United States Patent
`Schwartz
`
`[19]
`
`[11] Patent Number:
`
`4,682,248
`
`[45] Date of Patent:
`
`Jul. 21, 1987
`
`[54] AUDIO AND VIDEO DIGITAL RECORDING
`AND PLAYBACK SYSTEM
`
`[75]
`
`Inventor: David M. Schwartz, Englewood,
`C010.
`
`[73] Assignee: CompuSonics Video Corporation,
`Palo Alto, Calif.
`
`[21] Appl. No.: 776,809
`[22] Filed:
`Sep. 17, 1985
`
`[63]
`
`Related US. Application Data
`Continuation-impart of Ser. No. 651,111, Sep. 17, 1984,
`which is a continuation-in-part of Ser. No. 486,561,
`Apr. 19, 1983, Pat. No. 4,472,747.
`
`[51]
`Int. Cl.4 .......................... G11B 51/00; GIOL 5/02
`
`[52] US. Cl. ..................... 360/32; 381/51
`[58] Field of Search ...................... 381/51, 41; 360/32;
`358/22; 340/703, 717, 747
`
`[56]
`
`References Cited
`U.S. PATENT DOCUMENTS
`
`381/51
`8/1963 Clapper ..........
`3,102,165
`179/1
`3,236,947 2/1966 Clapper ,.
`
`.. 178/6
`3/1969 Richards .
`3,435,134
`340/ 174.1
`3,685,031
`8/1972 Cook ......
`
`3/1973 Kaul et a1.
`3,723,879
`325/38
`3,725,592 4/1973 Tanaka .......
`179/1555
`
`
`7/1973 Emerson et a .
`.. 179/1002
`3,745,264
`179/1002
`3,786,201
`1/1974 Myers et a1.
`
`3,855,617 12/1974 Jakowski et a1.
`360/32
`
`...........
`. 358/13
`4,015,286
`3/1977 Russell
`
`2/1978 Martin et a1.
`. 381/50
`4,075,423
`
`4,150,397 4/1979 Russell
`358/127
`
`7/1980 Rudnick et a .
`. 371/38
`4,211,997
`
`4,214,125
`7/1980 Mozer ........
`. 381/51
`340/1463
`4,225,885
`9/1980 Lux et a1.
`
`4,270,150
`5/1981 Diermann et a].
`..... 360/10
`
`7/1981 Wada et a1.
`4,281,355
`. 360/32
`4,302,776 11/1981 Taylor et al.
`. 360/39
`
`6/1982 Pearson ......
`4,335,393
`358/4
`
`.. 364/515
`4,345,314
`8/1982 Melamud
`
`4,365,304 12/1982 Ruhman et a1. ............. 364/515
`4,368,988
`1/1983 Tahara et al,
`..
`360/32
`
`4,375,650
`3/1983 Tiemann .
`1. 358/133
`4,387,406
`6/1983 Ott ..............
`.. 358/310
`4,389,537
`6/1983 Tsunoda et al.
`381/51
`
`.
`4,389,681 6/1983 Tanaka et al’.
`360/27
`7/1983 Lemoine et al.
`4,392,159
`358/319
`
`4,410,917 10/1983 Newdoll et a1.
`. 360/15
`4,411,015 10/1983 Scherl et al.
`. 382/51
`
`.
`.. 358/160
`4,417,276 11/1983 Bennett et al.
`
`4,417,283 11/1983 Hoshimi et al.
`358/310
`1/1984 Hashimoto et a1.
`.. 358/310
`4,429,334
`
`2/1984 Maier .................
`.. 358/260
`4,432,019
`
`4/1984 Henderson et al.
`4,441,201
`381/51
`4,455,635
`6/1984 Dieterich
`369/59
`
`4,458,110 7/1984 Mozer ........
`. 381/51
`4,493,106
`1/1985 Farhangi et al.
`382/41
`
`4,504,972
`3/1985 Scherl et a1.
`. 382/51
`
`4,516,246
`5/1985 Kenemuth ..
`. 375/37
`5/1985 Vogelsberg .. .
`4,519,027
`. 381/51
`
`5/1985 Takahashi et a .
`4,520,401
`358/310
`4,528,585
`7/1985 Bolger
`1 3513/22
`
`.....
`4,549,201 10/1985 Tanaka et a1.
`358/13
`
`Primary Examiner—Vincent P. Canney
`Attorney, Agent. or Firm—Jerry W. Berkstresser
`
`ABSTRACT
`[57]
`A microcomputer system for converting an analog sig-
`nal, such as an audio or video signal representative of
`sound or video into a digital form for storing in digital
`form in a highly condensed code and for reconstructing
`the analog signal from the coded digital form. The sys-
`tem includes reductive analytic means where the origi-
`nal digital data stream is converted to a sequential series
`of spectrograms,
`signal amplitude histrograms and
`waveform code tables. Approximately 100 times less
`storage space than previously required for the storage
`of digitized signals is thereby obtained. Additive synthe-
`sis logic interprets the stored codes and recreates an
`output digital data stream for digital to analog conver-
`sion that is nearly identical to the original analog signal,
`
`3 Claims, 18 Drawing Figures
`
`
`
`2 KBYTES/
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`
`Apple Exhibit 1323 Page 00001
`
`Apple Exhibit 1323 Page 00001
`
`

