offers significant advantages in terms of parameter identification time and computational complexity. Therefore, the Berktay far-field solution and the ODVF-based model are analyzed, and the model outputs are compared with experimental results to validate the model's feasibility.

Testing System:
Considering practical applications, the experiment was conducted in a standard room measuring 8m × 7m × 3.5m, as shown in the experimental setup below. First, the test signal is generated and modulated using an NI PXI-5412 arbitrary waveform generator. The modulated signal is amplified by an ATA-4052 high-speed amplifier and then transmitted to the ultrasonic transducer array. The ATA-4052 high-voltage power amplifier operates within a frequency band of 0–500 kHz. The ultrasonic transducer has a center frequency of 45 kHz and consists of 128 piezoelectric transducers, arranged as shown below. The ultrasonic waves emitted by the transducer array undergo self-demodulation in the air to produce audible sound, which is captured by a GRAS-40PH microphone placed along the axis of the parametric array loudspeaker, positioned 1.5m from the transducer surface. The signal collected by the microphone is amplified by a B&K NEXUS-2692 conditioning amplifier and finally acquired and stored by a PXI5015 oscilloscope. To mitigate pseudo-noise caused by ultrasound at 1.5m, an acoustic filter is placed in front of the microphone.

Experimental Results:

1. The distortion compensation effect of the compensation algorithm was experimentally validated. Input signals with frequencies f1 = 1500 Hz and f2 = 2200 Hz were used. The power series compensation algorithm and the MAM1 method were employed to modulate the input signals, with a modulation index of 0.7 and a carrier frequency of 45 kHz. All other settings were as described in Section 1.3. The compensation coefficients for the power series compensation algorithm were obtained offline using the ODVF-based model described in Section 1.2. The self-demodulation results up to the third order are shown below.

2.The Modified Amplitude Modulation (MAM) method is a category of orthogonal amplitude modulation preprocessing techniques based on the Berktay far-field solution. The modulation process is illustrated below.

Recommended Power Amplifier: ATA-4052C

ATA-4052C High-Voltage Power Amplifier Parameters and Specifications: