US H2015 H1 Abstract This invention is a communication system utilizing sharply bandlimited waveforms for sampled data communications computed for each sample value in a sequence of data samples. The computed waveform is centered at a sample point, weighted by a corresponding data value, and truncated outside an appropriate time interval. Sampled digital data in a sequence of data samples is received by a computer and scaled according to the value r(t
_{n}). A waveform generator, controlled by a computer, generates a sharply bandlimited keying waveform for each data sample and weights each waveform with the data and forms the sum of weighted waveforms to form the output signal in digital form which is converted to analog form. The analog output of the waveform generator is passed through a low-pass filter to filter out any harmonics generated, up-converted to produce a desired carrier frequency which can then be multiplexed, if required, and output as radio frequency (RF) energy which can be received by any standard receiver.Claims(3) 1. A communications system comprising:
means for generating a digital data sample;
means for generating a sharply bandlimited keying waveform responsive to the digital data sample centered at a sample point;
means for weighting the sharply bandlimited keying waveform by a corresponding data sample value and truncating outside an appropriate time interval; and
means for transmitting the weighted sharply bandlimited keying waveform.
2. A communications system, as in
3. A method for transmitting a digital signal comprised of the steps of:
sampling a first digital data signal to produce a digital data sample;
generating a sharply bandlimited keying waveform for the digital data sample;
weighting the sharply bandlimited keying waveform with a corresponding data sample value and truncating outside an appropriate time interval;
converting the weighted sharply bandlimited keying waveform into an analog signal; and
transmitting the analog signal.
Description 1. Field of the Invention This invention in general describes a communications system, specifically a communications system having sharply bandlimited waveforms for sampled data communications. 2. Description of the Related Art Proliferation of communications, radar, and other systems making use of electromagnetic wave propagation has resulted in overcrowding in the useful portions of the electromagnetic spectrum. Even line-of-sight communications links seldom utilize frequencies above the X-band because of the absorption and scattering by rain and other constituents of the troposphere. Consequently, it becomes more important for transmitters to radiate signals with well confined spectra so limited spectral space is used more efficiently. In order to communicate a sequence of sampled digital data, r(t It is well known to those practicing the art that the spectrum of a signal formed from appropriate combinations of cardinal functions will have zero energy outside the designated frequency band width. For this to be exact, it is required that the cardinal functions be of infinite length. Theoretically, this causes no intersymbol interference since cardinal functions are zero at all sample points except one, t=0. Thus the analog/digital converter, appropriately synchronized and in the absence of noise, reads values of the transmitted sequence. Functions of infinite length are not physically realizable. However, studies have shown that, by appropriately modifying the cardinal function, one can achieve excellent interpolation accuracies and resultant phase accuracies in direct sampling applications even if the function is truncated to just a few sample intervals. In the field of electromagnetic transmission of digital data there is a need for an alternative to FSK and various forms of PSK signals which would improve the confinement of the signal spectrum to an assigned frequency band in transmitters and receivers. It is well known that bi-phase code modulation consists of a sequence of equal-length intervals, often called “chips”. Within each chip a sinusoid at the carrier frequency is bi-phase modulated; more specifically, the carrier phase within a chip is constant but may jump from chip-to-chip by 180 degrees in accordance with modulating binary data. A drawback to the application of this waveform is the 180° phase “jump” which causes spreading of its spectrum. However, after a bi-phase signal is modified by the process which is the subject of this invention, its spectrum is well-defined to the desired band. Further, it is important that adjacent communication channel interference and mutual interference among radar, navigation, communications and other systems which depend upon electromagnetic radiation be prevented. It is the object of this invention to transform a communications sequence in a communications system into an analog signal which is spectrally confined to the band available for the transmission within a band limited communications channel without compromising communication accuracy. Another object of this invention is to improve spectral confinement thereby allowing closer channel spacing and better electromagnetic compatibility among radar, navigation, and communications systems. These and other objects are achieved by a communication system using sharply bandlimited signals for sampled data communications wherein a sharply bandlimited waveform is computed for each sample value in a