`

`US. Patent
`
`Jul. 21, 1987
`
`Sheet 1 of 18
`
`4,682,248
`
`DATA AQUISITION MODULE (DAM)
`—_-"‘l
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`
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`
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`
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`
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`
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`
`
`Page 00002
`
`Page 00002
`
`

`

`U.S.
`
`Patent
`
`Jul. 21, 1987
`
`Sheet20f18' 4,682,248
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`Page 00003
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`

`

`U.S. Patent
`
`Jul. 21, 1987
`
`Sheet30f18~
`
`4,682,248
`
`
`
`
`4BYTESRESERVEDFORRECORDSOFPREVIOUS
`
`LOCATIONS
`
`BWVOS 118 32
`
`Page 00004
`
`Page 00004
`
`

`

`US. Patent
`
`Jul. 21, 1987
`
`Sheet 4 of 18
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`4,682,248
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`US. Patent
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`Jul. 21, 1987
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`

`

`US. Patent
`
`Jul. 21, 1987
`
`Sheet 6 of 18
`
`4,682,248
`
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`Page 00007
`
`Page 00007
`
`

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`\ US. Patent
`
`Jul. 21, 1987
`
`Sheet7of 18
`
`4,682,248
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`
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`
`

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`US. Patent
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`Jul. 21, 1937
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`US. Patent
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`Jul. 21, 1987
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`US. Patent
`
`Jul. 21, 1987
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`Sheet 10 0118
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`4,682,248
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`US. Patent
`
`Jul. 21, 1987
`
`Sheet 11 of 18
`
`4,682,248
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`US. Patent
`
`Jul. 21, 1987
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`Sheet 12 of 18
`
`4,682,248
`
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`Page 00013
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`Page 00013
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`

`

`US. Patent
`
`Jul. 21, 1987
`
`Sheet 13 0f 18- 4,682,248
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`US. Patent
`
`Jul. 21, 1987
`
`Sheet 14 of 13
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`4,682,248
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`US. Patent
`
`Jul. 21, 1987
`
`Sheet 15 of 18
`
`4,682,248
`
`DIRECTORY DATA
`FOR AUDIO
`
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`Page 00016
`
`Page 00016
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`

`

`US. Patent
`
`Jul. 21, 1987
`
`Sheet 16 of 18
`
`4,682,248
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`U.S. Patent
`
`Jul. 21, 1987
`
`Sheet 17 of18. 4,682,248
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`US. Patent
`
`Jul.‘21,1987
`
`Sheet 18 of 18
`
`4,682,248
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`

