Real-Time Monophonic to Stereophonic Sound Synthesis

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1 Real-Time Monophonic to Stereophonic Sound Synthesis ENG 4000 Final Report Group 3 Faculty of Science and Engineering, York University April 30, 2007 Team Members: Danoush Dastgiri danoush@yorku.ca Jasmine Kaur jas3000@yorku.ca Ivan Ho ivanho@yorku.ca Usman Mahmood lavoizer@yorku.ca Superviser: Professor Amir Asif Course Director: Professor Eshrat Arjomandi

2 ACKNOWLEDGEMENTS First and foremost, we owe our sincere and heartfelt thanks to our adviser, Professor Amir Asif, for his continuous and unwavering support in this project. He has fostered immense learning and intellectual growth by demonstrating exceptional care, attention, enthusiasm, and encouragement to us all. We would like to extend our gratitude to Professor Eshrat Arjomandi, whose invaluable knowledge and guidance has directed and motivated us to bring this project to its full potential. Our sincere thanks to Professor Mokhtar Aboelaze, who always welcomed any queries and clarifications we needed during the course of the project. We are unduly grateful to Ms. Ulya Yigit and Mr. Paul Griffith, without whose assistance and support this project would not have been possible. Our many thanks go to Mr. Jason Keltz, Ms. Oana Ionita, and Mr. Harvey Emberley for their help in resolving the group s technical issues. ii

3 ABSTRACT A real-time monophonic to stereophonic sound synthesizer is designed and implemented in hardware using the TI TMS 320C6713 processor. Three major phases underlie the project: first, the conversion of a monophonic sound source to stereophonic sound; second, the enrichment of the two-channel sound using stereo enhancement techniques; and third, interfacing the MATLAB code with the TI TMS C6713 processor via Simulink. Several algorithms for monophonic to stereophonic sound conversion were tested and a selective frequency based approach that demonstrated the best performance was selected. The frequency selective approach used in the project divides the audible frequency range into several bands. The lower frequencies, representing vocal and bass components of sound, are extracted and form the DC band. The DC band and the even numbered bands are then combined and form the output of the left channel. Likewise, the DC band and the odd numbered frequency bands are combined and form the output of the right channel. To ensure that an optimal filter is used, the filtering qualities of the Butterworth, Chebyshev I, Chebyshev II, and Elliptic filters are analyzed using tools available in MATLAB, such as the FDA tool. The Butterworth filter was selected, mainly owing to its nearly constant magnitude response and nearly linear phase response in its passband. To further enhance the quality of the stereophonic sound, stereo enhancement techniques are also applied. To create the ambience of a recording hall, a reverberation effect is applied using time delay and the attenuation of certain frequency bands present within the left and right stereo channels. A quality Butterworth filter is again used to effectively filter the desired frequencies present in each channel. The third phase of the project involves porting the MATLAB source code to Simulink and interfacing this with the TI TMS C6713 hardware. This phase allows the real-time synthesis of stereophonic sound, which implies the immediate synthesis of stereophonic sound as a continuous stream of monophonic input is received. The project proposes an innovative addition to conventional stereo systems, by using the performance capability of the TMS board to synthesize a quality stereophonic output from a monophonic sound source in realtime. The project offers a multitude of applications in the acoustics and more generally the Digital Signal Processing (DSP) fields, including the conversion of old monophonic videos and music to stereophonic format and the development of home theatre systems. iii

4 TABLE OF CONTENTS 1.0 Introduction Phase I: Conversion of Monophonic to Stereophonic Sound The Monophonic to Stereophonic Conversion Algorithm Designing an Effective Filter Introduction to Filters in Audio Signal Processing Designing a Filter in MATLAB The Filter Selection Process...6 The Butterworth Filter...6 The Elliptic Filter...6 The Chebyshev Type I Filter...6 The Chebyshev Type II Filter...7 The Selected Filter Implementation of the Algorithm Prototype I Prototype II Prototype III Phase II. Enhancing the Stereo Sound Sound Localization Reverberation Prototype I Prototype II Prototype III Phase III. Real-Time Synthesis Developing a Simulink Model Configuring the ADC and DAC Blocks...17 Sampling Rate...17 Wordlength...18 Output Data Type...18 Scaling...19 Samples per Frame...19 Overflow Mode Rapid Prototyping of the Algorithm System Testing Technical Testing Behavioural Testing Acoustic Environment Testing...21 iv

5 6.0 Obstacles Environmental, Health, and Safety Constraints Environmental Constraints Health and Safety Constraints Final Budget Applications and Future Work Conclusion References...26 Appendix...28 v

