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US4703349A
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Method and apparatus for multi-dimensional signal processing using a Short-Space Fourier transform
Assignee: ACCEL CAPITAL (INTERNATIONAL) LP
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Filing: 1985-03-19
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Granted: 1987-10-27
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Expires: 2005-03-19
Abstract
Abstract A method and apparatus for representing a multi-dimensional, finite extent, information containing signal in a locally sensitive, frequency domain representation employs transforming the digital signal using a Short-Space Fourier transform having overlapping basis functions. The theory and application of the Short-Space Fourier transform provide, in one particular application of picture image transmission, an improved image quality over previously employed block transform coding methods and apparatus. A particularly preferred window function for use in connection with image signal processing is the multi-dimensional sinc function which has the unique advantage of a rectangular bandpass signal in the frequency domain.
Inventors
- 👤 Jeffrey G. Bernstein
Bibliographic Details
Application Number
—
Jurisdiction
US
Data Source
google_patents
Last Synchronized
2026-10-29 14:41
CPC Classifications
H; H04; H04N; H04N19/00; H04N19/60; G; G06; G06F; G06F17/00; G06F17/10; G06F17/14; G06F17/141; H04N19/85; H04N19/86
Claims Analysis
Total Claims: 45
Claim 1
Independent Claim
62 words
A method for representing a pictorial image comprising the steps of generating a digital representation of said image, and transforming said digital representation of said image, using a Short-Space Fourier transform having overlapping basis functions for generating a compacted digital representation of said image, wherein said compacted digital representation requires fewer bits of data than said digital representation for representing said image.
Claim 2
Independent Claim
62 words
A method for representing a pictorial image comprising the steps of generating a digital representation of said image, and transforming said digital representation of said image, using a Short-Space Fourier transform having overlapping basis functions for generating a compacted digital representation of said image, wherein said compacted digital representation requires fewer bits of data than said digital representation for representing said image.
Claim 3
Dependent Claim
105 words
The method of claim 1 wherein said transforming step comprises the steps of effecting a discrete Fourier transform of a reflectively extended representation of said digital representation of said image for generating a discrete, reflected, transform image representation of said image, multiplying said discrete, reflected, transform image representation by a windowing function for generating a block-windowed transform image representation of said image, effecting an inverse discrete Fourier transform of said block-windowed transform image representation of said image for generating an unquantized, inverse transform representation of said image, and quantizing said inverse transform representation of the image for generating said compacted digital representation of said image.
Claim 4
Dependent Claim
80 words
The method of claim 2 wherein said first effecting step comprises the step of employing the discrete cosine transform operating on said digital representation for generating said discrete, reflected, transform image representation of said image, and said multiplying step comprises the steps of scaling a DC component of said multiplication by a factor for compensating for said discrete cosine transform, and adjusting the phase wrap of said multiplication for compensating for a phase shift requirement of the discrete cosine transform.
Claim 5
Dependent Claim
27 words
The method of claim 2 further comprising the step of discarding a half of said data forming said unquantized, inverse transform representation prior to said quanitizing step.
Claim 6
Dependent Claim
31 words
The method of claim 2 further comprising the step of selecting a low frequency component portion of said block-windowed transform image representation for direct application to and by said quantizing step.
Claim 7
Dependent Claim
25 words
The method of claim 1 further comprising the step of providing for said Short-Space Fourier transform, a window function of the general form (sin x)/x.
Claim 8
Dependent Claim
20 words
The method of claim 1 further comprising the step of providing for said Short-Space Fourier transform, a frequency-dependent window function.
Claim 9
Dependent Claim
24 words
The method of claim 7 further wherein said window function has non-overlapping rectangular bands of different sizes in different regions of the frequency spectrum.