`1
`
`4,682,248
`
`AUDIO AND VIDEO DIGITAL RECORDING AND
`PLAYBACK SYSTEM
`
`BACKGROUND OF THE INVENTION
`
`This application is a continuation—in-part of US pa-
`tent application Ser. No. 651,111 filed Sept. 17, 1984
`which is a continuation in part of US. patent applica-
`tion Ser. No. 486,561, filed Apr. 19, 1983, now US. Pat.
`No. 4,472,747, directed to Audio Digital Recording and
`Playback System of David M. Schwartz.
`Conventional recording of sound and playback is
`performed by electronic systems of the analog type.
`The sound waves from a source being recorded are
`converted to electrical signals on a one to one basis; the
`acoustic sound waves have their analogy in the electri-
`cal current generated by the microphone or pre-
`amplifier circuit such as used in a receiver, turntable or
`magnetic tape source. On playback the electrical signal
`is amplified and used to drive loudspeakers which con—
`vert the electrical signal to sound waves by the mechan—
`ical motion of an electromagnet and speaker cone.
`Conventional video recorders store the electrical
`waveforms, generated by the video camera, represent-
`ing the visual image. The most common memory de-
`vices used to store the waveforms are magnetic tape or
`disk. These devices store an analogy to the electrical
`waveforms in the form of magnetic gradients in the
`medium of magnetic particles. The waveforms may be a
`composite of the color signal or discrete red, green, and
`blue signals, depending on the system. Due to the ana-
`log nature of the system, the noise level is high and the
`results of surface defects are readily seen in the image
`when it is played back.
`Similarly, the output of conventional recording and
`playback systems consists of electrical signals in the
`form of signal waveforms either cut into a vinyl me-
`dium or imposed on magnetic particles on tape. On
`playback,
`the signal waveforms are converted into
`sound waves as described above. The accuracy of the
`reproduced sound wave is directly dependent on the
`quality of the metal or plastic disk or of the tape itself.
`Both the production of disk copies and tapes and their
`means of playback tend to degrade the quality of the
`reproduced analog signal. Noise, in the form of contam-
`ination, wear and the inherent background output of the
`medium itself is therefore unavoidably present in the
`recording and playback systems utilizing conventional
`analog to analog recording and playback technology.
`Recent developments in audio-digital sound recording
`and playback systems represent efforts to reduce or
`eliminate this noise problem. Exemplary of such devel-
`opments are the kinds of systems and equipment dis-
`closed in the following patents: U.S. Pat. Nos. Meyers
`et
`a1, 3,786,201 issued Jan.
`15, 1974; Borne et a1,
`4,075,665, issued Feb. 21, 1978; Yamamoto, 4,141,039,
`issued Feb. 20, 1979; Stockham, Jr. et a1, 4,328,580 is-
`sued May 4, 1982; Tsuchiya et a1, 4,348,699 issued Sept.
`7, 1982; and Baldwin, US. Pat. No. 4,352,129 issued
`Sept. 28, 1982, the disclosures of which are specifically
`incorporated herein by reference. These systems are
`characterized generally as taking advantage of the high
`speed operation of digital electronic computers. The
`signal waveform, representative of sound in such digital
`sound recording and playback systems,
`is frequently
`sampled to produce a serial stream of data that is trans-
`lated into a binary code that assigns a numerical value
`for each sample. This can be visualized as slicing up a
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`continuous curve into a large number of very short
`step—like segments. The process is reversed on playback
`as each numerical value of each segment is converted
`into an output voltage. When this process is done rap-
`idly enough, the fact that the signal wave form repre-
`sentative of a sound wave has been “chopped up” and
`re-assembled cannot be detected by the human car.
`When sound is recorded in digitized binary code in this
`manner, the sound, such as music,
`is only a series of
`numbers represented by magnetic tracks on a recording
`medium which, when read by the appropriate elec-
`tronic means, are either “on” or “off” with no interme-
`diate values. Such binary signals are virtually immune
`to distortion, error, and degradation with time. All
`sources of noise normally associated with analog de-
`vices are eliminated that is, there is no tape hiss, no
`tracking errors, no surface effects. Signal to noise ratios
`are limited only by the digital to analog conversion
`circuit itself and the power amplifiers, rather than the