6 LIST OF FIGURES AND TABLES List of Figures 2.0 Phase I: Conversion of Monophonic to Stereophonic Sound 2.1 Implementation of the Monophonic to Stereophonic Algorithm Figure 2.1: Conversion of monophonic to stereophonic sound Designing an Effective Filter Figure 2.2: Frequency Response of the Butterworth Filter...5 Figure 2.3: Frequency Response of the Elliptical Filter...5 Figure 2.4: Frequency Response of the Chebyshev I Filter...5 Figure 2.5: Frequency Response of the Chebyshev II Filter Implementation of the Algorithm Figure 2.6: UML Data Flow Diagram for Using the FDA Tool...7 Figure 2.7: Magnitude Response of a Filter Designed Using the FDA Tool...8 Figure 2.8: Fletcher-Munson Curves...9 Figure 2.9: Frequency Representation of the Stereo Channels in Prototype III Phase II: Enhancing the Stereophonic Sound 3.1 Sound Localization Figure 3.1: Virtual Channel Reverberation Figure 3.2: Reverberation Effect...13 Figure 3.3: General Model of Phase II Algorithm...13 Figure 3.4: Phase II Prototype I Algorithm...14 Figure 3.5: Phase II Prototype II Algorithm...14 Figure 3.6: The Multiple-Order Reverberation Effect Real-Time Synthesis 4.2 Rapid Prototyping of the Algorithm Figure 4.2: Code Generation Process from a Simulink Model...20 List of Tables 2.0 Phase I: Conversion of Monophonic to Stereophonic Sound 2.3 Implementation of the Algorithm Table 2.1: Major Frequency Components of the Two Stereo Channels Real-Time Synthesis 4.1 Developing a Simulink Model Table 4.1: Parameters Under Consideration During DAC and ADC Configuration Final Budget Table 8.1: Project Expenditures...24 vi

7 1.0 INTRODUCTION Monophonic sound, also known as mono or non-stereo sound, refers to the most basic format of sound representation, in which a single channel of audio is used to record the input from a unidirectional plane. Hence, only one speaker is required [1]. Irrelevant of where one stands in the room, all elements of the monophonic sound, including the human voice and instrumental music, are heard equally and appear to originate from the same point in space [2]. In contrast to monophonic sound, stereophonic sound offers a major improvement in the quality of sound reproduction by utilizing two separate audio channels. This is done through a pair of widely separated speaker systems, in such a way as to create a pleasant and natural impression of sound heard from various directions as in natural hearing [3]. The conversion of monophonic to stereophonic sound is a significant advancement in enhancing the hearing experience. In order to achieve this, the original monophonic sound is modified with the aim of creating an output with a quality similar to that of a sound originally recorded in stereophonic format. Stereophonic sound is much more pleasant to the ear and provides a more natural listening experience, since the relative positions of objects and events can be distinguished. While recording stereophonic sound, two simultaneously recording microphones are placed in strategic locations relative to the sound source. The two recorded channels will differ in their timeof-arrival and sound-pressure-level information. When this sound is played back, the listener s brain differentiates between the timing and sound-level differences and triangulates the positions of the recorded objects, making the listening experience much more enjoyable [4]. The first two-channel audio system (a public broadcast entertainment system) was a theatrephone, which was invented by a French electrical engineer, Clement Ader, in Paris in In this system, multiple microphones were used to transmit the sounds of the Paris Opera to an exhibition hall over a distance of three kilometres, using lines laid through the Paris sewers. About fifty people could simultaneously hear the live transmission of the opera by each picking up a receiver for each ear [5]. In this system, binaural hearing was simulated through two separate channels. The listeners could distinctively differentiate the relevant positions of the actors on a set [4]. This brought the desire for a new technology that could convert monophonically recorded sound to stereophonic quality. This project aims to undertake this conversion in real-time using the MATLAB and Simulink software and the specialized hardware of the TI TMS 320 C6713 digital signal processing board. 1

8 MATLAB is among the most popular and widely used languages for signal analysis in the Digital Signal Processing (DSP) field today. Its unique ability to be programmed to perform repetitive analyses in a timeeffective manner corresponds to the repetitive nature of digital signals. Furthermore, its computational speed allows it to be ideally used for real-time signal sampling and analysis. The capability of rapid prototyping of digital signals offered by MATLAB is shared with certain digital signal processors, such as the TI TMS C6713 board, and hence it is no surprise that these often complement each other in traditional DSP analysis. The TI TMS C6713 microcontroller is embedded with a pipelined digital signal processor for real-time signal processing. This commercial DSP device is built with an optimized architecture to process sampled data at a high rate. This is what makes the programmable TI TMS C6713 board ideal for DSP signal analysis. The board s capability to process sampled data at high speeds makes it an effective resource for the real-time processing of digital signals, such as sound. The repetitive nature of signal processing is exploited in the TMS board by incorporating parallel operations and data pipelining. These features give this board the reputation of being fast and high in throughput, placing it as an ideal choice for the manipulation of sound required in this project [6]. This project introduces an innovative addition to conventional stereo synthesizers, by producing a high-quality stereophonic sound from a monophonic input in real-time, using the TI TMS C6713 microcontroller. Real-time synthesis implies that a continuous stream of inputs can be collected, analyzed and processed into outputs simultaneously. This will improve the time efficiency of DSP sound analysis, as a stream of data can be analyzed and processed in real-time. Monophonic to stereophonic sound synthesis can be incorporated into innumerable applications within the acoustics and Digital Signal Processing (DSP) fields. These include the development of home and commercial entertainment systems and the production of hearing aid devices for the audibly challenged. It can also be applied to the conversion of old monophonic soundtracks to stereophonic quality and more generally the real-time analysis of DSP signals. This project offers the addition of considerable functionalities to existing entertainment systems and a wide range of audio-related applications. 2.0 PHASE 1: CONVERSION OF MONOPHONIC TO STEREOPHONIC SOUND 2.1 The Monophonic to Stereophonic Conversion Algorithm Phase I of the project was concerned with producing a quality stereophonic sound from a monophonic source without the application of stereo enhancements. Sound enrichment will be explored in Phase II. 2

