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Sound Quality vs. Data Rate

Audio Processing

Profile image of PRIYANJANA GHOSH (11BEC1025)PRIYANJANA GHOSH (11BEC1025)

Abstract

Audio processing covers many diverse fields, all involved in presenting sound to human listeners. Three areas are prominent: (1) high fidelity music reproduction, such as in audio compact discs, (2) voice telecommunications, another name for telephone networks, and (3) synthetic speech, where computers generate and recognize human voice patterns. While these applications have different goals and problems, they are linked by a common umpire: the human ear. Digital Signal Processing has produced revolutionary changes in these and other areas of audio processing.

Figures (15)
ANU INKS foes Functional diagram of the human ear. The outer ear collects sound waves from the environment and channel: them to the tympanic membrane (ear drum), a thin sheet of tissue that vibrates in synchronization with the ai waveform. The middle ear bones (hammer, anvil and stirrup) transmit these vibrations to the oval window, : flexible membrane in the fluid filled cochlea. Contained within the cochlea is the basilar membrane, the supportin; structure for about 12,000 nerve cells that form the cochlear nerve. Due to the varying stiffness of the basila membrane, each nerve cell only responses to a narrow range of audio frequencies, making the ear a frequency spectrum analyzer.
ANU INKS foes Functional diagram of the human ear. The outer ear collects sound waves from the environment and channel: them to the tympanic membrane (ear drum), a thin sheet of tissue that vibrates in synchronization with the ai waveform. The middle ear bones (hammer, anvil and stirrup) transmit these vibrations to the oval window, : flexible membrane in the fluid filled cochlea. Contained within the cochlea is the basilar membrane, the supportin; structure for about 12,000 nerve cells that form the cochlear nerve. Due to the varying stiffness of the basila membrane, each nerve cell only responses to a narrow range of audio frequencies, making the ear a frequency spectrum analyzer.
The primary advantage of having two ears is the ability to identify the direction of the sound. Human listeners can detect the difference between two sound sources that are placed as little as three degrees apart, about the width of a person at 10 meters. This directional information is obtained in two separate ways. First, frequencies above about 1 kHz are strongly shadowed by the head. In other words, the ear nearest the sound receives a stronger signal than the ear on the opposite side of the head. The second clue to directionality is that the ear on the far side of the head hears the sound slightly /ater than the near ear, due to its greater distance from the source. Based on a typical head size (about 22 cm) and the speed of sound (about 340 meters per second), an angular discrimination of three degrees requires a timing precision of about 30 microseconds. Since this timing requires the volley principle, this clue to directionality is predominately used for sounds less than about 1 kHz.
The primary advantage of having two ears is the ability to identify the direction of the sound. Human listeners can detect the difference between two sound sources that are placed as little as three degrees apart, about the width of a person at 10 meters. This directional information is obtained in two separate ways. First, frequencies above about 1 kHz are strongly shadowed by the head. In other words, the ear nearest the sound receives a stronger signal than the ear on the opposite side of the head. The second clue to directionality is that the ear on the far side of the head hears the sound slightly /ater than the near ear, due to its greater distance from the source. Based on a typical head size (about 22 cm) and the speed of sound (about 340 meters per second), an angular discrimination of three degrees requires a timing precision of about 30 microseconds. Since this timing requires the volley principle, this clue to directionality is predominately used for sounds less than about 1 kHz.
ae ee ee ee ee Phase detection of the human ear. The human ear is very insensitive to the relative phase of the component sinusoids. For example, these two waveforms would sound identical, because the amplitudes of their components are the same, even though their relative phases are different. Timbre is more complicated, being determined by the harmonic content of the signal. Figure 22-2 illustrates two waveforms, each formed by adding a 1 kHz sine wave with an amplitude of one, to a 3 kHz sine wave with an amplitude of one-half. The difference between the two waveforms is that the one shown in (b) has the higher frequency inverted before the addition. Put another way, the third harmonic (3 kHz) is phase shifted by 180 degrees compared to the first harmonic (1 kHz). In spite of the very different time domain waveforms, these two signals sound identical. This is because hearing is based on the amplitude of the frequencies, and is very insensitive to their phase. The shape of the time domain waveform is only indirectly related to hearing, and usually not considered in audio systems.