`sensitivity of the mechanical or magnetic analog to
`analog conversion circuitry.
`These systems do, however, have several drawbacks.
`A representative system currently in use for recording
`master tapes in the record industry has excellent audio
`qualities as a result of a high speed sampling rate of 50
`KHz and good digital binary code resolution in the
`form of a 16 bit word for each sample. The problem
`with this system is that every sample must be preserved
`in mass storage for playback. The storage system thus
`must hold on the order of 4,320,000,000 bits of informa-
`tion for a 45 minute record. Storage systems of this
`capacity are large, expensive, and generally not suitable
`for a consumer product.
`Attempts to resolve the storage capacity problem
`have taken the approach of reducing the resolution of
`each sample (fewer bits per “word”) while at the same
`time reducing the sampling rate to 12 khz). Such reduc-
`tions have reduced the data storage requirement by as
`much as a factor of 4. The resulting fidelity of the out-
`put, however, is often below that acceptable for high
`fidelity sound recordings of music.
`Another approach much favored by telephone com-
`panies, employs the foregoing reduction of bits de—
`scribed above and in addition adds the restriction of
`input signal band width to that most used by talking
`voices (50 Hz to 3500 Hz). A total data reduction factor
`of about 12 is possible in this manner, again accompa-
`nied with a reduction in sound quality.
`Recent attempts at a solution to the storage problem
`and the fidelity reduction problem utilizes ultra high
`density digital storage by laser recording technology.
`This has been partially successful in that adequate play-
`ing times have been achieved with the improved stor-
`age capacity. However, the manufacturing technology
`and equipment presently necessary to create a “laser-
`burned hole”, “pit”, or “black spot” in the storage me»
`dium restricts “laser disks” or “laser fiches” to the
`“playback only” mode with no potential for in-home
`recording or erasing and editing.
`With respect to digital video recording, digital mem-
`ory devices identical to those used in conventional corn-
`puter systems have found use storing very high quality
`images. Small digital memories of 10 to 500 megabytes
`are frequently used as still frame stores for image pro-
`cessors that create special effects and enhancements.
`The digital memories tend to be small for cost reasons.
`Typically, the video images are recorded on magnetic
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`4,682,248
`
`3
`tape as they are produced, in analog form, then small
`portions of the tape are digitized and transferred to the
`digital
`image memory for manipulation. When the
`image processing task is complete, the data in the digital
`memory is converted back into analog form and stored
`on magnetic tape.
`The digital image storage and playback systems cur-
`rently in use have two principal problems: cost and slow
`access speed. The high cost of digital memory for image
`storage is a result of the large quantities of data pro-
`duced when analog video is digitized. The wide band-
`width of the video signal consumes memory at the rate
`of 80,000,000 binary numbers (bits) per second. Slow
`access to stored images is the result of the time consum-
`ing task of locating and transferring the desired image
`from analog tape to the digital system, and then back
`again before the next segment can be processed.
`Typical present day digital video recorders are com-
`posed of an imaging system such as a video camera, a
`digitizer, digital memory for frame buffering, and a
`Winchester disk or optical disk data storage subsystem.
`These recorders are restricted to non real time opera-
`tion due to the limited bandwidth of the data channel in
`and out of the storage subsystem. The fastest disk stor—
`age device will sustain an average data transfer rate of
`less than 10,000,000 bits per second. This is about one
`eighth the rate required to capture continuous moving
`images.
`Solutions to the above problems have been limited by
`the negative complementary nature of the relationships
`between access time, digital memory size, and tape
`transport speed.
`It is therefore an objective of the present invention to
`provide a system for high fidelity sound recording and
`playback that does not have the foregoing drawbacks
`and associated problems.
`It is therefore an objective of the present invention to
`store high quality digital video and audio data in a
`readily accessible, durable, and inexpensive form, and