9 To produce the fundamental stereophonic sound, the frequency spectrum of the input monophonic source was first analyzed. A low-frequency bandwidth contains important monophonic information, which must be present at half intensity in each stereo channel. This bandwidth is common to both channels and is typically representative of voice, which forms the backdrop of the stereophonic sound. Once this bandwidth was determined, the rest of the frequency spectrum was divided and added to either the left or the right channels. Prototypes I III present different algorithms for dividing this spectrum. The original signal was then filtered with respect to these divisions and consecutive frequency bands were alternately sent to one of the two channels. Depending on the stereo effect desired, optimal gains were then subjectively determined and applied to the filtered frequency spectrum. The gain settings for all the blocks were specifically adjusted to augment the quality of the output signal. This process is illustrated in Figure 2.1. The filter selection process, explained in Section 1.2, was a critical one. It involved the analysis of the properties of various filters and the determination of an appropriate filter for use in this project. The quality of the chosen filter significantly impacts the quality of the resulting stereophonic output. Once the filter characteristics were determined, Section 1.3 explores a number of implementations of the aforementioned algorithm, which were tested and from which an optimal algorithm was empirically deduced. Monophonic Audio Input Bandpass Filter Gain Lowpass Filter (Vocal and Bass Range) Bandpass Filter Gain Bandpass Filter Gain Gain Bandpass Filter Gain Gain Bandpass Filter + + Bandpass Filter Gain Gain Left Stereo Right Stereo Figure 2.1: Conversion of Monophonic to Stereophonic Sound 2.2 Designing an Effective Filter Introduction to Filters in Audio Signal Processing In audio signal processing, a filter may have dual functions. These include the removal or attenuation of unwanted frequency components of the signal such as background noise and the extraction of useful parts of the signal such as the components lying within a certain frequency range. For example, when an audio signal is recorded in a noisy environment, the signal may be filtered to better represent the original sound. 3

10 The process of filtering involves three steps. First, the input function is digitized and represented by its frequency spectrum, using the Fast Fourier Transform (FFT). Second, the resulting spectrum is multiplied and weighted with the frequency response of the filter transfer function. For this, the coefficients of the frequencies in the input spectrum are multiplied with the respective coefficients of the spectrum of the filter. Lastly, the output spectrum is transformed back into time domain using the Inverse Fast Fourier Transform (IFFT). The filtered signal would have a frequency spectrum which conforms to the transfer function of the filter. There are two main kinds of filters - analog and digital filters. Analog filters have an advantage in terms of cost, speed, and their dynamic range. However, an analog filter from an op-amp circuit has a much wider transition range compared to a digital filter. In the MATLAB environment, the filter implementations emphasize digital, or discrete, signals and filters. As a result, digital filters will be the choice for the project because of their superior performance and compatibility with the TI TMS C6713 DSP board [10]. Digital filters may be further subdivided into two categories. These are the Infinite Impulse Response (IIR) filters with an infinite pulse response and the Finite Impulse Response (FIR) filters with a finite impulse response [11]. Only IIR filters would be considered in this project because of their lower computing load and cost of implementation. Every linear filter is characterized by its impulse response, step response and frequency response. Each response completely represents a signal in unique form and describes how the filter will behave under different situations [10]. In the following subsections, the filter design and selection process will be illustrated through the comparison of the frequency response of various filters Designing a Filter in MATLAB In an ideal filter, the output is an exact replica of the input signal in the passband, except the possibility of two minor modifications: the scaling of amplitude and a constant time delay. This is known as distortionless transmission [1]. In order to achieve distortionless transmission, the frequency response of the filter must satisfy two conditions: 1. The magnitude response H(jω ) must be constant within the passband. 2. The phase response arg{h(jω )} must be linear with respect to frequency, carrying a negative slope within the passband. 4

11 Figure 2.2: Frequency Response of the Butterworth Filter Figure 2.3: Frequency Response of the Elliptical Filter Figure 2.4: Frequency Response of the Chebyshev I Filter Figure 2.5: Frequency Response of the Chebyshev II Filter The filter design process involves a selection amongst various filter design methods and the determination of a set of specifications that meet the two conditions noted above. A relevant tool used to do so is the Signal Processing Toolbox in MATLAB, which includes a set of functions for designing digital filters. The filter design process involves determining a set of filter coefficients to meet the project s design specifications. These specifications consist of the bandwidth of the passband and the corresponding gain, the range of the stopband(s) and their corresponding attenuations, and the peak ripple tolerable in the passband and the stopband(s). The filters considered in this project are IIR filters which include the Butterworth, Chebyshev Type I and Type II, and Elliptic filters. The primary advantage of IIR filters over FIR filters is that they are able to meet a given set of specifications with a much lower filter order than their corresponding FIR filters. Lower order filters require lesser past samples of the input and output to be stored. Therefore, the memory utilization of the TI TMS C6713 hardware will be reduced. 5

