Filter-subtract-decimate hierarchical pyramid signal analyzing and synthesizing technique

• US 4,718,104 A
• Filed: 05/15/1987
• Issued: 01/05/1988
• Est. Priority Date: 11/27/1984
• Status: Expired due to Term

• Current Assignee: RCA Corporation
• Original Assignee: RCA Corporation
• Inventors: Anderson, Charles H.
• Primary Examiner(s): Boudreau, Leo H.
• Assistant Examiner(s): Couso, Jose L.
• Application Number:
  US07/051,210
• Time in Patent Office: 235 Days
• Field of Search: 358/133, 358/160, 358/166, 382/17, 382/41-43, 382/49, 364/723, 364/724, 364/725, 364/728
• US Class Current: 382/240
• CPC Class Codes: G01R 23/16 Spectrum analysis; Fourier analysis
• CPC Class Codes: G06F 17/10 Complex mathematical operations function generation by table look-up G06F1/03; evaluation of elementary functions by calculation G06F7/544
• CPC Class Codes: H04N 19/63 using sub-band based transform, e.g. wavelets

Abstract

A pyramid frequency analyzing technique is taught in which an input sampled temporal signal is convolved with a spatially localized, gradual rolloff kernel weighting function, which is subtracted from the input signal in each pyramid stage prior to the convolved signal having its sample density decimated and applied as an input to the next pyramid stage (rather than subsequent to the convolved signal having its sample density decimated as in a Burt Pyramid analyzer). In addition, a synthesizing technique is taught which provides additional high-frequency peaking in each stage thereof, not provided by a Burt Pyramid synthesizer.

Claims

1. A filter-subtract-decimate (FSD) method for analyzing the frequency spectrum of an n-dimensional information component, defined by respective level-values of certain samples of an applied temporal-signal sample stream, into at least one bandpass sub-spectrum and a remnant sub-spectrum, where n is a given integer having a value of at least one, said certain samples of said applied sample stream defining each of said n-dimensions of said information component with a particular relatively high sample density;

said FSD method comprising the steps of;

(a) convolving said certain samples of said sample stream with a symmetrical, localized, equal-contribution, low-pass filter, n-dimensional kernel function having a low-ass transmission characteristic to derive a convolved sample stream, said convolved sample stream including filtered samples that individually correspond to each and every one of said certain samples;

(b) subtracting a level-value of each of said filtered samples from a level-value of that individual certain sample with which it corresponds to derive a first output sample stream that includes information-component samples corresponding to said certain samples that define said bandpass sub-spectrum with said particular relatively high sample density, and

(c) decimating said convolved sample stream to derive a second output sample stream that includes information-component samples corresponding to only a given sub-multiple of said certain samples that define said remnant sub-spectrum with a relatively lower sample density in each dimension than said particular relatively high sample density.

2. The method defined in claim 1, further comprising the step of:

substituting said second output sample stream for said applied temporal-signal sample stream and repeating at least steps (a) and (b) on said substituted sample stream.

3. The method defined in claim 1, further comprising the step of:

substituting said second output stream for said applied temporal-signal sample stream and repeating steps (a), (b) and (c) on said substituted sample stream.

4. In signal processing apparatus employing pipe-line architecture for analyzing in delayed real time the frequency spectrum of an information component of a given temporal signal, wherein said component corresponds to information having a given number of dimensions, and wherein said frequency spectrum has a highest frequency of interest no greater than a frequency f₀ ;

said apparatus comprising;

a set of N ordinally arranged sampled-signal translation means (where N is a plural integer), each one of said translation means including first and second input terminals and first and second output terminals;

said first input terminal of each one of said second to said Nth translation means of said set being coupled to said first output terminal of the immediately preceding one of said translation means of said set for forwarding a signal from each one of said translation means to its immediately following one of said translation means of said set;

means for applying said given temporal signal to said first input terminal of the first translation means of said set; and

