Improvement of recursive single sideband amplitude modulation through modeling

The effect of the nonlinear nature of air on sound propagation was extensively studied in the 20th century. Air demodulation, later called intermodulation, causes high amplitude sound waves to generate new frequencies as they propagate through the air. The new frequencies are equal to multiples, sums and differences of the frequencies originally transmitted into the air. In many fields this phenomenon is seen as a source of distortion and noise, but in others it can be a useful tool. Ultrasonic loudspeaker systems are one such field that uses air demodulation as a tool. Audible sound signals cannot be easily transmitted directionally due to their high wavelengths. In order to achieve directional sound transmission, the wavelength of the generated sound must be smaller than the surface area of the sound source. The fact that the audible sound range includes wavelengths as long as 17 meters makes it almost impossible for conventional loudspeakers to produce directional sound. As a result, today's loudspeaker systems produce sound waves that disperse in all directions. Ultrasonic loudspeaker systems take advantage of the low wavelengths of ultrasound waves, which are above the frequency range perceptible to the human ear, to create sound beams that can be concentrated in only one direction. Ultrasonic signals can be transmitted with high directivity due to their small wavelengths and can be converted into audible signals through demodulation in air. In this process, the frequencies resulting from air demodulation are used. As mentioned, the transmission of multiple high amplitude sound waves results in new frequencies equal to multiples, sums and differences of the transmitted waves. Considering that the frequencies used are ultrasonic, it is necessary to utilize the difference frequencies to obtain audible sound waves. Therefore, to obtain an audible frequency, it is necessary to use two ultrasonic waves whose difference is equal to the desired frequency. The ultrasonic signals required for the transmission of single frequencies can be easily calculated. However, the transmission of broadband complex signals through ultrasonic loudspeaker systems is not possible by means of a simple subtraction process. At this point, modulation methods are utilized. Modulation is the modification of one signal depending on another signal. For ultrasonic sound transmission, the most useful of the basic modulation methods is amplitude modulation. This is because the sidebands resulting from amplitude modulation are the sum and difference of the frequencies of the modulated waves. On the other hand, if desired, the wave used as a carrier in modulation can be transmitted audibly with sidebands without suppression. Therefore, for a complex audio signal to become audible through ultrasonic transmission, it is sufficient to subject it to amplitude modulation by modulating a carrier ultrasonic frequency. Many studies have been carried out to improve ultrasonic loudspeaker systems that naturally operate with lower efficiency than conventional loudspeaker systems due to their transmission systems. Modulation techniques prior to ultrasonic transmission have been an important area of focus in these studies. Basic amplitude modulation is not sufficient to transmit an audible sound signal with sufficient strength and audibility. This is because the use of high modulation depth in basic amplitude modulation method results in high noise and distortion, while the use of low modulation depth results in low audible signal level. Much work has been done to overcome the inefficiency of basic amplitude modulation. One of the most important of these is square root amplitude modulation (SRAM). In square root amplitude modulation, the square root of the modulator frequency is used, based on a mathematical model of the distortion in the air. The performed square root operation produces an infinite number of sidebands. The generated sidebands neutralize the distortion that would occur if they are produced together with the main audio. However, this method has several fundamental problems. First of all, the infinite number of sidebands greatly increases the bandwidth that the ultrasonic loudspeaker must be able to transmit. This is because the noise reduction is proportional to the number of sidebands that can be transmitted by the ultrasonic speaker. However, most of the transducers used in ultrasonic transmission cannot provide the required bandwidth. Therefore, very special transducers or complex transducer systems are needed to use this system. On the other hand, the infinite number of sidebands that occur uses a significant portion of the power sent to the system. Therefore, the signal region sent for noise reduction reduces the power of the main signal region, causing inefficiency. Another problem is that some of the resulting sidebands are within the frequency range audible to the human ear. This creates a new source of audible noise. In order to reduce the inefficiency caused by square root amplitude modulation, single sideband amplitude modulation (SSBAM) was tested. In single sideband amplitude modulation, one of the sum and difference sidebands of the fundamental amplitude modulation is mathematically eliminated or filtered out. The eliminated sideband will both prevent unnecessary power consumption in the signal sent to the system and reduce the demodulation distortion in the air. As a result of the experiments, it was discovered that single sideband amplitude modulation produces an output similar to square root amplitude modulation with higher efficiency and less requirements. One of the newest and most efficient modulation methods is recursive single sideband amplitude modulation (RSSBAM). The RSSBAM method is based on a mathematical model that calculates the distortion that will occur in the air during the modulation process and adds it to the main sound in negative phase. Accordingly, the main audio is first modulated by means of SSBAM. It is then processed by a Non-Linear Demodulator (NLD), which calculates the airborne distortion. This process is a mathematical model that predicts the response of the air. The signal from the NLD forms the first-order output. Subtracting the desired fundamental sound from the first-order output yields the first-order distortion expression. The first-order RSSBAM is completed by subtracting the resulting distortion expression from the initial audio signal. The recursive nature of the system allows the process to be repeated in any number of orders. An alternative to the mathematical model used in the NLD in the RSSBAM system is the use of techniques available in the field of system modeling. System modeling techniques allow the system to be represented by a filter by calculating the responses of complex systems to basic inputs. In this respect, we start from impulses, which are the simplest element of complex signals in the time domain. By measuring and calculating the response of the system to an impulse, a model of the system can be obtained. This modeling is close to the black box modeling method. Because, although the reason for the system's response to an impulse is unknown, the output to be obtained as a result can be modeled. System modeling methods utilizing impulse response are typically used for linear time invariant systems. This is because modeling both nonlinear and time-varying systems requires different techniques. However, although they are not suitable for use in nonlinear systems, it is possible that impulse response based models can give better results than the mathematical model used in the RSSBAM method. This study was carried out with the hypothesis that in the RSSBAM method, estimating the airborne distortion with a model obtained through measurement instead of a mathematical model can constitute an efficient modulation method. The idea behind the study is that predicting the complex interactions in the air with physical measurements instead of mathematical expressions can provide a more accurate distortion reduction. Accordingly, the effect of air on the ultrasonic sound transmitted by single sideband amplitude modulation was measured, an FIR filter was generated from the measurement output, and a novel modulation system (CRSSBAM) was designed to perform distortion estimation using this filter. Although the designed modulation system is similar to RSSBAM in terms of noise reduction steps, it differs in the distortion estimation stage. The present study aims to improve the usability of ultrasonic loudspeaker systems in music transmission. Therefore, for the comparison of CRSSBAM and RSSBAM methods, it was decided to use both the ultrasonic modulation measurement methods available in the literature and the measurement methods frequently used in the field of music technology. Accordingly, the frequency response, total harmonic distortion, intermodulation distortion and signal to noise ratio of the generated and measured modulation outputs were measured and compared. As a result of the comparisons, satisfactory results were obtained and it was revealed that FIR filters can make a significant contribution to the modulation methods used in ultrasonic sound generation. Based on this study, it is believed that further studies can be developed to create even more efficient FIR filters by means of more complex measurement methods used in modeling nonlinear systems.