1. Field of the Invention
This invention relates to a subsampling method in which the number of samples of a digital signal which is a sampled and quantized signal (including audio and various video signals) is reduced, an interpolation method in which the number of samples is increased by an inverse process, and a method of detecting additional information contained in the interpolated signal.
2. Description of the Prior Art
As a typically concrete example of the subsampling method and the interpolation method, a sampling rate converter is known. The subsampling method and interpolation method for this sampling rate converter has been reportedly proposed, for example, in the following investigations as; R. W. Schafer and L. R. Rabiner, "A Digital Signal Processing Approach to Interpolation", Proceedings of IEEE. Vol. 61, No. 6, PP. 692-702, June 1973, and S. Kato et al, "Digital Video Signal Processing in Home VTRs", IEEE Transactions in Consumer Electronics, Vol. CE-32, No. 3, PP. 372-378, August 1986.
FIG. 4(a) and FIG. 4(b) are respective block diagrams of a conventional subsampling apparatus in which the sampling rate is halved and a conventional interpolation apparatus which the sampling rate is doubled.
As shown in FIG. 4(a), this subsampling apparatus has an input terminal 401 of a signal A with a sampling rate of Fs, a digital low-pass filter 402, a subsampling switch circuit 403 for alternately removing an output sample of the digital low-pass filter 402, thereby obtaining a signal B, and an output terminal 404 for outputting the signal B whose sampling rate is Fs/2.
As shown in FIG. 4(b), this interpolation apparatus has an input terminal 405 for receiving the signal B, a zero insertion circuit 406 for inserting a sample having a value of zero in a one-by-one manner into the intermediate position of each sample data row of the signal B, a digital low-pass filter 407 for outputting an interpolated signal, and an output terminal 408 for outputting the interpolated signal.
With the subsampling apparatus and interpolation apparatus as arranged above, their operations will be explained below.
First, the operation of the subsampling apparatus shown in FIG. 4(a) will be explained. A signal having a sampling rate of F samples per time period has a frequency spectrum bisymmetric with respect to each frequency which is of an integral multiple of F, and the frequency band to be used ranges from zero to F divided by 2 (Nyquist's theorem). In order to have the sampling rate Fs of the signal A halved, or Fs/2, the frequency band thereof is required to be band-limited to the frequency band of 0 to Fs/4 in advance. As a result, the signal A is subjected by the band limitation to a value of 0 to Fs/4 by the filter 402, and samples are removed in a one-by-one manner by the subsampling switch circuit 403, thus obtaining the signal B whose sampling rate is Fs/2.
FIGS. 5(a)-5(l) is diagrams for explaining a generally used subsampling process and interpolation process which are commonly introduced into the embodiments of the prior art and this invention.
FIG. 5(a) is a spectrum diagram of an analog signal S. FIG. 5(b) is a spectrum diagram of a signal A obtained by sampling and quantizing the signal B with a frequency of Fs. FIG. 5(c) is an ideal frequency response diagram of a filter to be used the subsampling process FIG. 5(d) is a spectrum diagram of an output signal of the filter to be used for the subsampling process. FIG. 5(e) is a spectrum diagram of a signal B. FIG. 5(h) is a waveform diagram of the signal S. FIG. 5(i) is a waveform diagram of the signal A, and FIG. 5(j) is a waveform diagram of the signal B.
Next, the operation of the interpolation apparatus shown in FIG. 4(b) will be explained. The zero insertion circuit 406 inserts a sample having a valve of zero in a one-by-one manner between the adjacent samples, so that sampling rate of the signal B is doubled to be made Fs. However, the waveform of the signal thus obtained is similar to that of the signal B, and the spectrum thereof will be similar to that of the signal B. A signal of sampling rate F sample=Fs has a frequency spectrum bisymmetric with respect to each frequency which is of an integral multiple of Fs, so that referring to the output signal of the zero insertion circuit 407, a spectrum existing with a width of Fs/4 vertically about each frequency which is of an integral multiple of Fs is a pseudo spectrum, which means that it does not exist in the original signal A. As a result, the filter 407 removes the pseudo spectrum from the output signal of the zero insertion circuit 406 to obtain the interpolated signal with no distortion . The interpolated signal thus obtained is outputted from the terminal 408. FIG. 5(k) is a waveform diagram of an output signal of the zero insertion circuit 406. FIG. 5(f) is a frequency response diagram of a filter to be used for the interpolation process, and FIGS. 5(g) and 5(i) are respectively a spectrum diagram and a waveform diagram of an interpolated signal as an output signal of the filter to be used for the interpolation.
The digital filter 407 to be used for interpolation may comprise a shift register, a multiplier, an adder-subtracter or the like. An interpolation circuit effects a predetermined interpolation process using each sample of the input signal for increasing the number of samples, which can input to the zero insertion circuit and the digital filter to be used for the interpolation purpose.
However, it is impossible to realize such a filter that has an ideal frequency response as shown in FIG. 5(c) or FIG. 5(f) on an practical basis. Namely, the filters 402 and 407 which can be realized on a practical basis have a deviation from the ideal frequency response. In addition, in the filtering process, the sample value at any position is generally changed influenced by the sample value of an input positioned before or after of that any position, and an error due to the rounding of the operation results is generated. The repetition of the subsampling process and interpolation process for filtering purposes will cause a problem in that the deviation from the ideal frequency response and the generation of error due to the rounding operation will be accumulated to cause signal degradation to be further increased. On the other hand, if a subsampling apparatus and interpolation apparatus for which such a problem has been solved are practically realizable, audio, video or other signals whose copying is to be protected from the viewpoint of a protection of copyright can be copied with no degradation, which is also a problem to be solved. In addition, in spite of the fact that the interpolated signal has on increased sample data amount is compared to before interpolation, the data amount to be transmitted is increased, causing such a problem in that the transmission line is not applied effectively.