DE4327275C2 - Process for the digital processing of narrowband signals with variable center frequency - Google Patents

Description

The invention relates to a method that uses narrowband signals digitally processed and especially for digital determination the center frequency of these narrowband signals is suitable. Such narrow-band signals occur, for example, at Ground speed measurement based on the Doppler principle.

In order to be able to process narrowband signals digitally, with conventional solutions, the sampling frequency to at least twice the value of the ma occurring in the signal to be sampled ximal frequency set. The factor 2 results from the Shannon's sampling theorem and causes an overlap the repetitive frequency bands is avoided. Varies the maximum frequency of the signal to be sampled changes greatly the number of sampling points per vibration is equally strong. This means that if there are too many sampling points per swine signal evaluation takes an unnecessarily long time. The effectiveness decreases accordingly. Furthermore, the numerical In stability to. These effects are exemplarily based on the au toregressive procedure (AR procedure) and based on the fast Fourier transform (FFT) explained below.

In the case of autoregressive methods, these are methods in which it is checked whether there is a connection between two quantities x _n and y _n , without one quantity being deterministically dependent on the other, the numerical instabilities can be explained by the fact that the Difference between two successive samples can no longer be resolved. The reason is either quantization effects of the analog-digital converter or noise components in the signal. In the publication by HV Poor, R. Vÿayan, E. Arikan: "High-speed statistical signal processing: the Levinson and Schur problems", Procee dings of the 1990 Bilkent International Conference on New Trends in Communication Control and Signal Processing, Ankara, Turkey, July 1990 deals extensively with the problem of numerical instability in autoregressive methods. In the case of a low center frequency compared to the sampling frequency, a solution is proposed in which the model parameters converge to constants, which in turn depend on the statistical properties of the respective process. Another disadvantage is the inaccuracy and the high amount of computing power.

In the FFT there are instabilities as they occur in the AR procedure kick, not to be expected. However, the number increases of the sampling points per oscillation the spectral resolution of the Useful signal. As a result, the Spectral analysis of the useful signal becomes less precise.

Another problem when evaluating a narrowband Si gnals lies in the noise and the presence of interference signals. If you want to find out the center frequency of the narrowband signal filter, you need a filter with a variable pass frequency, which means that every time the center frequency changes the filter coefficients have to be recalculated.

For real-time systems, complex and therefore expensive pro are cessors required.

The object of the invention is to produce a narrowband signal prepare that its center frequency, which varies greatly, is exactly determinable.  

The object is achieved by a method and a Arrangement according to claims 1 and 2 and 6 solved.

Advantageous further developments of the invention can be found in characterized in the dependent claims.

The center frequency of a narrowband signal is digi determined talem ways. For this purpose, the sampling fre frequency at which the narrowband signal is discretized regulated that the number of sampling points per oscillation of the narrow-band signal to be sampled a predetermined values do not leave area.

A pre-filter for suppression is advantageously coupled the interference signals to the adapted sampling frequency. So you can a very simple bandpass filter around the center frequency realize. The effort of an adaptive filter is therefore up limited to a minimum.

The invention will be described in more detail below with reference to the drawings explained.

FIGS. 1a and b shows a typical narrow-band signal in the time and frequency domains.

Fig. 2 shows a basic block diagram for a re gel method with block-by-block determination of the center frequency f _M.

FIG. 3 shows a schematic block diagram of another control method for sequential determination of the center frequency f _M.

Fig. 4 shows a basic block diagram for another control method using an analog filter.

FIGS. 1a and 1b show a typical narrow-band Si gnal in the time and frequency range. The signal has a maximum at the center frequency f _M. The center frequency f _M can vary. The lower limit frequency f _-3dB and the upper limit frequency f _{+ 3dB} are frequencies which the spectrum has with a 3 dB signal drop in relation to the maximum. The bandwidth B results from:

B = f _{+ 3dB} - f _-3dB

The bandwidth B in relation to the center frequency f _M is referred to as the relative bandwidth b = B / f _M. The interference signal _spectrum lies below and above the fundamental frequencies f _-3dB and f _{+ 3dB} .

The above-mentioned characteristics of the spectrum require sophisticated digital signal processing in order to determine an excellent center frequency f _M with high accuracy.

Since the center frequency f _{M is} variable, it is necessary to regulate the sampling frequency f₀ in order to meet the requirement k _m = k _soll . For this purpose, a routine for determining the center frequency f _M can serve as a measuring element. Additional calculations, such as the determination of the bandwidth or the signal-to-interference ratio for further evaluation of the narrowband signal, therefore automatically have the numerically optimal number of sampling points per oscillation as a basis.