12 2.2.3 The Filter Selection Process This section demonstrates the filter selection process of a bandpass filter with the following given specifications: Sampling Frequency, fs = 400 Hz Maximum Frequency, Fmax = fs / 2 Passband Edge Start Frequency, fp1 = 80 Hz Passband Edge End Frequency, fp2 = 120 Hz First Stopband Start Frequency, fst1 = 20 Hz Second Stopband Start Frequency, fst2 = 180 Hz Passband Ripple allowed, ap = 1 db Maximum Fist Stopband Attenuation, ast1 = 15 db Maximum Second Stopband Attentuation, ast2 = 2 db Gain, gain = 2 db Based on the parameters given above, the frequency responses of various filters were plotted in MATLAB. Figures 2.2, 2.3, 2.4, and 2.5 illustrate the magnitude and phase responses of the Butterworth, Chebyshev I, Chebyshev II and Elliptic filters. The following observations were recorded from these graphs: I. The Butterworth Filter The magnitude response is flat in the passband, which satisfies the condition of a constant magnitude response in the passband. The phase response is approximately linear in the passband, which satisfies the second condition of an ideal filter. Also, the frequencies beyond the passband are attenuated smoothly, which conforms to the shape of the filters required. However, a transition band is included for which the gain is not zero. II. The Elliptic Filter The magnitude response is characterized by ripples in both the passband and the stopbands. Hence, the condition of a constant magnitude response in the passband is not satisfied. This characteristic may contribute to additional noise during stereophonic sound conversion. The phase response resembles that of the Chebyshev II filter in the passband; however, it is not as linear as required. Amongst the observed filters, the Elliptic Filter supplies the sharpest transitions for the passband. However, the presence of ripples in both the passband and stopbands diminishes the filtering quality that is required within the algorithm. III. The Chebyshev Type I Filter The presence of ripples was observed in the passband. Hence, the condition of a constant magnitude response in the passband is not satisfied. The stopband is monotonically decreasing, which is not the desired shape of the required filter. The phase response is non-linear in the passband, which fails the second condition of the ideal filter. 6

13 IV. The Chebyshev Type II Filter The magnitude response constitutes a flat passband, which satisfies the first condition. However, the frequencies beyond the passband are not significantly attenuated. This would result in significant overlap between the stereo channels, creating a low stereo separation. The phase response resembles the Elliptic filter, which is not sufficiently linear. Furthermore, significant ripples were observed in the stopband. The gains of these ripples are the same as the gain in the passband, which is an undesired characteristic for our filter. The Selected Filter: Compared with a Chebyshev Type I/Type II filter or an Elliptic filter, the Butterworth filter has a smoother roll-off. Furthermore, it exemplifies a constant magnitude response and a linearly negative slope in the passband of the frequency phase representation. Implementing such a filter would require a lower order to implement a particular stopband specification. In conclusion, the Butterworth filter best satisfies the distortionless transmission conditions required for a high-quality filter required in the conversion of monophonic to stereophonic sound. 2.3 Implementation of the Monophonic to Stereophonic Conversion Algorithm Prototype I The initial implementation of the Phase I algorithm employed the filter design characteristics of the FDA tool available within MATLAB. This tool offers a multitude of options that allow the programmer to design a filter in accordance with an algorithm s specifications. It supports the design of IIR and FIR filters and the Butterworth, Chebychev I, Chebychev II and Elliptic filter methods. In MATLAB, The FDA tool may be referenced using the fdesign and design functions, which design and manipulate a filter object. Figure 2.6 is a UML Data Flow Diagram depicting the relationships between the FDA tool and other functions used in the implementation of Prototype I. Note that a filled rectangle denotes a process, blue text denotes input data, green text denotes output data and orange text denotes both input and output data. Figure 2.6: UML Data Flow Diagram for Using the FDA Tool 7

14 In order to produce a fundamental stereophonic sound, it was first essential to extract the lower frequencies in the range of 85 Hz to 2 khz. This range consists of bass frequencies and vocal sound, where bass frequencies are those at the lower end of the frequency spectrum. Since the frequencies within the bass range have little directional effect, a low-pass filter was designed to separate this frequency range and include it in both the left and right channels as the monophonic backdrop. Frequencies between 2 khz to 22 khz, which represent the rest of the frequency spectrum recognizable by the human ear, were then equally divided to specify the passband widths of six filters. Three of these filters specified the frequency ranges within the left channel and the other three filters specified the ranges within the right channel. One such filter is illustrated in Figure 2.7, whose specifications are provided below: Passband range: 2000 Hz to 5333 Hz Attenuation in the passband: 1 db Stopband range: 1500 Hz to 5833 Hz Attenuation in the stopband: 10 db Figure 2.7: Magnitude Response of a Filter Designed Using the FDA Tool To test this implementation, a monophonic audio sample was processed using the described algorithm and its respective stereophonic sound was observed through headphones. It was found that the sound quality of the resulting sound was poor. Significant noise accompanied the stereophonic conversion and vocals from the original audio sample could not be clearly recognized. This required a reanalysis of the algorithm altogether. A further analysis of this prototype identified the culprit. The frequency range of casual human speech ranges from 85Hz to 255Hz, while singing can produce frequencies of up to 1400Hz, especially in the case of opera singers [12]. It was found that vocal components could not be clearly recognized in the output due to the overattenuation of frequencies between 85Hz to 1400Hz performed by the low-pass filter in the algorithm. In addition, it was also speculated that although the FDA tool designed fine filters, the filter object returned did not interface seamlessly with other functions in MATLAB. Hence, a different filter design tool was needed to synthesize a high quality stereophonic sound. The next prototype aimed to address these issues. 8