Claim 10
Dependent Claim
36 words
The method of claim 1 further comprising the step of providing for said Short-Space Fourier Transform, a window function which, for a size 2 N discrete Fourier transform of the aliased window has the form: ##EQU7##
Claim 11
Independent Claim
52 words
An apparatus for representing a pictorial image comprising means for transforming a digital representation of said image using a Short-Space Fourier transform having overlapping basis functions for generating a compacted digital representation of said image, wherein said compacted representation requires fewer bits of data than said digital representation for representing said image.
Claim 12
Independent Claim
52 words
An apparatus for representing a pictorial image comprising means for transforming a digital representation of said image using a Short-Space Fourier transform having overlapping basis functions for generating a compacted digital representation of said image, wherein said compacted representation requires fewer bits of data than said digital representation for representing said image.
Claim 13
Dependent Claim
109 words
The apparatus of claim 10 wherein said transforming means comprises means for effecting a discrete Fourier transform of a reflectively extended representation of said digital representation of said image for generating a discrete, reflected, transform image representation of said image, means for multiplying said discrete, reflected, transform image representation by a windowing function for generating a block-windowed transform image representation of said image, means for effecting an inverse discrete Fourier transform of said block-windowed transform image representation of said image for generating an unquantized, inverse transform representation of said image, and means for quantizing said inverse transform representation of said image for generating said compacted representation of said image.
Claim 14
Dependent Claim
80 words
The apparatus of claim 11 wherein said first effecting means comprises means for employing the discrete cosine transform operating on said digital representation for generating said discrete, reflected, transform image representation of said image, and said multiplying means comprises means for scaling a DC component of said multiplication by a factor for compensating for said discrete cosine transform, and means for adjusting the phase wrap of said multiplication for compensating for a phase shift requirement of the discrete cosine transform.
Claim 15
Dependent Claim
26 words
The apparatus of claim 12 further comprising means for discarding a half of said data forming said unquantized, inverse transform representation prior to said quanitizing means.
Claim 16
Dependent Claim
30 words
The apparatus of claim 11 further comprising means for selecting a low frequency component portion of said block-windowed transform image representation for direct application to and by said quantizing means.
Claim 17
Dependent Claim
24 words
The apparatus of claim 10 further comprising means for providing, for said Short-Space Fourier transform, a window function of the general form (sin x)/x.
Claim 18
Dependent Claim
19 words
The apparatus of claim 10 further comprising means for providing for said Short-Space Fourier transform, a frequency-dependent window function.
Claim 19
Dependent Claim
35 words
The apparatus of claim 10 further comprising means for providing for said Short-Space Fourier Transform, a window function which, for a size 2 N discrete Fourier transform of the aliased window has the form: ##EQU8##
Claim 20
Independent Claim
114 words
A method for communicating an image representation over a data channel comprising the steps of digitizing said image for producing a digital representation of said image, transforming said digital representation using a Short-Space Fourier transform having overlapping basis functions for generating a compacted digital representation of said image, wherein said compacted representation requires fewer bits of data than said digital representation for representing said image, transmitting said compacted representation over said data channel, receiving said transmitted compacted representation at a receiver location, transforming said received image representation using an inverse Short-Space Fourier transform for generating a received inverse transform representation representative of said image, and displaying said received, inverse transform representation of said image.
Claim 21
Independent Claim
114 words
A method for communicating an image representation over a data channel comprising the steps of digitizing said image for producing a digital representation of said image, transforming said digital representation using a Short-Space Fourier transform having overlapping basis functions for generating a compacted digital representation of said image, wherein said compacted representation requires fewer bits of data than said digital representation for representing said image, transmitting said compacted representation over said data channel, receiving said transmitted compacted representation at a receiver location, transforming said received image representation using an inverse Short-Space Fourier transform for generating a received inverse transform representation representative of said image, and displaying said received, inverse transform representation of said image.