sequence of data samples. Each waveform is centered at a sample point, is weighted by the corresponding data value, and is truncated outside an appropriate time interval. Resulting data-weighted waveforms are summed in the computer for all data samples of the sequence to be communicated, and the result is converted to analog form, up-converted to the desired carrier frequency, and transmitted. Because the signal spectrum is sharply bandlimited, communication channels may be spaced more closely, permitting more channels in the same frequency band. At the receiver, signal-plus-noise is down-converted, data is sampled and converted to digital form, de-multiplexed (if necessary), and delivered to corresponding users. FIG. 1 shows the error for low-pass interpolation using cardinal functions and self-truncating cardinal functions for B/W=¾ and ½ (33% and 100% over-sampling, respectively) as a function of the truncation length as measured by N, the number of samples within the truncated interval. FIG. 2 FIG. 2 FIG. 3 is a schematic of a transmission system utilizing a sharply bandlimited communications filter. FIG. 4 depicts a test configuration for testing a sharply bandlimited communications system. FIG. 5 shows (a) the measured spectrum of the output waveform of the waveform generator with interpolation and (b) the measured spectrum of the output waveform of the waveform generator without interpolation. FIG. 6 FIG. 6 FIG. 6 FIG. 6 FIG. 6 In order to communicate a sequence of sampled digital data over a bandlimited communications channel in a format other than the conventional analog format, a bi-phase code modulation utilizing a sharply bandlimited keying waveform may used. A sharply bandlimited keying waveform is computed for each sample value in a sequence of data samples and centered at a sample point, weighted by a corresponding data value, and truncated outside an appropriate time interval. For a predetermined carrier frequency, f A signal with no spectral energy outside the band from −W to +W is completely specified by samples taken at uniform intervals less than or equal to ½ W. The original signal may be exactly reconstructed from these sampled values, r(t where t A bandpass signal with no spectral energy outside the bands −MW to −(M−1)W and (M−1)W to MW may also be completely specified by samples taken at ½ W (or shorter) intervals. The original function may be reconstructed exactly from these sampled values by the interpolation defined by Eq.(1). Eq.(1) holds exactly only if s(t) as defined by Eq. (2) for the bandpass case is defined for all values of t from −∞ to +∞. The interpolation error (magnitude of the difference between right and left sides of Eq. (1)) grows as s(t) is truncated to shorter lengths, and as the width of the spectrum of the sampled signal, B, approaches ½ the sampling rate f FIG. 1 shows the error for low-pass interpolation (Eqs. (1) and (2)) for B/W=¾ and ½ (33% and 100% over-sampling, respectively) as a function of the truncation length as measured by N, the number of samples within the truncated interval. FIG. 1 also shows how the interpolation error shrinks dramatically (for large N) as a self-truncating “taper” is applied to the interpolation function. This tapered function is given for the low-pass case where q=1−B/W and m depends on both q and N.
where q=1−B/W. Since interpolation error is dramatically reduced using the “self-truncating” interpolation function, it is logically concluded that the spectrum of s(t) from Eq. (3) is better confined to the band −W to +W than of s(t) from Eq. (2). The same logic applies to the bandpass case since the taper of Eq. (3) (the bracketed factor raised to the power, m) may be used in the bandpass case with similar results. The interpolation waveforms s(t) have the property that the zeros are at the right points so as not to cause intersymbol interference. An example of s(t) is plotted in FIG. 2 In the preferred embodiment, referring to FIG. 5, sampled digital data in a sequence of data samples The sequence of data-weighted waveforms is summed in a computer The computer The output of the waveform generator A number of data channels may be grouped as sub-bands and a digital-to-analog (D/A) converter (not shown) would convert the data to an analog form at a rate consistent with the group bandwidth. Final separation of data channels may then be accomplished by digital filtering. At a receiving location, the transmitted signal, plus any induced noise, is preamplified by a low-noise amplifier In the formation and transmittal of the sharply bandlimited signals for sampled data communications, the waveform generator Operational data interpolation computer The better spectral confinement provided by this invention leads to closer channel spacing and better electromagnetic compatibility among radar, navigation, and communications systems. FIG. 4 depicts a sharply bandlimited keying waveform test configuration Directly sampled and digitized data Within the D/A converter To analyze the performance of the sharply bandlimited keying waveform system (ie., to determine fidelity with the digital sample The digital outputs of the A/D converters In the test configuration It will be understood by those skilled in the art that still other variations and modifications are possible and can be affected without detracting from the scope of the invention as defined by the claims.
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