means for applying a separate sampling frequency clock to the second input terminal of each one of said translation means of said set to derive a sample rate for respective signals derived at said first and second output terminals of that translation means equal to the sampling frequency of the clock applied thereto;

wherein;

each one of said translation means of said set exhibits for said information component a low-pass transfer function between its first input terminal and its first output terminal, said low-pass transfer function of each translation means of said set having a nominal cut-off frequency that is a direct function of the sampling frequency of the clock applied to the second input terminal of that one of said translation means of said set;

the clock applied to the second input terminal of said first translation means of said set has a sampling frequency that (1) is twice f₀, and (2) provides for said information component a nominal cut-off frequency for said low-pass transfer function of said first translation means of said set which is less than f₀ ;

the clock applied to the second input terminal of each one of said second to Nth translation means of said set has a sampling frequency that (a) is less than the clock frequency applied to the second input terminal of the immediately preceding one of the translation means of said set, (b) is at least equal to twice the maximum frequency of the information component of the signal applied to its first input terminal, and (c) provides a nominal cut-off frequency for its low-pass transfer function which is less than that of its immediately preceding translation means of said set;

the information component of a signal derived at said second output terminal of each one of said translation means of said set corresponds to the difference between the information component of a signal applied to said first input terminal thereof and a direct function of the information component of a signal derived at the first output terminal thereof;

each one of said translation means of said set is comprised of first means coupled to the first and second input and first output terminals of that one translation means for providing said low-pass transfer function of that one translation means;

said first means including an m-tap convolution filter (where m is a given plural integer) for convolving the information component of the signal applied to the first terminal of that one translation means with a predetermined kernel function at a sampling frequency corresponding to that of the clock applied to the second input terminal of that one translation means, said predetermined kernel function and said sampling frequency of the convolution filter of that one translation means defining respectively the shape and nominal cut-off frequency of the low-pass transfer function of that one translation-means in each dimension of said information component;

second means coupled to said first means and to the second input and second output terminals of that one translation means for deriving a difference signal at the second output terminal of that one translation means;

said second means including sample-subtractive means and third means comprising delay means for coupling said sample-subtractive means through said delay means to said first means for subtracting in temporal alignment, at the sampling frequency of the convolved samples of that one translation means, each of successively-occurring respective sample levels of convolved samples of that one translation means from each of corresponding successively-occurring respective levels of the information component of the signal applied to the first input terminal of that one translation means prior to its being convolved with said predetermined kernel function of the convolution filter of that one translation means, whereby said sample-subtracting means output comprises each of successively-occurring respective difference sample levels, at the sampling frequency of the convolved samples of that one translation means, said respective difference sample levels constituting the information component of the signal derived at the second output terminal of that one translation means;

said first means of at least one of said translation means of said set being comprised of said convolution filter and a decimator serially coupled between the output of said convolution filter and the first output terminal of that one of said translation means of said set;

said convolution filter of said given type of first means derives at its output a particular sample density in each dimension of said information component that corresponds with the sampling frequency of the clock applied to the second input terminal of that one translation means, and

said decimator of said first means of said one translation means forwards, in each of said dimensions of said information component, only certain ones, but not all, of the convolved samples appearing at the output of the convolution filter of said first means of said one translation means to said first output terminal of that one translation means,

whereby said convolved samples, in each of said dimensions of said information component at said first output terminal of that one translation means, has a decimated sample density that is reduced with respect to their particular sample density of the corresponding dimension of said information component at the output of the convolution filter of that one translation means;

The improvement wherein;

said third means further includes fourth means coupled to the junction between said convolution filter and said decimator and to said sample-subtracting means for applying said convolved samples in each dimension of said information component at their particular sampling density of that one translation means to said sample-subtracting means.

5. The apparatus defined in claim 4, wherein each of a first to an (N-1)th translation means of said set includes a first means that is comprised the same as said first means of said one translation means is comprised and also includes said fourth means.

6. The apparatus defined in claim 5, wherein said Nth translation means of said set also includes a first means that is comprised the same as said first means of said one translation means is comprised and also includes said fourth means.