This method is also readily applicable to the determination of the speed at, working on the Doppler principle, measuring devices. In the case of the Doppler signals, the method is simplified in that the relative bandwidth b remains constant. This means that the controlled sampling frequency f₀ can be used directly as a result variable proportional to the Doppler frequency f _d and thus to the center frequency f _M , provided that the resolution of the setting meets the required accuracy. However, the property of the constant relative bandwidth b is not a general requirement for the described method.

The block diagram in Fig. 2 shows a possible type of evaluation of the narrowband signal x (t). The evaluation takes place here in blocks, ie if the analog-digital converter (AD converter) 3 b has a complete data set - for example a discretized oscillation - ready, the center frequency f _M and the relative center frequency k _m can be calculated. This determination represents the measuring element 1 of the control loop.

FFT or autoregressive algorithms according to Burg or Marple [1] are examples of suitable methods for this. The FFT calculates nodes of the frequency spectrum. The maximum can then simply be taken from the support points in the useful signal spectrum, or the support points are expediently interpolated by a suitable function. The parameters of the interpolated function can then be used to infer the relative center frequency k _m . The algorithm according to Burg or Marple, on the other hand, supplies the AR coefficients of the underlying signal model, according to the z range

The maximum of the magnitude spectrum || G (z) ² || then delivers the rela tive center frequency k _m .

The specific in measuring element 1 relative center frequency is so then km _to k with the target ratio (also called setpoint identified net) compared. This quantity k _nominal indicates the desired number of sampling points per oscillation. A ratio of 3. . . 10 sampling points per oscillation, which values of 0.3. . . 0.1 for k _{should be found} to be favorable. The difference between the relative target frequency (the target ratio) _to k and the relative center frequency (the actual ratio) km is supplied as a control deviation .DELTA.k the controller. 2 Different versions of the controller are conceivable here. When using a pure I controller, the following control algorithm can be set up in a simplified manner:

Δf: = Δk _* f₀
f₀: = f₀-γΔf
T₀: = 1 / f₀
N₀: = f _{ref *} T₀

With:

.Delta..sub.k: deviation _should k frequency reference of the relative
f₀: sampling frequency
γ: integration constant
T₀: sampling period
N₀: counter reading of the programmable counter

The output variable of the controller is the counter reading N₀, with which the subsequent counter 3 a is programmed. The limits of the programmable counter 3 a, which are predetermined by the maximum and minimum counter reading, are not taken into account in the illustrated algorithm. The principle of operation is not affected, however, if the limits are outside the desired measuring range.

The programmable counter 3 a thus forms together with the AD converter, which is clocked by the sampling frequency f₀, the actuator 3 a + 3 b of the control loop. A special feature when using a programmable counter 3 a is that the output variable from the programmable counter 3 a represents a frequency, namely the sampling frequency f₀, while the input variable is a counter reading that is inversely proportional to the output variable. This compensates for large inaccuracies in the setting of low frequencies (f → 0 Hz), as would arise, for example, when using a simple voltage-frequency converter. The programmable counter 3 a is clocked at the clock frequency f _ref , which is provided by an oscillator. The maximum sampling frequency f _0max is _limited by the clock frequency f _ref or by the required setting _accuracy .

FIG. 3 shows another possible type of analysis of the narrowband signal, wherein the evaluation is performed here sequentially. This means that an entire data set of the discrete narrowband signal x (z) is no longer required for determining the center frequency as before. It is now carried out using a recursive calculation method, hereinafter also referred to as a sequential optimization routine. The essential difference from the system according to FIG. 2 is the design of the measuring element 1 and the controller 2 . The procedure is based on recursive identification methods, e.g. B. as described in [3]. Accordingly, the parameters of a sequential filter are optimized such that the mean energy of the filter output signal ε (z) assumes an extreme for a digital narrowband signal x (z), the sampling frequency f die remaining constant. However, since in the present case the sampling period T₀ or the division ratio N₀ should be the optimization variable, a different approach is taken. In contrast to the known recursive identification methods, the filter coefficients are a ₀ . . . a _n and b ₀ . . . b _m left constant and vice versa, the sampling period T₀ is optimized so that the mean energy of the filter output signal ε (z) in turn assumes an extreme. The optimization methods in controller 2 according to [3] can be adopted in principle and even simplify one-dimensional optimization. The sequential filter with constant coefficients is generally given by its z-transfer function:

b₀,. . ., b _m , a₁,. . ., a _n = const

The choice of constant coefficients b₀. . . b _m , a₁. . . a _n influences the convergence behavior of the filter and must be made dependent on the shape of the respective signal spectrum.

