Classifications

• • H—ELECTRICITY
  • H03—ELECTRONIC CIRCUITRY
  • H03D—DEMODULATION OR TRANSFERENCE OF MODULATION FROM ONE CARRIER TO ANOTHER
  • H03D3/00—Demodulation of angle-, frequency- or phase- modulated oscillations
  • H03D3/02—Demodulation of angle-, frequency- or phase- modulated oscillations by detecting phase difference between two signals obtained from input signal
  • H03D3/04—Demodulation of angle-, frequency- or phase- modulated oscillations by detecting phase difference between two signals obtained from input signal by counting or integrating cycles of oscillations
• • H—ELECTRICITY
  • H03—ELECTRONIC CIRCUITRY
  • H03K—PULSE TECHNIQUE
  • H03K9/00—Demodulating pulses which have been modulated with a continuously-variable signal
  • H03K9/06—Demodulating pulses which have been modulated with a continuously-variable signal of frequency- or rate-modulated pulses
• • H—ELECTRICITY
  • H03—ELECTRONIC CIRCUITRY
  • H03K—PULSE TECHNIQUE
  • H03K9/00—Demodulating pulses which have been modulated with a continuously-variable signal
  • H03K9/08—Demodulating pulses which have been modulated with a continuously-variable signal of duration- or width-mudulated pulses or of duty-cycle modulated pulses

Definitions

• This invention relates to a method and apparatus for detecting and demodulating signals with temporally modulated features, and particularly to frequency modulated signals.
• FM Frequency Modulation
• a sinusoidal carrier signal of constant amplitude and frequency is modulated by an input signal of a lower frequency and of varying amplitude.
• FM thereby produces an output signal that is constant in amplitude, varying in frequency in accordance with the input signal, and within a specified frequency range called the deviation bandwidth.
• the instantaneous amplitude of the input signal is linearly transformed into a change d ⁇ in the instantaneous frequency ⁇ (t) of the carrier frequency ⁇ c .
• frequency demodulation must be performed using an FM demodulator.
• FM demodulators are well known, and consist of devices such as ratio detectors, Foster Seeley discriminators, phase- locked loop detectors, pulse-counting detectors, and quadrature or coincidence detectors. All of these demodulators ⁇ whether implemented as analog or digital apparatus ⁇ pass data to post-processing stages, and ultimately to an output amplifier.
• the Heathkit AJ-1510 Digital FM Tuner employs a digital discrimination technique for demodulating a frequency modulated signal.
• the discriminator is of the pulse position modulation type, is inductorless and diodeless, and contains two integrated circuits: a retriggerable monostable multivibrator, and an operational amplifier.
• An input signal at the retriggerable monostable multivibrator causes it to change states for a fixed period of time, as determined by an RC network to provide a sequence of pulses of constant width and amplitude that are generated at about one-half of the IF rate. Each pulse represents a zero-crossing event.
• Signal information is represented as deviations in the frequency of the zero-crossing pulses from a constant IF frequency.
• the frequency modulated signals typically are amplified and "hard-limited” to produce square waves which have zero- crossings spaced in the same manner as the zero-crossings of the FM signals.
• the square waves are then converted into a sequence of constant width and amplitude pulses, one pulse for each zero-crossing of the modulated input signal.
• Each pulse is integrated (or filtered) and subsequently differentiated to reproduce the modulating input signal information.
• pulse integration demodulators that employ a single one-shot multivibrator that is triggered at each zero-crossing.
• recovery time difficulties are encountered during high frequency operation because the internal delay of the multivibrator approaches the period of the high frequency signals as the operating frequency is increased.
• a source of frequency modulated signals is coupled to a coincidence detector by a first and second signal path.
• the first and second signal paths have unequal signal delay characteristics, so that the coincidence detector provides an output signal that includes a series of constant width pulses, wherein pulse width is determined by a difference in signal delay between the first and second signal paths.
• a low pass filter is coupled to the coincidence detector to recover the signal modulation represented by the series of constant width pulses.
• An apparatus and method is provided for demodulating a frequency modulated (FM), pulse-width modulated (PWM), or other temporally modulated signal.
• modulating signal information is extracted from a modulated signal as numerical information.