15 2.3.2 Prototype II In the second implementation of Phase I, the required Butterworth filter was redesigned and the frequency characteristics of the two stereo channels were revised. Instead of using the FDA tool, the desired filter was manually designed using the butter and buttord functions provided in MATLAB. The commands were used to design the Butterworth filter which would introduce the smallest ripple to implement a particular design specification as compared to the Elliptic and Chebyshev Type I / Type II filters. Given that the filter coefficients may be extracted and used with numerous tools in MATLAB, these functions provided a better interface with other built-in functions and implied a better filtering quality overall. As was the case in Prototype I, the lower frequency range was initially separated from the rest of the audio sample. This range occupied the frequency spectrum of both the left and right channels to establish the fundamental monophonic backdrop. Frequencies ranging from 2 khz to 22 khz, which specifiy the rest of the frequency spectrum that the human ear can recognize, were then divided into six sections and included in either the left or right channels. Table 2.1 outlines the frequency components present in each channel. Table 2.1: Major Frequency Components of the Two Stereo Channels Left Channel Right Channel Common Frequencies: 50 Hz khz Common Frequencies: 50 Hz khz Filter L1: 2.0 khz khz Filter R1: 5.3 khz khz Filter L2: 8.6 khz khz Filter R2: 11.9 khz khz Filter L3: 15.2 khz khz Filter R3: 18.5 khz khz Figure 2.8 shows the Fletcher-Munson curves, which graphically illustrate the discrepancy between the actual sound intensity of a frequency and the perceived intensity by a human. The vertical axis represents the actual sound level produced. Each curve in the graph represents a set of conditions at which the sound pressure level of a sound is perceived to be the same by a human [13]. The lowest curve is the minimum audible level of sound. As depicted from the diagram, the human ear is most sensitive to frequencies between 2 khz Figure 2.8: Fletcher-Munson Curves 9

16 to 5 khz, since a lower sound intensity is required to perceive a desired level of loudness [13]. For example, a sound at 20Hz must be 80 db (approximately 100 million times) more powerful than a sound at 3 khz for the human ear to perceive it close to 10dB in intensity. In order to take this effect into consideration, an equalizing adjustment was performed to gains applied across the audible frequency range. More specifically, a lower gain was applied to frequencies closer to 2 5 khz and a higher gain was applied to frequencies farther apart from that range. The effect of this equalizing adjustment effectively balances the perceived volume of the sound across the audible spectrum. After an equalizing adjustment was performed, additional gains were applied to frequencies that required a greater representation in the output sound. This created the illusion that louder frequencies originated from a point closer to the listener, which enforced the localization effect within the output. This implementation provided a vast improvement from Prototype I in the resulting stereophonic sound quality. The equalization process significantly reduced the volume imbalance between different frequencies in the output. Additionally, the noise level was greatly reduced and a division in the frequency components of the left and right channels could be more distinctly recognized by the listener. A localization effect further enhanced the stereophonic sound experience. However, the actual stereo quality varied amongst audio samples, since this implementation did not consider the actual frequency components present in the original monophonic sound. For example, consider an audio sample that contains primarily human vocals and minimal music. It is expected that frequencies between 85 Hz to 1400 Hz would dominate the frequency spectrum of this sample. In this case, vocal components would be present as a common backdrop within both the left and right channels. Only a small amount of frequencies would be distinct to the left and right channels. Hence, a majority of the original monophonic sound would be heard with similar intensity in both channels, creating a low stereo separation. This necessitated a refined prototype, which took into account the characteristics of the input audio sample and processed an adapted stereophonic sound Prototype III The third implementation of stereophonic sound synthesis proposed an adaptive method of calculating frequency division between the stereo channels, which considered the characteristics of the sample monophonic input. This implementation was principally based on the maximum frequency present within a given audio sample. In order to create a high stereo separation, a considerable portion of the frequency spectrum in the original monophonic sound must be divided within the two stereo channels. However, a significant portion of the spectrum representing human voice must also be present within both channels in unity gain in order to 10

