Complex digital demodulator employing Chebychev-approximation derived synthetic sinusoid generation
First Claim
1. A method of demodulating a digital signal by a reference frequency signal, said digital signal including a series of digital values, said reference frequency signal including a series of phase angle values, each of said digital values having a corresponding one of said phase angle values, said method comprising the steps of:
- a) computing, with computing means, a numerical approximation of a sinusoidal function of each phase angle value;
b) multiplying, with a multiplier, each digital sample by the numerical approximation of the sinusoidal function of the phase angle corresponding to said each digital value, to produce a series of products of said sinusoidal function; and
c) digitally filtering, with a filter, the series of products.
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Abstract
To demonstrate a signal, the signal is sampled and each sample of the signal is multiplied by the sine and the cosine of a phase angle indicating when the sample was taken from the signal. The sinusoidal signal for producing an in-phase demodulated signal is Chebychev-approximation derived and computed as a selected even or odd polynomial, depending on whether the phase angle falls within one of a plurality of angular ranges. So that the error in the synthetic sinusoid is minimax and so that the even and odd polynomials have similar computational complexity, the angular ranges for the even polynomial exceed the angular ranges for the odd polynomial. Preferably, the sinusoid for producing a quadrature-phase demodulated signal is computed as a differential of the sinusoid spliced from the odd and even polynomials. Therefore the quadrature-phase demodulated signal can be provided with a minimal increase in computational complexity. The demodulation method permits a signal to be demodulated by a reference frequency signal to produce a demodulated digital signal that is synchronized to a system clock. The system clock need not be synchronized to the reference frequency signal. The demodulation method is computationally efficient, and permits a digital signal processor to be programmed for demodulating an angular rate signal from a quartz angular rate sensor vibrating at about 10 kilohertz.
19 Citations
28 Claims
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1. A method of demodulating a digital signal by a reference frequency signal, said digital signal including a series of digital values, said reference frequency signal including a series of phase angle values, each of said digital values having a corresponding one of said phase angle values, said method comprising the steps of:
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a) computing, with computing means, a numerical approximation of a sinusoidal function of each phase angle value; b) multiplying, with a multiplier, each digital sample by the numerical approximation of the sinusoidal function of the phase angle corresponding to said each digital value, to produce a series of products of said sinusoidal function; and c) digitally filtering, with a filter, the series of products. - View Dependent Claims (2, 3, 4, 5)
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6. A method of demodulating a digital signal by a reference frequency signal, said digital signal including a series of digital values, said reference frequency signal including a series of phase angle values, each of said digital values having a corresponding one of said phase angle values, said method comprising the steps of:
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a) computing, with computing means, a numerical approximation of a sinusoidal function of each phase angle value; and b) multiplying, with a multiplier, each digital value by the numerical approximation of said sinusoidal function of the phase angle corresponding to said each digital value, to produce a series of products of said sinusoidal function; wherein said numerical approximation is computed by comparing, with a comparator, said each phase angle to predefined angular limits, transforming, with transforming means, said each phase angle by a linear transformation to produce a transformed phase angle in response to the comparing of said phase angle to the predefined angular limits, and computing, with computing means, said numerical approximation of said sinusoidal function as either an even function or an odd function of said transformed phase angle in response to the comparing of said each phase angle to the predefined angular limits. - View Dependent Claims (7)
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8. A method of demodulating an analog signal by a reference frequency signal to produce a demodulated signal, said method comprising the steps of:
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a) sampling, with a sampler, said analog signal to produce a digital sample; b) determining, with a determiner, a phase angle of said reference frequency signal existing when said analog signal is sampled to produce said digital sample; c) computing, with computing means, a numerical approximation of a sinusoidal function of said phase angle; and d) multiplying, with a multiplier, said digital sample by said numerical approximation of said sinusoidal function of said phase angle, to produce a product that is a sample of said demodulated signal. - View Dependent Claims (9, 10, 11, 12, 13, 14, 15, 16)
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17. A method of demodulating a digital signal by a reference frequency signal, said digital signal including a series of digital values, said reference frequency signal including a series of phase angle values, each of said digital values having a corresponding one of said phase angle values, said method comprising the steps of:
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a) computing, with computing means, a numerical approximation of a pair of sinusoidal functions of each phase angle value, said pair of sinusoidal functions being in phase quadrature with each other; and b) multiplying, with a multiplier, each digital value by the numerical approximation of each sinusoidal function of the phase angle corresponding to said each digital value to produce a series of products of each of said sinusoidal functions. - View Dependent Claims (18, 19, 20, 21, 22, 23)
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24. A system for demodulating an analog signal by a reference frequency signal, and producing a digitized demodulated signal synchronized to a high-speed system clock, said system comprising, in combination:
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an analog-to-digital converter for producing digital samples of said analog signal at a predetermined sampling frequency synchronized to said system clock; a counter clocked by said system clock for counting during at least one cycle of said system clock; means including a set of latches connected to said counter and responsive to said reference frequency signal for determining a number of counts of said counter in a period of said reference frequency, and determining a number of counts into a period of said reference frequency when said analog signal is sampled by said analog-to-digital converter; means for computing a phase angle value for each of said digital samples from said number of counts of said counter in a period of said reference frequency, and said number of counts into a period of said reference frequency when said analog signal is sampled by said analog-to-digital converter; means for computing a numerical approximation of a pair of sinusoidal functions of each phase angle value, said pair of sinusoidal functions being in phase quadrature with each other; means for multiplying each digital sample by the numerical approximation of each sinusoidal function of the phase angle for said each digital sample to produce a series of products of each of said sinusoidal functions; a first digital filter for digitally filtering the series of products of a first one of said sinusoidal functions; and a second digital filter for digitally filtering the series of products of a second one of said sinusoidal functions. - View Dependent Claims (25, 26, 27, 28)
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Specification