• a high gain stage is applied to an incoming FM signal to produce a corresponding sequence of square waves.
• the period between zero-crossings of the square waves is precisely measured and represented numerically using a high-speed clock and at least one counter.
• Numerical period information is then provided to a signal processor that serves to convert the sequence of period measurement values into a demodulated signal with a high signal-to-noise ratio.
• the resulting FM intermediate frequency (IF) signal is "hard-limited" to yield a hard-limited FM IF signal that substantially resembles a sequence of square waves which are provided to a sign detector for detecting zero-crossings.
• the frequency of the local oscillator signal is chosen so as to yield relatively low FM IF frequencies.
• the sign detector is coupled to a pair of gating circuits, each gating circuit being coupled to a respective pulse counter, and to a clock. The gating circuits are alternately enabled in accordance with the instantaneous sign of the hard-limited FM IF signal.
• each sample gating circuit When enabled, each sample gating circuit provides a sequence of clock pulses from the clock to a respective pulse counter. Each pulse counter stores a respective count value that represents the period between zero-crossings of the hard- limited FM IF signal.
• the foregoing elements together constitute a digital discriminator.
• a numerical processor connected to the counters of the digital discriminator, is responsive to the changing respective count values, and reconstructs in real time the original modulating input signal.
• the numerical processor performs calculations upon the signal including: weighting, scaling, impulse response filtering, windowing, and interpolation/decimation. Increasing the rate of the clock yields improved resolution in the reconstructed modulating signal, up to the maximum resolution of the counting circuit. Subsequent digital filtering provides a low pass filter function that effectively eliminates high frequency components.
• the digital demodulator of the invention exploits the linearity of digital processing to provide excellent performance. Since the demodulation method of the invention requires only low level signals and introduces minimal noise, lower total noise levels result, and a high signal-to-noise ratio is achieved. Consequently, the demodulator of the invention can more easily receive weak signals, and suffers fewer "drop-outs", a problem that is now common in fringe reception areas, as well as in dense urban centers. Also, the invention reduces the need for amplification of a received signal, thereby increasing reliability and reception quality. Therefore, at a given level of transmission power, greater transmission range is possible. One potential product area is in satellite broadcast applications; a smaller antenna could be used when the method of the invention is employed within the receiver.
• the invention can be practiced using currently available, relatively inexpensive components. Also, since it is consistent and cooperative with existing modulation standards and transmission formats, the invention actually increases the value of the currently installed base of transmission equipment. Although the invention provides benefits when included in 2-way radio, cellular telephone, and FM broadcast applications, the invention is not limited to a specific frequency band, or to a particular application.
• the demodulation method and apparatus of the invention introduces negligible noise, as contrasted with the levels of noise added by conventional FM demodulation circuitry.
• a so-termed "reciprocal fit count scaling" method is employed that provides better performance than a linear count scaling method, and improved performance with respect to a least-squares-fit, nonlinear count scaling method.
• Such improved performance provides an estimated signal with significantly higher scaling accuracy, lower total harmonic distortion, and an excellent signal-to-noise ratio.
• the reciprocal count scaling method provides an exact analytic solution, and guarantees the most accurate and optimal results attainable from a system of this type.
• Fig. 1 is a block diagram of a digital discriminator cooperative with a numerical processor
• Fig. 1A is a block diagram of a digital discriminator cooperative with a signal processor
• Fig. 1B is a block diagram of a digital discriminator cooperative with a digital to analog converter
• Fig.2 is a schematic diagram of a digital discriminator of the type which may be used in the circuits of Figs. 1, 1A and 1B;
• Fig. 3 is a flow diagram of a process implemented by the numerical processor of Fig. 1;
• Fig. 3A is a flow diagram of a process that includes reciprocal fit count scaling
• Fig. 3B is a flow diagram of a process that includes reciprocal fit count scaling and window functions
• Fig. 3C is a flow diagram of a process that includes a bounds-checking routine and a second order fit
• Fig. 4 is a plot of linear scaled and weighted count values versus the original count values, together with a plot of scaled and weighted count values augmented with a second-order nonlinear term versus the original count values;
• Fig. 5 is a plot of the difference of the linear scaled and weighted count values and the scaled and weighted count values augmented with a second-order nonlinear term, versus the original count values;
• Fig. 6 is a plot of scaled and weighted count values augmented with a second-order nonlinear term versus the original count values, together with a plot of reciprocal fit count values versus the original count values;
• Fig. 7 is a plot of the difference of the scaled and weighted count values augmented with a second-order nonlinear term and the reciprocal fit count values, versus the original count values.