By choosing the filter coefficient is implicitly also the relative reference frequency (target ratio) k _to set. In analogy to the block-wise method, the sequential filter 1 can be called a measuring element. The filter output signal ε (z) and one or more states of the filter are then fed to the recursive optimization routine, which speaks to the actual controller 2 in the present control loop. As described, the recursive optimization routine links the incoming quantities to an optimized sampling period T₀ or an optimized division ratio N₀. The following actuator, consisting of programmable counter 3 a and AD converter 3 b is identical to the actuator and the AD converter of the block-wise method already described above. It is advantageous in the method described in FIG. 3 that after each sampling point a currently calculated division ratio N₀ for the programmable counter 3 a is available and thus a better adaptation of the sampling frequency f₀ is achieved. Otherwise, the same options are available as for block-by-block evaluation. If you set the denominator coefficients a₁,. . ., a _n = 0, the IIR (Infinit Impulse Response) filter is reduced to an FIR (Finite Impulse Response) filter. Depending on the desired slope and stability of the filter, either the IIR or the FIR filter must be selected. The order of the transfer function influences the computing time. This must also be taken into account when dimensioning the filter.

In addition to the block diagrams described in FIGS . 2 and 3, a digital pre-filter 4 between the A / D converter 3 b and the measuring element 1 or the measuring element / controller unit 1 + can be used to increase the accuracy and the error reduction 2 can be set. The pre-filters can either be integrated as hardware (additional adder necessary) or as software. The adaptive control of the sampling frequency f₀ makes it possible to couple the pre-filter to the sampling frequency by again keeping the coefficients of the filter constant. So z. B. realize a very simple bandpass filter that even requires only one addition per sampling point in arithmetic operations. The filter, a notch filter with the Z transfer function

F (z) = 1 - Z²,

has the shape of a semisine with zero digits at 0 and 0.5 in relation to the sampling frequency f₀ in the magnitude spectrum. If the sampling frequency f O to 4 times the center frequency f _M Gere gel, _should k = 0.25, so the filter curve is completely symmetrical to the measuring signal, with the result that the signal also symmetrical to the center frequency f _M is attenuated. Another advantage of the inventive regulation of the sampling frequency f₀ is that the otherwise computational problem of adaptive filtering can be considerably simplified.

The described method of adaptive sampling frequency f₀ be it is necessary to consider aliasing effects separately. Here is to be understood as the phenomenon that frequency components of the analog signal above half the sampling frequency f₀ / 2 im hereinafter also called the cut-off frequency - in the form of a mixed product can appear in the baseband. The following points are here considered.

• a) adaptive anti-aliasing filter,
• b) correct initialization of the sampling frequency f₀,
• c) Parallel procedure to increase reliability in a curved condition

a) Adaptive anti-aliasing filter

The anti-aliasing filter is a steep low-pass filter that Interference signals suppressed above the cutoff frequency. Are sturgeon signals above the cutoff frequency cannot be expected, then usually do without the adaptive anti-aliasing filter will. However, with interference signals above the To calculate the cutoff frequency, an anti-aliasing filter is included adaptive cut-off frequency required, because with the described Process the sampling frequency and thus also the cutoff frequency varies. So-called AD converters are particularly suitable here called sigma-delta converters, in which the oversam pling principle the anti-aliasing filter often becomes obsolete or at least a very simple adaptive anti-aliasing filter lower order is sufficient. You can achieve the same effect with so-called switched capacitor filters, whose corner frequency with an approx. 50 . . 100 times higher clock is controlled and the  can accordingly be coupled to the sampling rate. A further advantageous use of switched capacitor filters is described under c3).

b) Correct initialization of the sampling frequency

The described method of the adaptive sampling frequency requires a correct initialization of the sampling frequency at the time of switching on. In connection with aliasing effects, it must in particular be prevented that the cut-off frequency at the time of switching on is below the useful signal frequency spectrum. For this reason, a separate initialization routine is necessary, which has the highest required sampling frequency as the start value and can therefore safely converge into the steady state k _m = k _should .

c) Parallel procedure to increase reliability in a curved condition

Even in the steady state of the regulated sampling frequency, it cannot be completely ruled out that the cut-off frequency will fall below the useful signal frequencies due to some interference and thus lead to aliasing effects or even to a failure of the system. In order to increase the reliability, some parallel methods are proposed below, all of which can also be checked in the steady state to determine that the cutoff frequency is above the useful signal frequencies. All parallel methods deliver a redundant center frequency _m as comparison value, which is not as precise as in the method according to FIG. 2 or FIG. 3, but is determined independently of the regulated sampling frequency. If the redundant center frequency _m and the center frequency f _M deviate from each other to a certain extent, the initialization routine described under b) is jumped to immediately. In the simplest case, the decision about this can be made by means of a defined threshold value (e.g. maximum deviation of + 10%), or special estimation methods are used, e.g. B. the maximum Li kelihood method or the Kalman filter.