`to provide a system for video and audio playback of the
`stored data.
`
`BRIEF DESCRIPTION OF THE INVENTION
`
`The present invention, using high density recording
`on a low cost magnetic media, such as a magnetic tape
`or disc or magneto—optical discs, or optical discs in a
`system having a random access memory architecture
`and a unique bit rate reduction scheme for processing
`digital audio and video data, provides a digital audio,
`video recording and playback system.
`SUMMARY OF THE INVENTION
`
`The present invention is yet another approach to a.
`solution to the storage and reproduction problems asso-
`ciated with digital audio recording and playback sys-
`tems described herein and digital video recording and
`playback systems. Good audio fidelity can be achieved
`with limited computer storage capacity by the provi-
`sion of unique electronic signal processing means
`which: (1) converts analog data to digital data stream
`samples; (2) selects portions of the samples to produce
`at least three data streams indicative of amplitude, fre-
`quency and waveform characteristics; (3) stores data
`samples indicative of waveform having a predetermined
`time duration, comparing each such sample of wave-
`form data against predetermined waveform parameters
`to select and preserve only predetermined portions, said
`waveform data samples matching the preserved por-
`
`4
`tions with pre-existing waveform and real time data and
`generating a resultant waveform data code from such
`comparison, and then comparing the selected data from
`the data streams which are indicative of frequency and
`amplitude with the waveform data code to produce
`another data code proportional to the frequency and
`amplitude of the original analog signal, sequentially
`recording the data stream indicative of amplitude, the
`data code indicative of frequency and amplitude, and
`the data code indicative of waveform, onto a recording
`media, for subsequent playback by the processing of the
`sequentially recorded data.
`And if audio and video recording is desired, the fol-
`lowing description will apply.
`A micro computer recording system for recording
`analog audio and video signals in digital data form can
`comprise converting means for converting .an analog
`audio signal into a multiplicity of digital data streams
`wherein at least one of the data streams is a relatively
`broadband reference signal representative of the ampli—
`tude of a preselected range of audio frequencies, and
`wherein another of the data streams is produced by
`filtering the analog audio signal
`to produce a data
`stream channel indicative of a plurality of discrete fre-
`quencies encompassed by the bandwidth represented by
`the first data stream; and wherein another of the digital
`data stream is a reference signal representative of the
`amplitude of the audio signal for each of plurality of
`discrete frequencies; sampling means for producing a
`sequential stream of samples in each of the digital data
`streams, selection means for selecting a predetermined
`portion of the digital data samples produced by the
`sampling means in each digital data stream; means for
`separately storing each of the selected data samples
`produced by the sampling means; means for comparing
`the reference data stream containing amplitude data
`with the reference data stream containing frequency
`data to produce frequency spectrogram data representa—
`tive of the frequency and energy of the original audio
`signal; means for comparing the histogram data with
`selected waveform parameters and producing address-
`able data representative of the waveform of the original
`input data; means for sequentially assembling and stor-
`ing the frequency spectrogram data and the amplitude
`reference data and the addressable waveform data for
`subsequent use; and converting means for converting an
`analog video signal into a multiplicity of digital data
`streams wherein the first of the digital data streams is a
`sequential time code representative of the beginning of
`each video frame, and wherein another of the digital
`data streams is produced by filtering the analog time
`domain signal to produce a data stream channel indica-
`tive of chrominance; and wherein another of the data
`streams is indicative of brightness; and wherein another
`of the digital data streams is indicative of pixel spatial
`relationships; and wherein another of the data streams is
`indicative of the temporal frame to frame relationships;
`and coding means for receiving each data stream indi-
`vidually, the coding means including means for mathe-
`matically transforming each digital data stream into