• a digital discriminator 10 is shown in cooperation with a numerical processor 12.
• the digital discriminator 10 utilizes zero-crossing detection and period measurement of a "hard-limited" FM IF signal to recover an associated modulating signal by exploiting the fact that the instantaneous frequency of an FM IF signal is inversely proportional to the instantaneous period of the associated modulating signal.
• Discrimination is accomplished by applying a "hard-limited" FM IF signal to the sign detector 14.
• a hard-limited signal an input signal is amplified and then clipped to provide what is essentially a square wave.
• the sign detector 14 ascertains the instantaneous polarity along each corresponding half-cycle of the FM IF signal, thereby defining the moment of each zero-crossing.
• the period between zero-crossings is determined by providing information regarding the moment of each zero-crossing to gating circuits 16 and 18.
• the gating circuits 16 and 18 are alternately enabled or disabled in accordance with the instantaneous sign of the hard-limited FM IF signal provided by the sign detector 14.
• each sample gating circuits When enabled, each sample gating circuits provides a sequence of clock pulses from the clock 20 to respective pulse counter 16 or 18 until the other pulse counter 18 or 16 is enabled.
• a short sequence of clock pulses between zero-crossings corresponds to a large modulating signal amplitude, while a long sequence of system clock pulses corresponds to a small modulating signal amplitude.
• Each sequence of clock pulses is integrated by a respective counter 22 or 24 to provide a count value that represents the period of a half cycle of the FM IF signal
• the counters 22 and 24 alternately provide count values to the numerical processor 12, which can be a commercially available digital signal processor, such as the 2101 Digital Signal Processor by Analog Devices.
• the counters 22 and 24 alternately provide count values to a signal processor 12' that can perform at least digital-to -analog conversion.
• the output of the signal processor is usable demodulated signal.
• FIG. IB a preferred embodiment of the discriminator 10 of FIG. 1 will now be discussed.
• a hard limited IF FM signal 26 is applied to the primary winding of transformer 28.
• This transformer stage provides the required impedance matching to the preceding circuit stages and dc decoupling or blocking to the succeeding stage.
• the center tap of the secondary of transformer 28 is biased by a reference voltage source 29 at the mid-point of the circuit supply voltage to provide a DC reference voltage.
• the reference voltage source 29 establishes a voltage level about which the oppositely phased voltages developed across the secondary winding of transformer 28 are symmetrical.
• the signal 30 from the transformer 28 is limited in amplitude by small signal diodes 31-36, and is low pass filtered by resistor and capacitor pairs 38, 40 and 42, 44.
• This limited and filtered signal 46 is applied in a differential manner to the inverting and non-inverting inputs of comparator 48.
• Switching hysteresis is provided by applying positive feedback from both Q and outputs via resistors 50 and 52, respectively.
• the comparator outputs Q and produce gate pulses proportional in width to the zero crossings of the FM IF signal. This gate pulse is applied to one of the inputs on each of the NAND gates 54 and 56.
• Clock 58 provides a source of high frequency clock pulses which is similarly applied to the other inputs of NAND gates 54 and 56.
• the resultant output of NAND gates 54 and 56 contain multiple sample clock periods wherein the number of sample clock periods are directly proportional to the width of the gating pulse.
• Comparator 48 outputs Q and are applied to one input of OR gate 60 and 62 this signal is combinatorially or'd with the signal to provide a
• the system shown in the embodiment of FIG. 1B provides complete demodulation of an FM IF signal, in the sense that a voltage proportional and commensurate with the binary pulse-count data is output to the DAC 12.
• Low-pass filtering can then be used to reduce inband noise, and smooth out residual quantization jitter.
• the filters used include, but are not limited to, direct form (DF), finite impulse response (FIR), and infinite impulse response (IIR) filter realizations.
