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`A/It connected for ---- iptilar operation has ail anaktg input range front 0 volts
`is 1 1511. A/I) converters can exhibit an offset tutor as welt as gain error. An
`input values for which a given output ctxle will occur. 'Ilse ideal code width
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`Offset voltage, gain error, or noise error can affect this specification. For the
`occurs. A good A/O converter should have an error of less than t
`the supposed level at which a digital transition occurs and where it actually
`Absolute accuracy error. shown in figure 4.22. is the difference between
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`both linearity and differential linearity errors.
`are +V. LSD wide, others are + IV. ISIS wide. Conversion speed can affect
`not exist. The convertor In figure 4.21 has an error of t3 LSI!: some levels
`and others would be 0 ISB wide; in other words. Mat output code would
`fication were exceeded, to perhaps t I LSD. some levels could be 21.511s wide
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`fast conversion time.
`and right channels; however, cost is always relatively high for any A/D with
`converters simultaneously process two waveforms, alternating between left
`quired for full fidelity audio digitization can be achieved. Indeed, some A/D
`severe with demand for higher conversion speed. In practice, speeds re-
`preparation for the noxt measurement. Obviously, dynamic errors grow more
`for B may be different because of the device's inability to properly settle in
`from voltage A to B and then later from C to B. the resulting digital output
`plishing one conversion may influence the next. If a converter's input moves
`because of settling time or propagation time errors. The result of accom-
`is sometimes difficult to achieve accurate conversion from sample to sample
`system. conversion time must be within the span of one sampling period. It
`called its conversion time. For an A/D converter used in an audio digitization
`The time It takes for an A/I) converter to output each digital word is
`error of t Vs 1.511—an inherent limitation of the quantization process Itself.
`ments for any A/0 converter. Of course, any A/D converter will have an
`resulting word are meaningful. Thus, speed and accuracy are key require-
`throughout the amplitude range, so that even the least significant bits in the
`linear PCM system. each of the 65,536 intervals must be evenly spaced
`must be en accurate representation of the input binary voltage. In a 16-bit
`sional audio digitization system. Furthermore, the digital word it provides
`time—for example. 48,000 conversions per second per channel in a profes-
`The A/0 Converter Must perform a complete conversion at each sample
`
`•
`
`means that the input voltage may have to increase ur decrease as little as Va
`should be 1 1-511 wide. A maximum differential linearity error of
` ISB
`illustrated in figure 4-21. Ideally, all of the bands of an A/D transfer function
`voltages—that is, the widths of input voltage bands. Differential linearity is
`Differential linearity error is a measure of the distance between transition
`t
`LSD linearity. The converter in figure 4-20 has a t 1/41S0 integral linearity.
`An .n•bit converter Is not a true n-bit converter unless It guarantees at least
`Integral linearity is the most important A/D specification and is not adlustable.
`and the reference line is drawn across the converter's full output range.
`-the converter. Integral linearity is illustrated in figure 4.20. Linearity is tested
`bit transition from the Ideal transition value, at any level over the range of
`through them. In other words, linearity specifies the deviation of an actual
`digital output changes from one code to the next—are to a straight line drawn
`close the transition voltage points—the analog, input voltages at which the
`measures the "straightness" of an A/D converter's output. 11 describes how
`been devised to evaluate the performance of A/D converters. Integral linearity
`Accuracy is another important consideration. Several specifications have
`
`1/2
`
`Analog-to-Digital Converter Requirements
`
`converter
`an A/I)
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`Integral linearity
`Fig. 4-20,
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`verters. are considered in Chapter 5.
`methods are examples of the latter. Overaampling, or decimating A/D con-
`approximation and parallel methods are examples of the former; integration
`he timed with a counter that generates an output digital word. Successive
`voltage can be allowed to decrease and the time it takes to reach zero can
`
`DISH-Blue Spike-246
`Exhibit 1010, Page 0802
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`------
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`and the word 10100000 is applied to the D/A; this produces 6.25 volts, so
`too high, so the second bit is reset to 0 and stored. The third bit is set to 1.
`11000000 is applied to the 0/A, with an interim output of 7.5 volts. This is
`stored at logical 1. The next most significant bit is set to 1 and the word
`greater than the D/A output. the comparator remains high. The first bit Is
`the U/A output at its half value of 5 volts. Since the input analog voltage is
`at 0; thus the word 10000000 Is applied to the internal t)/A. This word places
`4-24. The most significant bit in the SAR Is set to 1. with the other bits still
`converter. The operational steps of the SAN converter are shown in figure
`For example, let's assume an analog input of 6.92 volts and an 8-bit A/D
`digital word to match the analog Input.
