Electrical computers: arithmetic processing and calculating – Electrical digital calculating computer – Particular function performed
Reexamination Certificate
2000-01-20
2003-01-14
Mai, Tan V. (Department: 2124)
Electrical computers: arithmetic processing and calculating
Electrical digital calculating computer
Particular function performed
Reexamination Certificate
active
06507859
ABSTRACT:
BACKGROUND OF THE INVENTION
1. Field of the Invention
The present invention relates to a signal processing method for eliminating the aliasing occurring due to sampling so as to broaden the band of a signal, more particularly relates to a signal processing method suitable for use when performing a plurality of sampling operations having different phase differences on a pseudo-periodic signal (pseudo static image) having a high correlation occurring at a constant period, such as a television signal, or an identical signal so as to obtain a higher resolution signal (static image).
2. Description of Related Art
In general, when sampling a continuous analog signal on a time basis by a sampling frequency fs to produce a digital signal, the sampling theorum results in the frequency component of the continuous signal above the Nyquist frequency (fs/2) being transformed to the low band side and causes so-called aliasing distortion. Therefore, to avoid this distortion, normally low band pass filtering is performed before the sampling so as to remove the frequency component above fs/2.
The characteristics of this low band pass filtering, however, are not at all ideal. Some frequency component above fs/2 even ends up remaining. As a result, aliasing occurs due to the sampling. This aliasing, for example, in the case of an image, causes the phenomenon of what originally should be a slanted line appearing as steps.
Further, for example, a large number of pixels CCD is expensive, so when using a small number of pixels CCD, the sampling interval becomes larger and the sampling frequency becomes lower. In this case as well, the aliasing is suppressed by cutting the frequency component above fs/2, so only the extremely low frequency component remains and only a blurry image is obtained. That is, in this case, a slanted line does not become steps, but sharp lines end up become blurry edged belts.
The following techniques have been proposed to obtain a high resolution signal with a high sampling frequency from a signal with a low sampling frequency.
Interpolation Method
This technique simply raises the sampling frequency. That is, it creates a new sampling point between sampling points of the original signal. Among the simpler forms, the technique called 0-th hold which repeats the previous value as it is, the linear interpolation method using the linearly interpolated value of the previous and subsequent values, and the techniques called B-spline or cubic convolution are well known. These techniques enable the number of the sampling points to be increased, so for example are suitable for enlarging the display of an image etc.
Technique Using Prediction
This technique reproduces the high band not by simple interpolation, but by estimating what the original analog signal including the high frequency component was like at the same time as raising the sampling frequency.
If an image, for example there is the technique of performing linear interpolation, then changing the pixel values based on the hypothesis that the pixel values of a natural image inherently change smoothly and repeating this several times to reconstruct the high frequency component.
Further, there is the technique of outputting a high-definition signal when an NTSC signal is input by learning in advance the correspondence between the pixels in high definition signals and corresponding pixels in the NTSC signal or several nearby pixels.
Further, there is the technique of outputting the corresponding broad band signal when a narrow band signal is input by learning in advance in the same way for an audio signal.
Sub-Nyquist Sampling Method
FIGS. 16A
to
16
D are views for explaining the sub-Nyquist sampling method.
FIG. 16A
shows the spectrum of a sampled signal. The ordinate shows the signal level, while the abscissa shows the frequency of the signal.
In general, if a sampled signal having the spectrum shown in
FIG. 16A
is sampled at a sampling frequency fs, a signal having the spectrum shown in
FIG. 16B
is obtained. In the figure, the hatched portion shows aliasing where the component of the sampled signal above the frequency fs/2 is transformed into a low band.
To suppress this aliasing, first, two series of sampling having a 180 degree relative phase difference are performed on the sampled signal having the spectrum shown in FIG.
16
A.
As a result, signals having the spectra shown in
FIGS. 16C and 16D
are obtained.
Here, the odd number order modulation component of the spectrum of the signal shown in
FIG. 16D
becomes opposite in phase from the odd number order modulation component of the spectrum of the signal shown in FIG.
16
C.
Therefore, by adding the signal having the spectrum shown in FIG.
16
C and the signal having the spectrum shown in
FIG. 16D
, a signal having the spectrum shown in
FIG. 16E
is obtained.
That is, it is possible to cancel out the primary modulation component included in the signal having the spectrum shown in FIG.
16
C and the primary modulation component included in the signal having the spectrum shown in FIG.
16
D and thereby eliminate the aliasing. As a result, the signal band can be doubled.
In this sub-Nyquist sampling method, when the phase difference between the two series of sampling operations is 180 degrees, the aliasing can be removed and the signal band doubled. Further, even when performing n number of series of sampling operations with phase differences between adjoining operations of 360
degrees, it is similarly possible to eliminate the aliasing occurring at the sampling operations and increase the signal band n-fold.
Technique Disclosed in Japanese Unexamined Patent Publication (Kokai) No. 8-336046
In the above sub-Nyquist sampling method, the aliasing was eliminated conditional on the phase difference of the two series of sampling operations being 180 degrees. In this technique, however, aliasing can be eliminated even if the phase difference of the sampling operations is other than 180 degrees.
In this technique, note is taken of the fact that the signal observed as aliasing is due to the M number of imaging (high harmonic) components occurring due to the sampling. The H number of imagings are removed by establishing simultaneous equations by preparing (M+1) number of images.
For example, by sampling a signal having a frequency component up to two times the Nyquist frequency and preparing three digital images including aliasing, a component up to two times the original Nyquist frequency is reconstructed.
The imaging component ends up overlapping the basic spectrum since the sampling frequency is low. This cannot be broken down, so the result is aliasing. Therefore, if the basic spectrum is found, the aliasing is removed.
Specifically, first, the digital signals E
0
, E
1
, and E
2
of the three images, as shown by
FIGS. 17A
to
17
C, are combinations of the basic frequency F(&ohgr;), the primary imaging F(&ohgr;−&ohgr;
S
), and the negative primary imaging F(&ohgr;+&ohgr;
S
)
Due to the sampling phase difference, each term is subject to an exp term. This can be expressed by the following equations (1).
E
0
=F
(&ohgr;+&ohgr;
S
)+
F
(&ohgr;)+
F
(&ohgr;−&ohgr;
S
)
E
1
=
exp(
j&agr;
1
)
F
(&ohgr;+&ohgr;
S
)+
F
(&ohgr;)+exp(−
j&agr;
1
)
F
(&ohgr;−&ohgr;
S
)
E
2
=
exp(
J&agr;
2
)
F
(&ohgr;+&ohgr;
S
)+
F
(&ohgr;)+exp(−
j&agr;
2
)
F
(&ohgr;−&ohgr;
S
) . . . (1)
In the above equations (1), &agr;
1
and &agr;
2
are phase differences (rad) with the digital signal E
0
. These are detected by a known detection method and are considered known. Further, &ohgr;
S
shows the sampling frequency.
If it were possible to use the above equations (1) to eliminate the imaging (&ohgr;−&ohgr;
S
) and F(&ohgr;+&ohgr;
S
) and leave only the frequency F(&ohgr;), then the aliasing could be cancelled.
Here, if the weighting coefficients w
0
, w
1
, and w
2
are multiplied with the equations (1), the following equations (2) are obtained.
w
0
E
0
=w
0
Omori Shiro
Ueda Kazuhiko
Mai Tan V.
Sonnenschein Nath & Rosenthal
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