ae ee ee ee ee Phase detection of the human ear. The human ear is very insensitive to the relative phase of the component sinusoids. For example, these two waveforms would sound identical, because the amplitudes of their components are the same, even though their relative phases are different. Timbre is more complicated, being determined by the harmonic content of the signal. Figure 22-2 illustrates two waveforms, each formed by adding a 1 kHz sine wave with an amplitude of one, to a 3 kHz sine wave with an amplitude of one-half. The difference between the two waveforms is that the one shown in (b) has the higher frequency inverted before the addition. Put another way, the third harmonic (3 kHz) is phase shifted by 180 degrees compared to the first harmonic (1 kHz). In spite of the very different time domain waveforms, these two signals sound identical. This is because hearing is based on the amplitude of the frequencies, and is very insensitive to their phase. The shape of the time domain waveform is only indirectly related to hearing, and usually not considered in audio systems.
Violin waveform. A bowed violin produces a sawtooth waveform, as illustrated in (a). The sounc heard by the ear is shown in (b), the fundamental frequency plus harmonics.
Violin waveform. A bowed violin produces a sawtooth waveform, as illustrated in (a). The sounc heard by the ear is shown in (b), the fundamental frequency plus harmonics.
The Piano keyboard. The keyboard of the piano is a logarithmic frequency scale, with the fundamental frequency doubling after every seven white keys. These white keys are the notes: A, B, C, D, E, F and G. The term octave means a factor of two in frequency. On the piano, one octave comprises eight white keys, accounting for the name (octo is Latin for eight). In other words, the piano’s frequency doubles after every seven white keys, and the entire keyboard spans a little over seven octaves. The range of human hearing is generally quoted as 20 hertz to 20 kHz,
The Piano keyboard. The keyboard of the piano is a logarithmic frequency scale, with the fundamental frequency doubling after every seven white keys. These white keys are the notes: A, B, C, D, E, F and G. The term octave means a factor of two in frequency. On the piano, one octave comprises eight white keys, accounting for the name (octo is Latin for eight). In other words, the piano’s frequency doubles after every seven white keys, and the entire keyboard spans a little over seven octaves. The range of human hearing is generally quoted as 20 hertz to 20 kHz,
Audio data rate vs. sound quality. The sound quality of a digitized audio signal depends on its data rate, the product of its sampling rate and number of bits per sample. This can be broken into three categories, high fidelity music (706 kbits/sec), telephone quality speech (64 kbits/sec), and compressed speech (4 kbits/sec).
Audio data rate vs. sound quality. The sound quality of a digitized audio signal depends on its data rate, the product of its sampling rate and number of bits per sample. This can be broken into three categories, high fidelity music (706 kbits/sec), telephone quality speech (64 kbits/sec), and compressed speech (4 kbits/sec).
The answer is an encoding scheme called eight-to-fourteen modulation (EFM). Instead of directly storing a byte of data on the disc, the 8 bits are passed through a look-up table that pops out 14 bits. These 14 bits have the desired bunching characteristics, and are stored on the laser disc. Upon playback, the binary values read from the disc are passed through the inverse of the EFM look-up table, resulting in each 14 bit group being turned back into the correct 8 bits.
The answer is an encoding scheme called eight-to-fourteen modulation (EFM). Instead of directly storing a byte of data on the disc, the 8 bits are passed through a look-up table that pops out 14 bits. These 14 bits have the desired bunching characteristics, and are stored on the laser disc. Upon playback, the binary values read from the disc are passed through the inverse of the EFM look-up table, resulting in each 14 bit group being turned back into the correct 8 bits.
“~F— R E e Compact disc playback block diagram. The digital information is retrieved from the disc with an optical sensor, corrected for EFM and Reed-Solomon encoding, and converted to stereo analog signals.
“~F— R E e Compact disc playback block diagram. The digital information is retrieved from the disc with an optical sensor, corrected for EFM and Reed-Solomon encoding, and converted to stereo analog signals.
Figure 22-7 graphs these equations for the input variable, x, being between -1 and +1, resulting in the output variable also assuming values between -1 and +1. Equations 22-1 and 22-2 only handle positive input values; portions of the curves for negative input values are found from symmetry. As shown in (a), the curves for u255 law and "A" law are nearly identical. The only significant difference is near the origin, shown in (b), where 255 law is a smooth curve, and "A" law switches to a straight line. Two nearly identical standards are used for companding curves: 4255 law (also called mu law), used in North America, and "A" law, used in Europe. Both use a logarithmic nonlinearity, since this is what converts the spacing detectable by the human ear into a linear spacing. In equation form, the curves used in u255 law and "A" law are given by:
Figure 22-7 graphs these equations for the input variable, x, being between -1 and +1, resulting in the output variable also assuming values between -1 and +1. Equations 22-1 and 22-2 only handle positive input values; portions of the curves for negative input values are found from symmetry. As shown in (a), the curves for u255 law and "A" law are nearly identical. The only significant difference is near the origin, shown in (b), where 255 law is a smooth curve, and "A" law switches to a straight line. Two nearly identical standards are used for companding curves: 4255 law (also called mu law), used in North America, and "A" law, used in Europe. Both use a logarithmic nonlinearity, since this is what converts the spacing detectable by the human ear into a linear spacing. In equation form, the curves used in u255 law and "A" law are given by:
Companding curves. The 1255 law and "A" law companding curves are nearly identical, differing only near the origin. Companding increases the amplitude when the signal is small, and decreases it when it is large.
Companding curves. The 1255 law and "A" law companding curves are nearly identical, differing only near the origin. Companding increases the amplitude when the signal is small, and decreases it when it is large.
Human speech model. Over a short segment of time, about 2 to 40 milliseconds, speech can be modeled by three parameters: (1) the selection of either a periodic or a noise excitation, (2) the pitch of the periodic excitation, and (3) the coefficients of a recursive linear filter mimicking the vocal tract response.
Human speech model. Over a short segment of time, about 2 to 40 milliseconds, speech can be modeled by three parameters: (1) the selection of either a periodic or a noise excitation, (2) the pitch of the periodic excitation, and (3) the coefficients of a recursive linear filter mimicking the vocal tract response.
Spectra of speech and noise. While the frequency spectra of speech and noise generally overlap, there is some separation if the signal segment is made short enough. Figure (a) illustrates the spectrum of a 16 millisecond speech segment, showing that many frequencies carry little speech information, in this particular segment. Figure (b) illustrates the spectrum of a random noise source; all the components have a small amplitude. (These graphs are not of real signals, but illustrations to show the noise reduction technique). Another way to view this technique is as a time varying Wiener filter. As you recall, the frequency response of the Wiener filter passes frequencies that are mostly signal, and rejects frequencies that are mostly noise. This
Spectra of speech and noise. While the frequency spectra of speech and noise generally overlap, there is some separation if the signal segment is made short enough. Figure (a) illustrates the spectrum of a 16 millisecond speech segment, showing that many frequencies carry little speech information, in this particular segment. Figure (b) illustrates the spectrum of a random noise source; all the components have a small amplitude. (These graphs are not of real signals, but illustrations to show the noise reduction technique). Another way to view this technique is as a time varying Wiener filter. As you recall, the frequency response of the Wiener filter passes frequencies that are mostly signal, and rejects frequencies that are mostly noise. This
An interesting twist in Fig. 22-12 is that the linear filtering is dealing with frequency domain signals in the same way that time domain signals are usually processed. In other words, the time and frequency domains have been swapped from their normal use. For example, if FFT convolution were used to carry out the linear filtering stage, the "spectra" being multiplied would be in the time domain. This role reversal has given birth to a strange jargon. For instance, cepstrum (a rearrangment of spectrum) is the Fourier transform of the logarithm of the Fourier transform. Likewise, there are long-pass and short- pass filters, rather than low-pass and high-pass filters. Some authors even use the terms Quefrency Alanysis and liftering.
An interesting twist in Fig. 22-12 is that the linear filtering is dealing with frequency domain signals in the same way that time domain signals are usually processed. In other words, the time and frequency domains have been swapped from their normal use. For example, if FFT convolution were used to carry out the linear filtering stage, the "spectra" being multiplied would be in the time domain. This role reversal has given birth to a strange jargon. For instance, cepstrum (a rearrangment of spectrum) is the Fourier transform of the logarithm of the Fourier transform. Likewise, there are long-pass and short- pass filters, rather than low-pass and high-pass filters. Some authors even use the terms Quefrency Alanysis and liftering.
SAVIUINE Lev id Homomorphic separation of multiplied signals. Taking the logarithm of the input signal transforms components that are multiplied into components that are added. These components can then be separated by linear filtering, and the effect of the logarithm undone.
SAVIUINE Lev id Homomorphic separation of multiplied signals. Taking the logarithm of the input signal transforms components that are multiplied into components that are added. These components can then be separated by linear filtering, and the effect of the logarithm undone.

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