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The content presented in this chapter includes relevant topics in digital signal processing such as the mathematical foundations of signal processing (viz., convolution, sampling theory, etc.), basics of linear and time-invariant (LTI) systems, minimumphase and all-pass systems, sampling and reconstruction of signals, discrete time Fourier transform (DTFT), discrete Fourier transform (DFT), -transform, bilinear transform, and linear-phase finite impulse response (FIR) filters.

In this chapter we present a summary of various approaches for finite impulse response (FIR) and infinite duration impulse response (IIR) filter designs.

This chapter introduces the theory behind sound propagation in enclosed environments, room acoustics, reverberation time, and the decibel scale. Also included are basics of loudspeakers and microphone acoustics and responses, room impulse responses, and stimuli for measuring loudspeaker and room responses. We conclude the chapter with a brief discussion on the structure of the ear, and some relevant concepts such as loudness perception and frequency selectivity.

Multichannel sound systems such as those used in movie or music reproduction in 5.1 channel surround sound systems or new formats such as 10.2 channel immersive audio require many more tracks for content production than the number of audio channels used in reproduction. This has been true since the early days of monophonic and two-channel stereo recordings that used multiple microphone signals to create the final one- or two-channel mixes.

This chapter is concerned with the equalization of acoustical responses, simultaneously, at multiple locations in a room. The importance of equalization is well known, in that it allows (i) delivery of high-quality audio delivered to listeners in a room, and (ii) improved rendering of spatial audio effects for a sense of audio immersion. Typical applications include home theater, movie theaters, automobiles, and any loudspeaker based playback environment (headphones, cell phones, etc.). Because experiencing movies and music is now primarily a group experience (such as in home theaters, automobiles, and movie theaters), and headphone/earbud acoustics vary due to ear coupling effects, it is important to include acoustic variations in the design of an equalization filter. Thus, an equalization filter designed to compensate for the room effects (viz., multipath reflections) at a single location performs poorly at other locations in a room. This is because room impulse responses vary significantly with differing source receiver (viz., listener) positions. Agood equalization filter should compensate the effects of multipath reflections simultaneously over multiple locations in a room. This chapter briefly introduces some traditional room equalization techniques, and presents in detail a new multiple listener (or multiple position) equalization filter using pattern recognition techniques. Because the filter lengths can be large, a popular psychoacoustic scheme described in this chapter allows design of low filter orders, using the pattern recognition technique, for real-time implementation. Additionally, a room response and equalization visualization technique, the Sammon map, is presented to interpret the results. Furthermore, one of the major factors that affects equalization performance is the reverberation of the room. In this chapter, the equalization performance of the pattern recognition method [60] is compared with the well-known root mean square averaging-based equalization, using the image method [61] for synthesizing responses with varying reverberation times .

Given a multichannel loudspeaker system, the selection of the crossover frequency between the subwoofer and the satellite speakers is important for accurate (i.e., distortion-free), reproduction of playback sound. Presently, many home theater systems have selectable crossover frequencies, which are part of the bass management filter capabilities, which are set by the consumer through listening tests. Alternatively, if the loudspeakers are industry certified, the crossover frequency is set at 80 Hz. Adesirable feature is that, besides distortion-free sound output from the individual subwoofer and the satellite speakers, the combined subwoofer and satellite room acoustical response should exhibit negligible variations around the selected crossover frequency. In this chapter, we present an automatic crossover frequency selection algorithm based on an objective measure (viz., the spectral deviation measure) for multichannel home theater applications that allows better control of the combined subwoofer and satellite response, thereby significantly improving audio quality. Initially, some results are presented that show the effect of crossover frequency on low frequency performance. Additional parameter optimization of the bass management filters is shown to yield improved performance. Comparison between the results from crossover and all-parameter optimization, of the bass management filters, for multiposition equalization is presented. As also shown, cascading an all-pass filter, or adding in time-delays in loudspeaker channels, can provide further improvements to the equalization result in the crossover region. Alternative techniques for fixing the crossover blend, using a cascade of all-pass filters, are also presented.

Traditionally, multiple listener room equalization is performed to improve sound quality at all listeners, during audio playback, in a multiple listener environment (e.g., movie theaters, automobiles, etc.). Atypical way of doing multiple listener equalization is through spatial averaging, where the room responses are averaged spatially between positions and an inverse equalization filter is found from the spatially averaged result. However, the equalization performance will be affected if there is a mismatch between the position of the microphones (which are used for measuring the room responses for designing the equalization filter) and the actual center of listener head position (during playback). In this chapter, we present results of the effects of microphone and listener mismatch on spatial average equalization performance for frequencies above the Schroeder frequency. The results indicate that, for the analyzed rectangular listener configuration, the region of effective equalization depends on (i) distance of a listener from the source, (ii) amount of mismatch between the responses, and (iii) the frequency of the audio signal. We also present some convergence analysis to interpret the results.

In a multiple listener environment, equalization may be performed through magnitude response spatial averaging at expected listener positions. However, the performance of averaging-based equalization, at the listeners, will be affected when there is a mismatch between microphone and listener positions. In this chapter, we present a modal analysis approach, targeted at low frequencies, to map mismatch to an equalization performance metric. Specifically, a closed-form expression is provided that predicts the equalization performance in the presence of mismatch. The results, which are particularly valid at lower frequencies where standing wave modes of the room are dominant, indicate that magnitude average equalization performance depends on (i) the amount of displacement/mismatch, and (ii) the frequency component in the modal response. We have provided validation of the theoretical results, thereby indicating the usefulness of the proposed analytic approach for measuring equalization performance due to mismatch effects. We also demonstrate the importance of average equalization over single listener equalization when considering mismatch/ displacement effects.

Selectively canceling signals at specific locations within an acoustical environment with multiple listeners is of significant importance for home theater, automobile, teleconferencing, office, industrial, and other applications. The traditional noise cancellation approach is impractical for such applications because it requires secondary sources to “anti-phase” the primary source, or sensors to be placed on the listeners. In this chapter we present an alternative method for signal cancellation by preprocessing the acoustical signal with a filter known as the eigenfilter [103, 104]. We examine the theoretical properties of such filters, and investigate the performance (gain) and tradeoff issues such as spectral distortion. Sensitivity of the performance as a function of the room impulse response duration (reverberation) modeled in the eigenfilter is also investigated.