7. The apparatus defined in claim 4, wherein said decimator of said first means of said translation means forwards, in each of said dimensions of said information component, every other one of the samples appearing at the output of the convolution filter of said first means of said one translation means to said first output terminal of that one translation means,

whereby said decimated sample density, in each of said dimensions of said information component, is reduced to one-half said particular sample density of the corresponding dimension of said information component.

8. The apparatus defined in claim 4, wherein said predetermined kernel function of at least one of said translation means of said set defines a low-pass transfer-function shape for that translation means having a gradual roll-off that extends beyond said nominal cut-off frequency thereof.

9. A synthesizing method, for responding to an ordinally-arranged set of N, where N is a plural-integer, separate temporal sampled signals that have been derived by analyzing the frequency spectrum of an information component having a given number of dimensions of a first single temporal sampled signal according to a filter-subtract-decimate (FSD) pyramid analysis procedure, to synthesize a second signal temporal sampled signal that corresponds to said first temporal sampled signal;

wherein the first (N-1) sampled signals of said ordinally-arranged set are contiguous bandpass sub-spectra sampled signals of said frequency spectrum starting with that bandpass subspectrum sampled signal defining the highest frequency band of said frequency spectrum, and an Nth sampled signal of said ordinally-arranged set is comprised of a remnant sub-spectrum sampled signal that includes all frequencies of said frequency spectrum lower than those contained in the (N-1)th bandpass sub-spectrum, and wherein each of a second to said Nth sub-spectra sampled signals of said ordinally-arranged set has a sampling density in each dimension of said information component that is a given sub-multiple of a sampling density in that dimension of its immediately preceding sub-spectrum sampled signal of said ordinally-arranged set;

said method comprising the steps of;

(a) inserting zero-valued samples into said remnant Nth sub-spectrum sampled signal to expand its sample density in each dimension thereof to that of said bandpass (N-1)th sub-spectrum sampled signal, which step introduces undesirable image responses in addition to said remnant N^th sub-spectrum resampled to said expanded sample density;

(b) adding respective level values of corresponding samples of said remnant Nth sub-spectrum sampled signal and said bandpass (N-1)th sub-spectrum sampled signal to provide a sum sampled signal at the same sampling density in each dimension as that of said bandpass (N-1)th sampled signal;

(c) low-pass filtering said sum sampled signal in each dimension thereof to suppress said undesirable image responses and to derive an interpolated-value sampled signal at a sampling density in each dimension thereof that is the same as that of the bandpass (N-1)th sampled signal in that dimension, which interpolated-value sampled signal is afforded high-frequency peaking by step (b) of said method;

(d) adding respective level values of corresponding samples of said bandpass (N-1)th sub-spectrum sampled signal and said interpolated-value sampled signal to derive an output sampled signal at sampling density in each dimension thereof that is the same as that of the (N-1)th bandpass sub-spectrum sampled signal in that dimension, which output sampled signal is equivalent to a remnant (N-1)th sub-spectrum sampled signal.

10. The method defined in claim 9, wherein N is equal to two, whereby said output sampled signal derived in step (c) is said second signal temporal sampled signal.

11. The method defined in claim 9, wherein N is greater than two, and wherein said method comprises the further step of:

(d) substituting the output sampled signal derived in step (c) for the remnant sub-spectrum sampled signal of step (a) and successively repeating steps (a), (b) and (c) (N-2) times, whereby the output sampled signal derived by the (N-2)th repetition of step (c) is said second single temporal sampled signal.

12. The method defined in claim 11, wherein:

step (c) comprises the step of low-pass filtering in each dimension with a five tap symmetrical, equal contribution kernel weighting function in which the central weighting multiplier coefficient has a value in the range of between 0.3 and 0.4.

13. The method defined in claim 9, wherein:

step (b) comprises the step of low-pass filtering in each dimension with a five tap symmetrical, equal contribution kernel weighting function in which the central weighting multiplier coefficient has a value in the range of between 0.3 and 0.4.