17 establish important common information between the stereo channels. This required a sound judgment of typical frequency spectra of music and a decision upon the optimal frequency division between the channels. The frequency spectra of various audio samples were analyzed to deduce this optimal frequency division. It was found that the lowest one-fifth of the frequencies could be established as the common frequencies amongst the channels. This would typically involve frequencies up to 2000 Hz, which provide a fine representation of human voice. The other four-fifths of the frequency spectrum would be divided amongst the passbands of six Butterworth filters, representing frequency separation between the channels. In order to retain the localization effect, an equalizing operation was first performed, as explained during Prototype II analysis. Higher gains were then applied to higher frequencies and a lower gain to those near the frequency spread common between the channels, namely 50 Hz to 2000 Hz. The frequency representation in the left and right channels is illustrated in Figure 2.9. Note that each frequency is normalized with respect to the maximum frequency that can be captured from an audio sample, which is 22 khz (the maximum frequency audible by the human ear). Hence, each normalized frequency in the aforementioned figure lies between 0 and π radians/s. Magnitude response in db Frequency representation of the left and right stereo channels Common Filter L1 Filter R1 Filter L2 Filter R2 Filter L3 Filter R Frequency, in radians/sample Figure 2.9: Frequency Representation of the Stereo Channels in Prototype III This implementation succeeded in creating the highest separation between the stereo channels amongst the three prototypes. A majority of frequency spectra present in mainstream music were accommodated to generate a customized stereophonic experience. However, this implementation fared less favourably with more extreme frequency spreads. For example, a monophonic input with very low frequency components would result in very few common frequencies between the channels. Hence, only a minimal component of human voice would be present in both channels, resulting in a softer sound. Similarly, audio samples represented by very high frequencies would not produce enough stereo separation, resulting in a lower 11

18 localization effect. Despite that, this implementation was favoured for its quality stereophonic sound synthesis for music with archetypical frequency spectra. 3.0 PHASE II: ENHANCING THE STEREOPHONIC SOUND The second phase of the project dealt with enhancing the stereophonic sound that was generated using the algorithm in Phase I. In this section, details are presented about adding virtual channels to the dual channel output to enhance the stereo effect. 3.1 Sound Localization Sound localization significantly contributes to the binaural characteristic of the human ear. This effect gives the listener a perception of the origin of the sound with respect to the position of the listener. This is illustrated in Figure 3.1. This results when a sound source reaches one ear before the other, depending on its location relative to each ear. The difference between the times of arrival of the sound signal to each ear determines the angular position of the sound within the three-dimensional space encircling the listener. However, the illusion of additional planes of origin for a sound source may be implemented through the creation of virtual channels. Virtual channels bring the surround effect to the atmosphere. Surround system virtual speaker technology is an audio virtualization technology that incorporates localization and reverberation effects to form a highly natural and Figure 3.1: Virtual Channel realistic multi-channel surround sound using two stereo speaker outputs. In a virtual channel, the output from a single channel originates from a unidirectional source and the listener deciphers the resulting sound from a point in that unidirectional plane. In a stereo system, this effect allows the listener to distinguish between the virtual positions of sounds within the immediate three-dimensional space [14]. 3.2 Reverberation Reverberation refers to the collection of reflected sounds from bounded surfaces such as walls and crowds in an enclosure like an auditorium. When a sound is produced in an enclosed space, some proportion of the incident sound energy is absorbed by bounded surfaces such as walls, floors and ceilings. The non-absorbed energy is reflected off these bounded surfaces. These reflections will continue to reflect off other surfaces in their enclosed environment, progressively losing energy as they propagate further. Friction with the air and successive absorption by each surface they encounter result in signal attenuation before the sound redirects itself in lower intensity to the listener s ear [15]. 12

19 To a listener in the room, reflected instances of the original sound will overlap and merge so that the sound will appear reinforced in volume and continue to be heard by the listener even after the original source has ceased. This prolonged recognition of sound after the source has stopped is referred to as reverberation, which is illustrated in Figure 3.2. Note that this effect is sometimes incorrectly classified as an echo. Reverberation refers to the merging of multiple reflections of the incident sound, whereas Figure 3.2: The Reverberation Effect an echo refers to a single reflection that is largely delayed from the original source and hence can be separately identified. Once a fundamental stereophonic sound has been produced, its enhancement through the incorporation of the reverberation effect provides a sensational sound experience that mimics the natural hearing model. In order to simulate the reverberation effect, time delays were introduced in the output of the fundamental stereophonic sound produced in Phase I and both the original and reflected sounds were represented in both stereo channels. This process is depicted in Figure 3.3. Figure 3.3: General Model of Phase II Algorithm The following prototypes represent three different models that incorporated the reverberation effect. Although similar in their underlying design, as depicted in Figure 3.3, they differed in their implementation of this design and each produced a different audible effect Prototype I In this implementation, all frequencies within the left channel sound were attenuated and a delay of twenty milliseconds was introduced to generate the delayed signal. This signal was then combined with the original left channel sound to simulate the effect of reverberation. This process is illustrated in Figure