`In operation, the device follows an algorithm that, bit by bit, sets the output
`word converted into analog, until the two agree within the given resolution.
`In essence, this convertor compares the analog input with its interim digital
`to-analog converter In a feedback loop, a comparator. and a conu'ol section.
`shown in the block diagram in figure 4-23. This converter employs a digital-
`digitization is the successive approximation register (SAR) A/D design. It is
`limits the choices to a few types. The classic. A/D converter used in audio
`cations. For audio digitization, the necessity for both speed and accuracy
`There are many types of A/D circuit design appropriate far various appli-
`
`Successive Approximation Analog-to-Digital Converter
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`while supplying these fast current changes.
`tests bits. The output voltage of the driving source must remain constant
`caused by changes in the output current of the Internal D/A converter as it
`amplifier) source. Transitions in an A/D converter's input current may be
`by a very low impedance (e.g., output of a wide•band, fast•settling operational
`Generally, a converter uses a low input intpedance, which should be driven
`input range as possible, to utilize the converter's maximum signal resolution,
`The analog input signal should be scaled to be as close to the maximum
`
`eters are recommended for minimum drift over temperature and time.
`may be further zeroed using external potentiometers. MultIturn potentiorn•
`full scale value. Gain and offset errors are often trintmed at the factory, and
`transition occurs for an analog Input value 11/2 LSB below the nominal positive
`at the last transition point from the ideal value, where the last output code
`negative full scale value. Gain error is the deviation of the actual analog value
`actual transition value from the ideal transition value at Vz 15B above the
`above the negative full scale value. Bipolar offset error is the deviation of the
`in a bipolar configuration, bipolar offset Is set at the first transition value
`deviation of the actual transition value from the Ideal value. When connected
`input value of Vi LSB above 0 volts. Unipolar offset error
`is defined as the
`
`codes over a specified temperature range.
`signals. In addition, good A/D converters are assured of having no missing
`put code either increases or rentains the same for increasing analog input
`Quality A/D converters are guaranteed to be monotonic: that is, the out•
`be carefully filtered.
`noise•free operation. Noise and spikes from a switching power supply must
`itor (e.g., I to 10 microfarad tantalum) located close to the converter, to obtain
`ripple are recommended. Power supplies 6hould
` with a capac-
`that is, a gain error. Normally, regulated power supplies with 1% or less
`This change results in a proportional change in all code transition values—
`Power supply deviations can cause changes In the positive full scale value.
`Changes in the DC power supply will affect an A/D converter's accuracy.
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`DISH-Blue Spike-246
`Exhibit 1010, Page 0803
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`

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`'lb :wine% I' high recording
`density. the fidelity el ilia modulation rude wave:
`is so few in liwel that processing can he accomplished only alter asnialificatiott.
`A primitiplilier is required to boost the signal from the nualiten. The signal
`
`Operation of 1.temodtilution Circuits
`
`and demodulated to restore the original literal data.
`must be processed to recover the data. Finally, the data must he synchronized
`low amplitude and must be amplified. This waveform is highly distorted and
`several important functions. The signal derived from the medium is of very
`converted to an analog signal. The demodulation circuits must accomplish
`audio signal in which the coded waveform recorded on the medium is again
`The demodulation circuits are the first step in reproduction of the digital
`
`Demodulation Circuits
`
`figure 5.1. Oversampling techniques art considered as well.
`duction circuits used in a linear PCM audio digitization system, as shown lit
`hold circuit, anti output low-pass filter. This chapter describes the repro.
`ceasing circuits, demultiplexer, digital-to-analog converter, output sample and
`duction subsystems include the denexlula tints circuit, reproduction pro•
`signal path are largely reversed from those on the record side. The repro-
`tlzation system. the functions of subsystems no the reproduction side of the
`ceased signal to analog form. Ina linear pulse code modulation (PCM) digl-
`in" a signal suitable for digital storage, then reconverting the stored or pro•
`serve as input anti output tranducers• converting the analog audio waveform
`In an audio digitization system, the reccrding and reproduction processors
`
`5 Digital Audio Reproduction
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`processing marks the end of the digital recording chain.