Claim 22
Dependent Claim
107 words
The method of claim 18 wherein said digital representation transforming step comprises the steps of effecting a discrete Fourier transform of a reflectively extended representation of said digital representation of said image for generating a discrete, reflected, transform image representation of said image, multiplying said discrete, reflected, transform image representation by a windowing function for generating a block-windowed transform image representation of said image, effecting an inverse discrete Fourier transform of said block-windowed transform image representation of said image for generating an unquantized, inverse transform representation of said image, and quantizing said unquantized, inverse transform representation of said image for generating said compacted representation of said image.
Claim 23
Dependent Claim
85 words
The method of claim 18 wherein said received image representation transforming step comprises the steps of effecting a discrete Fourier transform of said received image representation for generating a received, block-windowed image representation of said image, multiplying said received, block-windowed image representation of said image by a synthesizing function for generating a received discrete, reflected transform image representation of said image, and effecting an inverse discrete Fourier transform of said received, discrete reflected transform representation for generating said received, inverse transform representative of said image.
Claim 24
Dependent Claim
81 words
The method of claim 20 wherein said receiver inverse transform effecting step comprises the step of employing an inverse discrete cosine transform operating on said received, reflected transform image representation of said image, and said receiver multiplying step comprises the steps of scaling a DC component of said multiplication by a factor for compensating for said inverse discrete cosine transform, and adjusting the phase wrap of said receiver multiplication for compensating for phase shift associated with said inverse discrete cosine transform.
Claim 25
Dependent Claim
30 words
The method of claim 20 further comprising the step of selecting from said received image representation, a low frequency component portion for direct application to and by said multiplication step.
Claim 26
Dependent Claim
32 words
The method of claim 18 further comprising the step of reconstructing from said received image representation a previously discarded half of said received representation for delivery to said received image transforming step.
Claim 27
Dependent Claim
25 words
The method of claim 18 further comprising the step of providing, for said Short-Space Fourier transform, a window function of the general form (sin x)/x.
Claim 28
Dependent Claim
20 words
The method of claim 18 further comprising the step of providing for said Short-Space Fourier transform, a frequency-dependent window function.
Claim 29
Dependent Claim
24 words
The method of claim 25 further wherein said window function has non-overlapping rectangular bands of different sizes in different regions of the frequency spectrum.
Claim 30
Dependent Claim
36 words
The method of claim 18 further comprising the step of providing for said Short-Space Fourier Transform, a window function which, for a size 2 N discrete Fourier transform of the aliased window has the form: ##EQU9##
Claim 31
Independent Claim
123 words
An apparatus for communicating an image representation over a data channel comprising means for digitizing said image for producing a digital representation of said image, means for transforming said digital representation using a Short-Space Fourier transform having overlapping basis functions for generating a compacted digital representation of said image, wherein said compacted representation requires fewer bits of data than said digital representation for representing said image, means for transmitting said compacted representation over said data channel, means for receiving said transmitted compacted representation at a receiver location, means for transforming said received image representation using an inverse Short-Space Fourier transform for generating a received inverse transform representation representative of said image, and means for displaying said received, inverse transform representation of said image.
Claim 32
Independent Claim
123 words
An apparatus for communicating an image representation over a data channel comprising means for digitizing said image for producing a digital representation of said image, means for transforming said digital representation using a Short-Space Fourier transform having overlapping basis functions for generating a compacted digital representation of said image, wherein said compacted representation requires fewer bits of data than said digital representation for representing said image, means for transmitting said compacted representation over said data channel, means for receiving said transmitted compacted representation at a receiver location, means for transforming said received image representation using an inverse Short-Space Fourier transform for generating a received inverse transform representation representative of said image, and means for displaying said received, inverse transform representation of said image.
Claim 33
Dependent Claim
112 words
The apparatus of claim 28 wherein said digital representation transforming means comprises means for effecting a discrete Fourier transform of a reflectively extended representation of said digital representation of said image for generating a discrete, reflected, transform image representation of said image, means for multiplying said discrete, reflected, transform image representation by a windowing function for generating a block-windowed transform image representation of said image, means for effecting an inverse discrete Fourier transform of said block-windowed transform image representation of said image for generating an unquantized, inverse transform representation of said image, and means for quantizing said unquantized, inverse transform representation of said image for generating said compacted representation of said image.