`modified data streams each capable of being subse-
`quently analyzed by comparison of the chromanance,
`brightness and spatial factors present respectfully in the
`modified data streams, and means for selecting prede-
`termined data bits from each of the modified data
`streams after comparison, in a sufficient amount to re-
`construct each chromanance, brightness and spatial
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`5
`factors for video presentation, and means for storing the
`digital data bits for retrieval.
`BRIEF DESCRIPTION OF THE DRAWINGS
`
`4,682,248
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`FIG. 1 is a schematic diagram of the digital recording
`and playback systems of the present invention.
`FIG. 2 is a pictorial representation of the analytical
`model of the function of the Data Acquisition module of
`FIG. 1.
`FIG. 3 contains a diagrammatic representation of the
`recorded waveform data.
`FIG. 4 is a pictorial representation of a single module
`of binary code as stored on disk, from which reproduc-
`tion will be obtained according to the system of the
`present invention.
`FIG. 5 is a diagrammatic representation of the layout
`of the electronic components used in the present inven-
`tion.
`FIG. 6 is a pictorial representation of a warehouse
`inventory system.
`FIG. 7 represents an analog signal output of the appa-
`ratus of FIG. 6.
`FIGS. 8 and 80 together are a schematic block dia-
`gram of the digital video recorder in the system of the .
`25
`present invention.
`FIGS. 9 and 9a together are a schematic diagram of
`the software modules for the digital audio and video
`recording and playback system of the present invention.
`FIG. 10 is a diagramatic representation of the trans-
`formed digital, video signal for one video frame (VFn)
`displayed.
`FIG. 11 is a diagramatic representation of the trans-
`formed digital video signal for the video frame (VFn+1)
`following that depicted in FIG. 10.
`FIG. 12 is a diagramatic representation of the differ-
`ence between the frames depicted in FIGS. 10 and 11,
`or (VFn)—(VFn+ 1)-
`FIG. 13 is a diagrammatic representation of the audio
`and video data disposition on a 55" flexible magnetic
`diskette.
`'
`FIG. 14 is a diagrammatic representation of the anal-
`ysis and synthesis factors related to a single digital video
`image picture element (pixel).
`FIG. 15 is a diagrammatic representation of the bit
`map of a digital video frame image.
`FIG. 16 is a diagrammatic representation of the en—
`coding of tri-stimulus values of a single picture element
`(pixel).
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`DETAILED DESCRIPTION OF THE
`INVENTION
`
`The present invention provides a system for convert-
`ing input analog signals such as audio signals, and/or
`video signals into digital signals and subsequently coded
`into structured data sets for recording in condensed
`digital form; and, for reconstructing a digital data set
`similar to the original digital signal input prior to recon-
`- version to the analog form of signal.
`In its broadest sense, therefore, the recording of the
`audio signals into a digital form for subsequent playback
`is accomplished by the provision of a microcomputer
`recording system which comprises electronic compo-
`nents for converting an analog audio signal into at least
`three digital data streams, wherein the first of the digital
`data streams is a relatively broad band reference signal
`representative of the amplitude of a pre-selected range
`of audio frequencies, and the second of the data streams
`is produced by filtering the analog audio signal to pro-
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`duce at least one data stream channel indicative of a
`sampled bandwidth of frequencies narrower than the
`bandwidth represented by such first data stream, and a
`third reference data stream representative of the sam—
`pling frequency of the audio signal; sampling means for
`producing a sequential stream of data samples from
`each of the digital data streams, selection means for
`selecting a pre-determined portion of the digital data
`sample produced by the sampling means in each of the
`data streams; means for separately storing each of the
`selected digital data samples produced by the sampling
`means; means for comparing the reference signal data
`stream containing amplitude data with the second data
`stream containing frequency data to produce frequency
`spectrogram data representative of the frequency and
`amplitude of the original audio signal; means for trans-
`forming data samples of the third data stream channel