20 Figure3.4: Phase II Prototype I Algorithm This simulates a three-dimensional surround sound effect and a better quality of sound is experienced. The drawback to this design is that it does not closely model the natural sound experience. In this implementation, all frequencies present in the delayed version are attenuated at the same intensity. However, when we analyze the natural hearing model, a reflected sound is lower in intensity than the direct sound. Furthermore, only some of the frequencies are absorbed by the surroundings; hence, only a certain range of frequencies are heard back. Lower frequencies, which include vocal signals, are more likely to be absorbed by the surroundings and hence are rarely reflected back and heard in the delayed version. In order to simulate natural binaural hearing, these aspects must be integrated into the stereo enhancement algorithm Prototype II In order to simulate the reverberation effect described earlier, this prototype incorporated varying degrees of attenuation in the delayed versions of the left or right channel signals. Doing so more closely modelled natural binaural hearing. + Left Channel Speaker Sound from Left Channel Add Delay Attenuate Selected Frequencies Sound from Right Channel Add Delay Attenuate Selected Frequencies + Right Channel Speaker Figure 3.5: Phase II Prototype II Algorithm As shown in Figure 3.5, once the delayed signal (representing reflected sound) was produced, selected frequencies were attenuated in varying intensities and then added to the original signal. Frequency selection was 14

21 performed by a bandpass filter, which eliminated vocal sound (typically represented by the frequency range of 50 Hz 2 khz) from the delayed signal. Additionally, the filter ensured that higher frequencies were better represented within the delayed signal, since these frequencies are more likely to be reflected and retain greater information about the original sound. It is to note that in this model, delays are added to both the left and right channels, which simulate reflected sounds arriving at each channel, and certain frequencies of the delayed signals are attenuated. This effect is observed when a certain sound seems to propagate from either the left or the right of the listener s position simulating localization. In this case, the reflected sound may be more dominant within one of the channels. Bandpass filters of different specifications are needed to reflect the varying intensity of the reflected signal within the stereo channels. This enhances the localization effect within the reproduced stereophonic sound. However, this model only considers the frequency representation of the first-order reflected sounds. Although higher frequencies that propagate further during reflection are better represented in the delayed signal, multipleorder reflections are not integrated and hence a full-fledged reverberation effect is not experienced by the listener Prototype III Prototype III introduces a further improvement to the implementation suggested in Prototype II by incorporating multi-order reflections that compose natural binaural hearing. A first-order reflection refers to the reflection of a signal from a single bounded surface. Likewise, an N-order reflection implies the reflection of a signal from N surfaces. As a signal hits additional surfaces and propagates further, it is successively attenuated from the effects of air friction and signal absorption by the environment. Hence, instances of the original signal that redirect themselves to the listener s ear after greater delays are heard back at lower intensities. Furthermore, higher frequencies are better represented in all reflected instances, since these frequencies are more likely to navigate longer distances and be reflected. This effect is shown in Figure 3.6, which Figure 3.6: The Multiple-Order Reverberation Effect depicts that lower gains are applied to instances of sound arriving after a greater delay. Incorporating the process of merging multiple-order reflections significantly enhances the quality of the fundamental stereophonic sound. 15

22 4.0 REAL-TIME SYNTHESIS Once an algorithm for monophonic to stereophonic conversion was developed, the final step involved interfacing this software implementation with the TI TMS320C6713 microcontroller to allow its real-time execution. This phase represented the integration of software and hardware components used in the project and was critical in establishing a high quality output from the board. In order to do this, a meticulous analysis of the board s architecture was conducted and the processor was configured to optimize the quality of the output during realtime synthesis. The following section explores the design elements that were encountered during this phase of the project. 4.1 Developing a Simulink Model The first step in synthesizing a real-time output involved porting the MATLAB source code into Simulink. Since there is currently no available means to convert MATLAB code directly into assembly language specific to the TI TMS C6713 processor, the quality of the converted code was a major contributor towards the resulting quality of the output. A simplified code was necessary in establishing a lower processing time and supporting a larger input sampling frequency. The Simulink model was then used to generate the assembly language code for execution on the TI TMS C6713 microcontroller. Simulink offers a platform for implementing real-time systems using a model-based approach. Reproducing the MATLAB source code into a Simulink model first required assembling the source code into a hierarchy of design components which could be represented as blocks within the model. These components were then implemented with the assistance of Simulink libraries and a detail-encapsulated representation of the monophonic to stereophonic conversion algorithm was developed. Although the majority of blocks within the model performed signal processing and calculation-intensive services related to software implementation, some blocks were dedicated to hardware integration and real-time synthesis. These included the Target Preferences Block for the C6713 target processor, Analog-to-Digital (ADC) and Digital-to-Analog (DAC) blocks. Options on the Target Preferences Block mask were programmed to set features of code generation for the C6713 processor-based target. Adding this block to the Simulink model provided access to the processor's hardware settings, such as its memory allocation settings, that needed to be configured in order to generate the assembly code which could be run on the target microcontroller [6]. 16