c1) Block-by-block initialization routine in parallel operation

This method requires the least additional effort from all described parallel processes. As the central routine, a block-wise routine for determining the relative center frequency k _m - as described in FIG. 2 - is used, which can generally be implemented in the same signal processor. Externally, only an additional AD converter is required, but the sampling frequency is now not variable, but is constantly set to the highest necessary value. After a data set has been read in, the relative center frequency k _{m is} determined with the routine. If k _{m is} below k _should , the same data record is used again, but now only with every 2nd data point. A software-based division of the sampling rate is thereby achieved. The process is repeated (division by 3, by 4, etc.) until k _{m is} above k _target or until the divided data set falls below a minimum length. In the first case, the redundant center frequency _m determined in parallel can be compared with the center frequency f _M , in the second case the frequency 0 is assumed to be the redundant center frequency _m .

c2) Phase Locked Loop (PLL)

The PLL is state of the art and z. B. sufficiently written in [4]. Of all the parallel processes described, the PLL works the least precisely. Especially with strong frequency changes of the Doppler signal, at frequencies going towards 0 Hz or even with strong disturbances outside the useful signal spectrum, the PLL can easily "snap". Nevertheless, the procedure should be mentioned here because it is widespread. It is important for the present application to use a PLL with a frequency-sensitive phase detector, ie with an arbitrarily large "capture range". If the frequency of the PLL, which represents the redundant center frequency _m determined in parallel, is to be compared with the center frequency f _{M of} the main routine, two additional counters are expediently used, whose counter readings are then read out by the signal processor at the same time intervals.

c3) Filtering the narrowband signal with switched capacitor filters (SC filtering)

Of all the parallel methods mentioned, the filtering with SC filters does require the greatest additional effort, but it also achieves approximately good accuracy like the methods described in FIG. 2 or FIG. 3. The filtering with SC filters can therefore also be carried out independently Procedure, cf. Fig. 4, are used, and even then require a lower implementation complexity than the method of FIG. 2 or FIG. 3.

So-called SC filters are analog active filters in which ent speaking feedback resistances by switched capacitance ten be replaced. The switched capacities have one equivalent ohmic resistance that is inversely proportional to the switching frequency (see e.g. [4]). So the SC filters are on the one hand analog filters, but also have to pass through the switched capacities, especially with regard to aliasing effects hits, can also be considered as scanning systems. By ent speaking wiring of the analog filter is achieved that the Corner or center frequencies of the filters to the switching frequency can be coupled. This fact is shown here filtering with SC filters.

The method is described in FIG. 4 as an independent method and, like the method according to FIG. 3, is based on a recursive optimization routine. In contrast to the method according to FIG. 3, however, the digital sequential filter is swapped out of the signal processor and replaced by a suitable SC filter 1 , whose Laplace transfer function is generally composed of several biquadratic elements:

The choice of constant coefficients Q _b1 . . . Q _bm , Q _a1 . . . Q _an , b₁. . . b _m and a₁. . . a _n influences the convergence behavior of the optimization routine and must be made dependent on the shape of the respective Doppler spectrum. A change in the switching frequency accordingly only changes the characteristic resonance frequency ω₀, ie the frequency response of the filter is stretched on the frequency axis in proportion to the switching frequency. Via a control loop, the switching frequency of the SC filter is now regulated according to an optimization criterion and thus simultaneously serves as a proportional result variable for the center frequency f _{M of} the narrowband signal. The analog filtering of the narrowband signal eliminates the computational filter routines, so that the signal processor can be replaced by a more cost-effective microcontroller. The AD converter for the narrowband signal is also omitted, since the SC filter already filters the analog narrowband signal. The states of the SC filter required by the recursive optimization routine, which can be referred to as a measuring element in the control loop, are supplied to the microcontroller. It should be noted that the states in this case represent analog signals and therefore still have to be converted digitally. The AD converters integrated in the microcontroller can be used for this, which generally only have a resolution of 8 bits, which is sufficient for this purpose. The microcontroller has the sole task of the controller. It calculates an optimal sampling frequency f₀ from the filter states according to the recursive identification methods [3] mentioned above, which corresponds to a switching frequency for the SC filter under the additional condition that the mean energy of the filter output ε (t) assumes an extreme. The calculation is controlled by the sampling frequency f₀ itself, ie after the relevant period T₀ = 1 / f₀, an interrupt is triggered in the microcontroller and the calculation is started. Since the switching frequency of an SC filter is usually 50-100 times above the center or corner frequency of the filter, a calculation at time intervals of integer multiples v of T₀ is also sufficient as long as the sampling theorem and thus the condition f₀ / (2 v) <f _{m is} satisfied. This measure allows the required computing power of the microcontroller to be reduced to a minimum. The calculated sampling frequency f₀ is finally according to