• the direct form filter for example, has the following form.
• A(x), the filter output is the result of the recursion step where previous outputs, A(x-k), are convolved with IIR coefficients a k , and previous inputs are convolved with FIR coefficients b k .
• a low order (e.g. 5-10 zeros and poles) IIR For example, a low order (e.g. 5-10 zeros and poles) IIR
• Butterworth filter can be applied to a signal template, in real time, just prior to signal output to the DAC stage 12.
• a Butterworth filtering technique was chosen due to its exceptionally flat passba d response, and approaches a true "brick-wall" type filter in its digital realization.
• weighting and scaling can be adequately peroormed using simple analog circuitry, as is well-known in the art.
• the numerical processor 12 of Fig. 1 will now be discussed.
• DSP digital signal processing
• DSP chip technology Another important innovation in DSP chip technology is the so-termed single cycle instruction set. This capability allows each instruction in a DSP chip to be executed in one clock cycle, brought about by implementing the instruction sets of DSP chips as part of the architecture itself, rather than in microcode, as is common in most non-DSP processors.
• Parallelism refers to the capability of a signal processing device to carry out more than one operation at a time. For example, data may be read from the parallel data bus via a parallel input/output port, while the address of the incoming data is being placed into the shifter stack and the next program instruction is concurrently being fetched from the instruction stack. Conversely, it is also possible to transmit previous results from the serial port of the processor to the DAC during data processing steps.
• An excellent "pseudocode" example of parallelism in a DSP processor is as follows: fetch an instruction; compute the next instruction's address; perform one or two data transfers; update one or two data address pointers; and perform a computation, all within a single cycle.
• Pelining refers to a process whereby the result (s) of a first operation within the processor are immediately available as input (s) to a second operation, without the added requirement that data be moved via a program step.
• the result of a shifter operation may be directly used as an input to a multiplier accumulator section.
• pipelining is considered only one level deep. Future processors will most likely allow for several levels of pipelining.
• the numerical processor 12 of Fig. 1 receives zero- crossing interval information from the counters 22, 24, and performs a differentiation process, to be described below, on successive interval values to recover modulating amplitude information. Since there are two zero-crossing events in a sinusoidal wave, an instantaneous frequency value F(t) can be recovered by taking the reciprocal of twice the period T(t) between successive zero-crossing events. Thus,
• T(t) N(t) * T clock , (2) where "N(t) " is the number of "counts", i.e., clock pulses, within a given zero-crossing period, and "T clock " is the period of the clock, i.e., the time between clock pulses. Quantization errors e(t) exist due to ambiguities in the pulse counting process. During a clock period, an actual zero-crossing could take place at any point in time from:
• the accuracy of the digitization process is therefore dependent upon the frequency of the clock.
• a typical system clock speed is 50 Megahertz, which results in an uncertainty e of ⁇ 10 nanoseconds, as calculated from equation (3).
• the mean error in e(t) is zero, since the ideal quantization error probability density function is symmetric.
• the standard deviation is approximately 0.29*T clock , which is also the rms value of the uncertainty e(t).
• the rms value of e(t) can also be considered as a measure of signal noise due to digitization. For example, if the maximum period between zero-crossings is quantized using 256 quantizing increments, the peak signal-to-rms-noise ratio would be 0.4%, or about 48 db.
• the actual number of quantizing increments i.e., clock pulses that fit within a zero-crossing period is bounded by the deviation frequency (DF) bandwidth.
• the width of a zero-crossing period is simply the clock frequency divided by twice the quantity "IF frequency ⁇ the DF frequency”.
• N max [ 2T clock ( IF + DF min ) ] -1. (4) while the minimum number of clock pulses in a digitized sample is given by:
• N min [ 2T clock ( IF + DF max ) ] -1 . (5)
• Count values provided to the numerical processor 12 are scaled and weighted, as explained below, to exploit the full n-bit range of the numerical processor.
• a "windowing" process for pulse averaging, using a Rectangular Window, or a Hamming Window, for example, and for providing data filtering and a preliminary treatment of digital quantization errors; and low-pass filtering, for limiting the data to a specific frequency band, and for removing noise, thereby improving the signal-to-noise ratio.