23 4.1.1 Configuring the ADC and DAC Blocks An analog-to-digital converter (ADC) was required to convert the analog sound input from the input jack of the microcontroller to digital form. Similarly, a digital-to-analog converter (DAC) was necessary to output the digitally processed signal to the analog output jack of the board. A digital signal provides a vast set of advantages over an analog signal, including the ability to better recover the original signal after signal processing, retaining the sampling rate at which the signal is recorded, and the ability to be regenerated infinitely without degradation. These reasons prompted the use of digital signals for real-time processing instead of analog ones captured by the microcontroller [17]. The configuration of the ADC and DAC blocks required the analysis of several parameters that were pertinent to the resulting quality of the stereo output. Please refer to Table 4.1 for a list of these considerations and the relevant blocks affected by each. Table 4.1: Parameters Under Consideration During DAC and ADC Configuration Parameter Relevant Block Sampling Rate ADC, DAC Wordlength ADC, DAC Output Data Type ADC Scaling ADC, DAC Samples per frame ADC Overflow Mode DAC Sampling Rate In the context of this project, the sampling rate, measured in Hz, refers to the number of samples per second taken from the continuous input sound signal. These samples are then used to construct the discrete signal that can be processed by the monophonic to stereophonic conversion algorithm. The Nyquist-Shannon sampling theorem states that the sampling frequency (referred to as the Nyquist frequency) must be greater than twice the bandwidth of the signal being sampled in order to perfectly reconstruct the signal. A sampling rate lower than the Nyquist frequency results in a phenomenon known as aliasing, in which certain frequencies cannot be distinguished from one another. This implies that the original signal's information may not be completely recoverable from the sampled signal. However, it is desirable to oversample the signal (i.e. sample greater than the Nyquist frequency) to counter the effects of noise that may distort the original signal. 17

24 The audible frequency range for the human ear is between 0 Hz to 22 khz. Hence, in order to reconstruct the signal in digital form, the sampling rate must be greater than 44 khz. To allow the reconstruction of the signal with the presence of noise, a sampling rate of 44.1kHz was selected in the project. Wordlength The wordlength of the recorded signal indicates the number of discrete values that may be produced over the range of voltage values retrieved from the input analog signal. In order words, a wordlength of M bits specifies 2 M quantization levels that the analog signal may be fit into during digital conversion. The wordlength may also be described electrically and expressed in volts. This is given by the formula Q = E FSR / 2 M, where Q represents the wordlength (or resolution) in volts, E FSR represents the full scale range of the input voltage (e.g. ten volts if the input ranges from negative five to positive five volts), and M is the wordlength in bits [17]. A wordlength of up to 32 bits is offered by the TI TMS C6713 microcontroller. This threshold is largely determined by the signal-to-noise ratio that the processor can support. If the noise present in the analog input is excessive, it will be impossible to accurately capture the relevant signal beyond a certain number of bits of resolution. In order to retain the highest precision possible during signal processing, a wordlength of 32 bits was selected for the ADC and DAC blocks. For this project, the TI TMS C6713 uses a +5V power supply; hence, it captures analog signals in the voltage range of -5V to 5V. A wordlength of 32 bits implies that the voltage resolution of the digital signal will be Q = [+5V - (-5V)] / 2 32 = 2.33 x 10-9 V = 2.33 nv. Output Data Type This parameter selects the data type with which the input signal is sampled and recorded. One of three types may be selected: single, double, and integer. As the names suggest, integer precision rounds a floating point number to the nearest integer, single precision represents a number with one significant digit after the decimal, and double precision records a number with two digits after the decimal. Double precision was selected for this project, to retain as much information from the original input signal as possible. Scaling This parameter selects whether the signal information sent to the input jack of the microcontroller represents unmodified data, or data that has been normalized to the range -1 to 1, with respect to the highest magnitude 18

25 present in the transferred input frame. A normalized scaling was selected, to easily reference the magnitude of any signal with the highest magnitude present. Samples per frame This specifies the number of samples from the original signal that are buffered into a frame and sent together to be processed by the algorithm's functions. This is heavily dependent on the sampling rate parameter mentioned earlier. For example, if the input is recorded at 8kHz samples per second and 64 samples per frame are selected, the frame rate would be 125 frames every second. In real-time synthesis, the sampling rate is extremely important when considering the value of this parameter. A high input sampling rate requires a lower sample size per frame, which implies a higher frame throughput every second. In this case, a high sample size per frame would cause a large sample size to be processed simultaneously. Hence, a larger number of samples will be delayed and outputted to the board together, degrading the real-time quality of the output. On the other hand, an excessively low value would imply that the processed signal would be outputted to the board much before the next batch of frames are processed and ready for output. It was found that at a sampling rate of 44.1 khz, a value of 8 samples per frame provided the best output quality during real-time synthesis. Overflow mode This parameter is directly related to the condition specified in the scaling parameter. This selection determines what action will be performed if the input signal does not meet the conditions of the specified scaling parameter. If wrap mode is selected, the deviant input will be wrapped around to the beginning of the acceptable input range. If the saturate mode is selected, the deviant input is cut off to fit the most appropriate value within the acceptable input range. Consider an example in which scaling is programmed to be normalized from -1 to 1 and the wrap during overflow mode is selected. In this case, if an input value of 2 is received, it will be wrapped to the beginning of the normalized scale and overwritten with the value -1. The saturate overflow mode was selected to fit any unexpected input to the closest accepted input value and avoid unintended data modification. It may be further noted that in audio applications, an input value may be distorted due to the presence of noise and it may be more desired to redirect the input to the nearest acceptable value. 4.2 Rapid Prototyping of the Algorithm Once a Simulink model had been developed, the Embedded Target for TI C6000 DSP was used to allow the rapid prototyping of the algorithm. This software allowed the generation of assembly code specific to the TI TMS C6713 microcontroller, which was both readable and editable for manual modification. 19

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