Claim 34
Dependent Claim
89 words
The apparatus of claim 28 wherein said received image representation transforming means comprises means for effecting a discrete Fourier transform of said received image representation for generating a received, block-windowed image representation of said image, means for multiplying said received, block-windowed image representation of said image by a synthesizing function for generating a received discrete, reflected transform image representation of said image, and means for effecting an inverse discrete Fourier transform of said received, discrete reflected transform image representation for generating said received, inverse transform representative of said image.
Claim 35
Dependent Claim
82 words
The apparatus of claim 30 wherein said receiver inverse transform effecting means comprises means for employing an inverse discrete cosine transform operating on said received, reflected transform image representation of said image, and said receiver multiplying means comprises means for scaling a DC component of said multiplication by a factor for compensating for said inverse discrete cosine transform, and means for adjusting the phase wrap of said receiver multiplication means for compensating for phase shift associated with said inverse discrete cosine transform.
Claim 36
Dependent Claim
29 words
The apparatus of claim 30 further comprising means for selecting from said received image representation, a low frequency component portion for direct application to and by said multiplication means.
Claim 37
Dependent Claim
31 words
The apparatus of claim 28 further comprising means for reconstructing from said received image representation a previously discarded half of said received representation for delivery to said received image transforming means.
Claim 38
Dependent Claim
24 words
The apparatus of claim 28 further comprising means for providing, for said Short-Space Fourier transform, a window function of the general form (sin x)/x.
Claim 39
Dependent Claim
19 words
The apparatus of claim 28 further comprising means for providing for said Short-Space Fourier transform, a frequency-dependent window function.
Claim 40
Dependent Claim
35 words
The apparatus of claim 28 further comprising means for providing for said Short-Space Fourier Transform, a window function which, for a size 2 N discrete Fourier transform of the aliased window has the form: ##EQU10##
Claim 41
Independent Claim
48 words
A method for representing a multi-dimensional, finite extent, information containing signal in a locally sensitive, frequency domain representation comprising the steps of generating a digital representation of said information, and transforming said digital representation of said information containing signal using a Short-Space Fourier transform having overlapping basis functions.
Claim 42
Independent Claim
48 words
A method for representing a multi-dimensional, finite extent, information containing signal in a locally sensitive, frequency domain representation comprising the steps of generating a digital representation of said information, and transforming said digital representation of said information containing signal using a Short-Space Fourier transform having overlapping basis functions.
Claim 43
Dependent Claim
39 words
The method of claim 37 wherein said transforming step comprises the steps of critically sampling said information containing signal, and selecting a window function for use in said Short-Space Fourier transform for which a synthesis function can be generated.
Claim 44
Dependent Claim
20 words
The method of claim 37 further comprising the step of providing for said Short-Space Fourier transform, a frequency-dependent window function.
Claim 45
Dependent Claim
36 words
The method of claim 37 further comprising the step of providing for said Short-Space Fourier Transform, a window function which, for a size 2 N discrete Fourier transform of the aliased window has the form: ##EQU11##
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USPTO Annuity & Maintenance Windows
| Annuity Stage | Window Opens | Payment Deadline | Surcharge Period Until | Estimated Fee | Status |
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| 3.5 Years (Year 4) | 1990-10-26 | 1991-04-27 | 1991-10-27 | $2000.00 | Window Closed / Lapsed |
| 7.5 Years (Year 8) | 1994-10-26 | 1995-04-27 | 1995-10-27 | $3760.00 | Window Closed / Lapsed |
| 11.5 Years (Year 12) | 1998-10-26 | 1999-04-27 | 1999-10-27 | $7700.00 | Window Closed / Lapsed |