• Data thus processed by the numerical processor 12 is subsequently provided to a digital-to-analog converter (DAC).
• DAC digital-to-analog converter
• A(i) a * N(i) + b (9) where a and b are scaling and weighting constants, respectively, N(i) represents the "i"th time-period count value between zero-crossings "i-1" and "i", and A(i) is the "i"th scaled and weighted count value.
• N(i) represents the "i"th time-period count value between zero-crossings "i-1" and "i”
• A(i) is the "i”th scaled and weighted count value.
• the constants a and b are found using the full-sca le positive (FSP), and full-scale negative (FSN) DSP processor values.
• the FSP and FSN values are determined by the "full-range" n-bit value, e.g., 65,536 for 16 bits, such that FSP is equal to (Full-Range)/2-1, and FSN is equal to -(Full-Range)/2, expressed in a two's complement binary representation.
• a and b are given by:
• a so-termed rectangular averaging window of width M slides over the scaled and weighted count values A(i), where M is the number of count values within the averaging window, and the M count values are averaged together to provide an average scaled and weighted count value A(j) over the last M count values.
• a value A(j) can be generated for each A(i) by advancing the window by one count value to A(i+1), or a value A(j) can be generated for every nth count value A(i+n) to reduce the data rate, thereby allowing more time for other operations.
• Window functions such as the simple window averaging just described are used to pre-condition incoming data.
• Other typical window functions are, for example, of the Hamming or Von Hann type, that generally serve to deemphasize the effect of certain coefficients within a sliding window, while augment the effect of others within the window.
• the Hamming window coefficients w H (n) are of form:
• M 3
• the window can advance by one or more count values, and upon each advance, the inner product of the array w H (m) and the array of values within the window is computed to yield a scalar quantity. To reduce the data rate, the window can advance by more than one value each time it advances.
• the Hamming or Von Hann window function can be used in addition to, or in place of, the simple rectangular window averaging scheme discussed above.
• the method of the invention employs low-pass filtering to reduce inband noise, and smooth out residual quantization jitter.
• the filters used include, but are not limited to, direct form (DF), finite impulse response (FIR), and infinite impulse response (IIR) filter realizations.
• the direct form filter for example, has the following form, where, A(x), the filter output, is the result of the recursion step where previous outputs, A(x - k), are convolved with IIR coefficients a k , and previous inputs are convolved with FIR coefficients b k .
• a low order (e.g. 5-10 zeros and poles) IIR Butterworth filter is applied to a signal template, in real time, just prior to signal output to the
• Fig. 3 illustrates the sequence of processes used to transform the sequence of count values provided by the discriminator 10 of Fig. 1 to the numerical processor 12.
• the values N are first weighted and scaled (90), and then are window averaged (92), thereby reducing the rate of data passed to subsequent calculations.
• a window transformation technique such as a
• the clock rate for measuring zero-crossing intervals is preferably a rate of generally at least 8 times the Nyquist rate of the highest audio frequencies encountered so as to minimize distortion.
• the zero-crossing periods T(t) of equation (1) are given within the limits of count sample quantization uncertainty, i.e., one clock period (e,g., about 100 nanoseconds), by equation (2).
• a so-termed "bounds-checking" routine is used.
• noise manifests itself as count anomalies. These count anomalies occur throughout the full range of count values, including "In-Band Noise", which falls within the range of N min to N max .
• the numerical processor implements the bounds-checking routine, which routine parses through incoming zero-crossing count data, and identifies data which falls outside of the range N max to N max by testing for data below N min and testing for data above N ⁇ . Should a value fall outside of the range of N min to N max , it is assigned a value at a corresponding extremum point, i.e., the FSN or FSP point.
• the bounds- checking routine is shown in Fig. 3C as step 126, occurring after the step of period measurement 124. Steps 128-136 illustrate subsequent steps in a polynomial curve-fitting method, described below.
• Equation (9) in conjunction with incoming binary count data, represents a complete signal demodulation estimation process.
• Equation (9) is the equation of a straight line
• equation (1) is the equation of a reciprocal function. Over a very short region, a straight line can sufficiently model a curve.