`binary Os. In any event, storage to media or other real-time digital audio
`in pits. Each pit edge represents a binary 1, while spaces between represent
`master glass plate used In CI) manufacturing. The modulation code results
`digital tape Is played through a laser cutting machine, which produces the
`densities. In optical systems such as the compact disc, a previously recorded
`does not affect the Integrity of the data, and permits the recording of higher
`modulated data. The recorded waveforms may appear highly distorted; this
`flux reversals recorded on the tape thus represent the bit transitions of the
`circuit, which generates the current necessary for saturation recording. The
`case of a stationary head digital recorder, the data Is applied to a recording
`Following modulation, the data is ready for storage on the medium. In the
`
`Recording
`
`modulation codes precipitate incompatibility among digital recording media.
`a greater data density can be achieved overall. On the other hand, different
`higher coding efficiency is achieved; although more bits may be recorded,
`delineating the recorded logical states. Moreover, through modulation, a
`and thus the audio waveform. Modulation facilitates data reading by further
`recorded and interpreted upon playback to recover the original binary data
`which represents the bit stream. It Is thus a modulation waveform that is
`binary code Is not recorded directly. Rather, a modulated code Ls stored,
`to involve the storage of is and es, it may be surprising to learn that the
`audio data before its storage. Because digital audio is commonly considered
`Record modulation processing is the final electronic manipulation of the
`
`Record Modulation
`
`design. This is discussed in further detail in following chapters.
`aro not equal. Additionally, the choice of medium strongly influences format
`in determination of a format, and the relative efficiency and success of each
`plexed bits of audio data. There Is obviously considerable latitude involved
`contains many data words, including samples that contain the time-multi-
`synchronization, address, identification, data, and redundancy. Each frame
`of data, arbitrarily Interleaved. Each frame consists of group codes, such as
`may be variously determined. A digital recording may consist of many frames
`out in many ways, and the way in which the resulting data is assembled
`the selection of format. Each of these record processing steps may be carried
`The transformation process from raw data to coded data is dependent on
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`DISH-Blue Spike-246
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`However. the output of the butler occurs at an all:Matt:1y (1/111rOlitli 11111%
`01-‘• 111111 W1{11111111! data is fed Irregularly. as it arrives ftuto Ilie medium
`bottom of the pail supplies a constant stream. Specifically. a buffer is a mem-
`a pail of water: water is poured into the pail carelessly. but a spigot at the
`overconte this problem, a data buffer is used. A buffer may be thought of as
`as jitter, as data is read front the medium: this is shown in figure 5-3. 'ro
`Mechanical instability in the transport will introduce tinting errors, such
`
`process Is shown in figure 5.2.
`correct because of their Isolation. The entire interleave and de-Interleave
`defects are now scattered through the bit stream. where they are caster to
`leaving. the data Is again properly assembled, and errors caused by medium
`that a defect in the medium does not affect consecutive data. With de.inter-
`Prior to recording, the data has been scattered in the bit stream to ensure
`The reproduction processing circuits must Initially citi•interleave the dots.
`
`Description of Reproduction Processing Circuits
`
`modate the large disruptions of data that occur at an edit point.
`tronic tape editing; reproduction processing circuits must be able to accom-
`electrical noise. Additionally, errors are caused by both manual and elec-
`in the heads or associated wiring. or errors due to power supplies with
`A badly designed digital recorder could additionally cause crosstalk errors
`drifting of timing, errors from tape stretching. and improper head alignment.
`Transport problems include rapid variation in timing, low frequency
`values may be substituted for missing or had data.
`the errors exceeds the error correction circuit's ability to correct, estimated
`data. making digital recording a highly reliable technique. if the nature of
`errors may be detected and corrected with absolute fidelity to the original
`with certainty: only their frequency and severity vary. If within tolerance,
`storage. !ler:nose of the packing density used in digital recording. errors occur
`the reproduction circuits must check for errors that have occurred during
`in addition land the primary reason for performing the record processing),
`signal manipulations performed on the record side of the digitization chain.
`The reproduction processing circuits must accomplish the reverse of the
`
`Necessi1yfor Iteproduclion Processing,
`
`data.
`(Minn, duntuhipiexing Is performed to restore parallel structure to the audio
`chanical variation, In the medium, and to perform error correction. In ad•
`production processing circuits buffer the data to minimize the effects of me-
`encoding also presents the opportunity to correct for many errors. Tho re-
`the potential for error ass result of storage la much greater. However. digital
`be kept accurate. With digital systems, because of the density of the storage,
`itself: for example, to minimize wow and flutter, the turntable's speed must
`analog storage, the problem must generally be corrected within the medium
`tations, such as mechanical variations and potential for damage to data. With
`
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`Digital Audio Reproduction
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`mizing the effects of data storage. Every storage ntedituit suffers from
`The reproduction processing circuits are primarily concerned with mini-
`
`Reproduction Processing
`
`duction processing. Modulation codes are discussed further in Chapter 7.