`selected from the narrower bandwidth into data repre-
`sentative of a time versus amplitude histogram for each
`bandwidth means for comparing the histogram data
`with selected waveform parameters and producing and
`storing addressable data representative of the waveform
`of the original audio input and means for sequentially
`assembling and storing the frequency spectrogram data
`and the amplitude reference data of the first data stream
`and the addressable waveform data for subsequent play-
`back use.
`In the preferred embodiment shown in FIG. 1, for
`digital audio recording and playback the input signal is
`conditioned and amplified in the first stage of the Data
`Acquisition Module (DAM). The DAM is a multichan-
`nel programmable microprocessor based device that
`utilizes standard integrated circuits to perform three
`functions:
`1. To sample at the rate of 42 Khz, hold, digitize, and
`output the broadband (20 hz to 20 Khz) audio sig-
`nal level (dc voltage) of amplitude every 0.01 sec-
`ond. Thus, 100 times every second a digital “word”
`composed of from 4 to 14 bits is created for assem-
`bly as part of a disk record file.
`2. To sample, hold, digitize and output an audio fre-
`quency spectrogram every 0.01 second from a 128
`segment array of logical bandpass filters which
`sample 128 channels and are arranged logarithmi-
`cally over the overall band width used. The data
`set produced by this function may range from null
`(no signals on any channel) to (n) [(7 bit
`iden-
`tifier+(7 bit scaler)'+(2 bit pointer)] where (n) is
`the number of channels with signal content.
`3. To act as a digital storage oscilloscope loader,
`assembling strings of digitized amplitude versus
`time datajhistograms) corresponding to the array
`of bandpass filters selected in paragraph 2, above.
`This assembled data set is produced every 0.01
`second and is the largest single data structure and
`contains time continuous listing for every active
`bandpass filter. The number of “words” in each
`string is a function of the filter center frequency
`and requires as many as 4,000 samples for a 20 Khz
`channel, or as few as five samples for a 20 hz chan-
`nel. This data set'is not sent to the file assembler as
`in paragraphs 1 and 2, above, but is loaded into a
`Random Access Memory (RAM) buffer where it is
`accessible by the Waveform Analyzer and Coder
`module.
`The function of the Waveform Analyzer and Coder
`module (WAC FIG. 1) is to be a digital numeric proces-
`sor array that is programmed to extract characteristic
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`4,682,248
`
`7
`waveforms from the data set stored in the RAM by the
`DAM described above. The waveform data are re-
`duced to tabular form in which one period of each
`waveform codified is assigned to one wave table which
`preferably is a digitized x-y coordinate system consist-
`ing of 1,024 bytes along the x axis and an 8 bit “word"
`in each byte location to scale the y axis in 256 incre—
`ments; 127 above zero and 127 below. A set of waveta-
`bles is therefore generated for all active bandpass filter
`channels every 0.10 second. A range of 0 to 128
`(P.M.S.) tables may be generated per cycle (0.01 sec-
`end).
`The WAC utilizes either one of several P.M.S. reduc-
`tive analytic methods to find waveforms. The first being
`the Fast Fourier Transform (FFT) and the second the
`Fast Delta Hadamard Transform'(FDHT). The two
`methods may be briefly described as follows:
`The FFT is based on the principal that almost any
`periodic function f(x) of period 2 of vibrations can be
`represented by a trigonometric series of sines and co-
`sines. The full expression in general terms is:
`
`_ -1— 00
`flx) — 27f
`_°c
`
`cc
`_°C j(v)e
`
`iw(x—y)d
`
`v
`
`d
`
`w
`
`The algorithm for executing this equation efficiently
`was first published by Rabiner & Gold, 1974 and Op-
`penheim and Schafer, 1975.
`The FDHT is utilized for the analysis of spectral
`composition of a data set where the spectrum ‘11 is in the
`form:
`
`44/) = E; i [[F — (Fi + 1+ Fi)/z]
`
`wher Fi is the frequency and ‘1’ i is signal intensity. In
`the present application of this method the digital output
`of the logical filters from hereinbefore‘numbered para-
`graph 2, is summed at each filter and added to the next
`output until all frequencies have been sampled. At the
`last step the total output is:
`II
`11/: _E si+jtlji
`I=0
`
`Then an estimation of the spectrum \11’ can be found by
`matrix multiplication:
`
`1
`w' =7,-SB'7I =,‘,—SB-S-w = w
`
`The algorithm for implementing the FDHT was pub-
`lished in 1983 by E. E. Fenimore at Los Alamos Na-
`tional Laboratory. B—splines computationa