• the range of numbers encompassed here is large, suggesting that a "linear fit" might perform well only at the endpoints of the range of the fit, i.e., between N min and N max , and poorly in the middle of this range, i.e., at the linear IF. This can be tested by examining the fit at the value of A(i) where N(i) corresponds to 100 Khz, the IF.
• the FSP Value, FSN Value, and an Intermediate Value are used to generate a second-order nonlinear equation with coefficients that make the nonlinear equation "closest” to the expression of equation (1) in a "Least Squares” sense.
• the coefficients for estimating data in the range N min to N max can be found using a least-squares-fit process, such as one employing the Vandermonde matrix, as can be found in the PC-MATHLAB User's Guide, by the MATHWORKS, October 1990.
• A(N) c 0 + c 1 N + c 2 N 2 , (17) where c 0 , c 1 , and c 2 are the zeroth, first, and second order coefficients respectively, and N is an incoming zero-crossing count value.
• Fig. 4 shows the second order solution in the range of zero-crossing count values from 166 to 250, with the data curve corresponding to the linear equation overlaid as a reference.
• a so-termed "reciprocal fit count scaling" method is employed that provides better performance than the linear count scaling method, and improved performance with respect to the least-squares-fit nonlinear count scaling method.
• Such improved performance provides an estimated signal with significantly higher scaling accuracy, lower total harmonic distortion, and an excellent signal-to-noise ratio.
• the reciprocal count scaling method provides an exact analytic solution, and guarantees the most accurate and optimal results attainable from a system of this type.
• the value of the average instantaneous frequency F(t) is bounded by the deviation frequency extrema DF max and DF min , where DF min is equal to -DF max .
• the number of counts N(t) within a period T(t) is directly proportional to the reciprocal of the product of the system clock period T clock with the instantaneous deviation frequency "IF + DF(t)".
• N(t) [ 2T clock (IF + DF(t) ) ]-1. (18)
• N max [ 2T clock (IF + DF min ) ]-1. (4)
• N min [ 2T clock (IF + DF max ) ] -1 .
• Count values N(t) are provided to the numerical processor 12 that scales and weights the count values N(t) according to a set of scaling and weighting coefficients to provide scaled and weighted values.
• the numerical processor employs its full "n-bit" range, and may apply a linear fit method, a least squares fit method, or a reciprocal fit (RF) method.
• A(i) a/N(i) + b (19)
• the inverse slope parameter a and the y-intercept parameter b represent scaling and weighting coefficients.
• N(i) represents the "i"th time-period sample count value between zero-crossings "i-l" and "i”
• A(i) represents the "i"th scaled and weighted count value, with maximum/minimum extrema of ⁇ 2 15 .
• Equation (19) in conjunction with the incoming binary count data and a precalculated knowledge of the count extrema, represents a complete signal demodulation method. One need only to calculate the values of a and b.
• the parameters a and b are found using full-scale positive (FSP) and full-scale negative (FSN) numerical processor values.
• the FSP and FSN values of the numerical processor are determined by the "full-range” n-bit value, i.e., 65536 for 16 bits, where FSP is equal to "full range/2 - 1", and FSN is equal to "-full range/2".
• a and b are evaluated by
• A(i) [FSP/ (N min -N max ] * ⁇ (2*N min *N max /N i ) - (N min +N min +N max ) ⁇ .
• the least squares fit nonlinear scaling method provides a very high level of signal resolution, making the theoretically predicted difference between the least squares method and the exact reciprocal fit scaling method apparently inconsequential.
• the average theoretical error associated with the least squares approximation as compared to the reciprocal fit scaling method is 0.20%, i.e., 0.02 dB difference, while the maximum theoretical error associated with any given data point is just 1.0%, i.e., 0.1 dB difference. While these theoretical results might lead one's intuition to assume that the two methods are effectively equivalent, in practice, the reciprocal fit scaling method provides an improvement in signal-to-noise ratio of approximately 1 dB. Thus, since the reciprocal fit scaling method does not incur an implementation penalty, the optimal choice is the reciprocal fit scaling method.
• Figs. 3A and 3B show how the reciprocal fit steps 102 and 112, respectively, occur in two exemplary embodiments of the method of the invention. Steps 100, 104-108, 110, and

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