`has thus regained its original binary form and is ready for further repro-
`amplitude and logical 0 when there is a low level amplitude. The music data
`The method for interpreting leFtZ is to read a logical I when there is a high
`is, a simple code in which amplitude level represents the binary information.
`1, EFM, MFM, or another code—Is typically demodulated to NIIZ code, that
`content of each pulse. The modulated music signal data—whether it Is HI)M-
`ft-ante and to synchronize the playback signal, thus determining the I or 0
`nization pulses are derived and used to identify individual bits within each
`synchronization pulses are used to identify individual frames. Bit synchro-
`arated into frame synchronization and bit synchronization signals. Frame
`separated from the peripheral data, which is additionally Identified and sep-
`The music signal data and its error correction code are identified and
`amount of data has been permitted.
`as clean as if it had been literally. recorded. but storage of a much greater
`recovered with no penalty for the waveform's deterioration. The data is again
`reconstruct the is and Os of the signal,. In this way, data can be entirely
`inal signal. A waveform shaper circuit Is used to identify the transitions and
`are rounded, and only the transitions between levels correspond to the orig-
`data. Rather. the aniplitudos of the recorded data as read front the tape head
`signal from the medium does not have the clean characteristics of the original
`form as recorded on the medium has been allowed to deteriorate. Thus, the
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`

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`in figure 5 7. Settling
`runverter is the elapsed lime 15:15ve::11
`small ntlscl. and I last settling time. lite criteria for settling time arc shown
`is shown in figure 5-6. A 0/A converter must have good absolute accuracy.
`es the input decreases. An example of a 1)/A converter that is not moninonic
`Is, the analog output must increase as the digital input increases, and decrease
`should change by ono veltage step. A D/A converter must be ntonotonic: that
`tSB; hint is. when the input code changes by one bit, the analog output
`must be good. Its differential linearity must maintain an error of lees than
`tegral linearity; that is. the "straightness- of its transfer from digital to analog
`nearly approximated by U/A converters. A U/A converter must exhibit in-
`scribed In Chapter 4. The kleal transfer function, shown in figure 5-5. Is more
`is prone to many of the same errors as the analog-to-digital converter, de-
`The digital-to-analog convertor is subject to many of the requirements and
`
`for u
`
`Digital-to-Analog Converter Requirements
`
`low cost.
`verters arc available. and these integrated circuits are available osekittoly
`under varying conditions. Fortunately, several excellently designed 1)/A con-
`tem, the D/A converter must bo carefully designed to permit stable operation
`conversion process. In playback-only systems, such as the compact disc sys-
`a quantization error, theie is no corresponding quantization error In the 0/A
`the analog domain. However, whereas A/D conversion inherently introduces
`converter determines how accurately the digitized signal will be restored to
`determines the overall quality of the record system, the digital-to-analog
`system. Just as the analog-to-digital IA/U) converter largely
`the repnxluction
`The digital-to-analog (D/A) converter is one of the most critical elements in
`
`is now ready for digital-to-analog conversion.
`storage, and domultiplexed to again form hs parallel sample words. The data
`timing stability. been do-interleaved, =reeled for errors incurred during
`On leaving the reproduction processing circuitry, the data has regained
`
`shown in figure 5-4.
`and again as the data is applied. An example of a demultiplexer circuit is
`all of the bits of the entire word simultaneously. performing its task again
`ing its the bits are clocked in. When a full word has bean received, it outputs
`one sample value. The &multiplexer circuit accepts a serial bit input. count-
`parallel form, in which It again appears as discrete words, each representing
`remaining manipulation must be performed on the data to convert it to its
`least as original as the error correction circuitry has achieved. I lowever, one
`Waxer. The serial hit stream now consists of the original audio data, or at
`The final circuit in the reproduction processing chain is the demulti-
`
`may be found in Chapter 8..•
`data resumes. A more complete discussion of error correction techniques
`
`103
`
`Digits! Audit, neprnduction
`
`%.4
`
`• . . . • • . •
`
`Digital-to-Analog Conversion
`
`22 22 34 3)
`
`error compensation is not sufficient. the audio signal will be muted until valid
`values differ widely front the lost original values. In extreme cases. when
`become insufficient, and error concealment becomes marginal: the presumed
`error. For larger errors. interpolation and other compensation techniques
`terpolation is a methol of calculating new data to form a bridge over the
`simply, the last data value can be held until valid data resumes. Linear in-
`recovery, error compensation techniques are used to conceal the error. Most
`may be determined and substituted: When the error is too extensive for
`values. Using parity bits, checksums. or redundant data, the missing values
`bad audio data, error correction techniques are used to recover the correct
`isolate the error and determine where the fault has occurred. In the case of
`audio data or In the parity and checksum data. Several methods are used to
`agree with those read from the medium, an error has occurred either in the
`checked for errors. When the parity bits or checksums calculated do not
`Using redundancy techniques such as parity and checksums, the data is
`al which they were taken, guaranteeing the lossless nature of lime sampling.
`ensuring precise data liming. Samples are Thus assembled at the same rate
`
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`than that from the input word 01111111i iiiiitt. In other words, the sum
`output from the input word 1000000000000000 should be 3 millivolts larger
`between quantization levels of 20/65,536
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`Most Importantly, a quality 1)/A converter must be highly accurate. A
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`DISH-Blue Spike-246
`Exhibit 1010, Page 0807
`
`

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`to produce an analog output:
`the third switch. etc. Digital input bits are used to control ladder switches
`flows through the first switch, 1/4 through the second switch, 1/8 through
`by binary powers of two. If a current t flows from the reference voltage, 1/2
`ladder, resulting in currents through the switch resistors that are weighted
`weighted component to the output. The current splits at each node of the
`ever, there are two resistors per bit. Each switch contributes Its appropriately
`ladder shown In figure 5-9. This circuit contains resistors and switches; how-
`A more suitable design approach for a D/A converter Is the R-211 resistor
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`- 2 R Ladder Digital-to-Analog Converter
`
`creates conditions that are difficult to meet in manufacturing.
`current may be 30 nanoamps and the largest 2 milliamps. In short, this design
`resistor value is le ohm, the largest Is over 65M ohms. Similarly, the smallest
`converter, the largest-to-smallest resistor ratio Is 2"
`65,536. If the smallest
`previous one, widely varying values result. For example, In a 16-bit D/A
`Because each next resistor value must be a power of two greater than the
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`compleilty in manufacturing resistors with sufficient accuracy. Consider this
`design looks good on paper, it is rarely used in practice because of the
`with many is closes more switches and a high voltage results. While this
`keeps many switches open and a small voltage results. A high value word
`converts them to an output voltage. A low value binary word with many Os
`and prevents current flow. An operational amplifier sums the currents and
`and contributes a current, while a digital 0 causes the switch to remain open
`voltage Is used to generate currents In the resistors. A digital 1 closes a switch
`spending resistor represents the value associated with that bit. A reference
`This type of converter contains a switch for each input bit; the corre•
`weighted resistor WA converter. An example is shown in figure 5-8.
`converter contains a series of resistors and switches, and is known as a
`converts it to an output analog voltage or current. The simplest kind of D/A
`converter. A digital-to-analog converter accepts an input digital word and
`we must begin with a simple design that Illustrates the operation of the 0/A
`monly employed In audio digitization systems. To understand their function.
`Many types of digital-to-analog conineiers are available. Three types are com-
`
`Weighted Resistor Digital-to-Analog Converter
`
`verter may have a separate. complementing input for the MSII.
`be inverted before the ward 19 15115151 to the WA converter, or the WA con-
`MSB is complemented to serve as a sign bit. To accomplish this, the MSB can
`and a must negative value of 10000000. As we have seen. in this formal the
`ample. an 8-bin WA converter would have a most positive value of 01111111
`Most D/A converters operate with a two s complement input. For ex-
`signals are converted.
`tortion. Moreover, the percentage of error increases when low level audio
`accuracy at the center of the D/A convertor's range leads to crossover dis-
`quantization level, or 0.0015%. as should the MSB. Difficulty in achieving
`of the highest bit. The lower 15 bits should have a relative envy of one-half
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`Exhibit 1010, Page 0808
`
`

`

`signals xln) and produces one or more slim:rots oulinal signals ylnl. in
`A disrrett: system Is any system that accepts one or untie discrete input
`
`Linearity and Time Invariance
`
`disadvantages.
`analog or digital in nature. Either representation offers both advantages and
`indirectly. As we observed In Chapter 2. their representation con be either
`signals that can be recorded. transmitted, or manipulated either directly or
`in barometric pressure, temperature. oil pressure, current. or voltage are all
`of some 'dependent variable. For example. when the variable is time. changes
`A signal can be any natural or artificial phenomenon that varies as a function
`
`Fundamentals of Digital Signal Processing
`
`aims of eMcient signal manipulation.
`from simple d