N₀ = f _ref / f₀

converted into a meter reading. This is used to program the following programmable counter 3 a, which thus represents the actuator in the control loop. The output of the programmable Zäh coupler 3 a is again the sampling frequency fo at which the SC-Fil is driven ter. When used as a parallel system, this frequency can control two counters together with the sampling frequency, which are read at constant time intervals by the superordinate signal processor and their counts are then compared. Finally, it should also be mentioned that the Mikrocon troller and the programmable counter 3 a can also be replaced by a corresponding analog circuit consisting of multiplication, analog controllers and a voltage-frequency converter. At a comparable cost, this solution, however, only allows a much less precise control, especially as far as the control for frequencies f → 0 Hz is concerned.

The process for digital processing of narrowband signals was gete using the example of a speed measuring device continuous A microwave transmitter with a serves as the signal source Carrier frequency of 24 GHz, which has a wavelength λ = 1.25 cm corresponds. After demodulation one was speed over the ground (0 ... 300 km / h) proportional LF frequency between 0 and approx. 10 kHz to measure. The signal to noise ratio (ratio from useful signal to interference signal) is typically included 20th . . 30 dB.

The method according to the invention is suitable for all measuring tasks ben where there is a narrow-band measurement signal.  

literature

[1] SM Kay, SL Marple, Spectrum analysis - A modern per spective. Prc. IEEE, vol. 69, no. 11, pp 1380-1419, 1981.
[2] HV Poor, R. Vÿayan, E. Arikan: High-speed statistical signal processing: the Levinson and Schur problems. Proceedings of the International Conference on New Trends in Communication, Control and Signal Processing, Anakara, July 1990.
[3] T. Söderström, L. Ljung, I. Gustavsson: A theoretical analysis of recursive identificatoin mehtods, Automatika, vol. 14, pp 231-244, 1978.
[4] U. Tietze, Ch. Schenk, semiconductor circuit technology, Springer publisher, 9th edition 1991.

Claims (7)

1. Method for determining the actual center frequency from a narrow-band signal x (t),

• a) in which the narrowband signal x (t) is converted into a digital signal x (z) by sampling at a first sampling frequency f₀,
• b) at which a center frequency f _{M of} the digital signal x (z) is determined,
• c) in which the quantity k _m = f _M / f₀ _is compared with a predetermined target value k _soll ,
• d) in which the narrowband signal x (t) is sampled at a second sampling frequency f₀ 'which differs from the first sampling frequency f₀, provided that the variable k _m deviates from the target value k _soll ,
• e) in which the process steps b) to d) are repeated until the quantity k _m corresponds to the target value k _soll or the condition | k _m -k _soll | <ε is sufficient, where ε denotes a predeterminable threshold value and
• f) at which the last-determined center frequency f _{m is taken} as the actual center frequency.

2. Method for determining the actual center frequency from a narrow-band signal x (t),

• a) in which the narrowband signal x (t) is converted into a digital signal x (z) by sampling at a first sampling frequency f₀,
• b) in which an error signal ε (z) is generated with the digital signal x (z) and a filter with constant filter coefficients,
• c) in which the narrowband signal x (t) is sampled at a second sampling frequency f₀ which differs from the first sampling frequency f₀,
• d) in which process steps b) and c) are repeated until the mean square of the error signal ε (z) assumes a minimum,
• e) at which the last generated sampling frequency f₀ 'is taken as a measure of the actual center frequency.

3. The method according to claim 1 or 2, in which the narrowband signal x (t) is converted into a digital signal x (z) by means of an analog-digital converter ( 3 b). 4. The method according to any one of the preceding claims,

• - in which the digital signal x (z) is pre-filtered and
• - in which the filter frequency limits of the pre-filtering depend on the sampling frequency f₀.

5. The method according to claim 1 or 2,

• in which the narrowband signal x (t) is additionally used to generate a third frequency f _vco by means of a voltage-controlled oscillator,
• - In addition, the third frequency f _vco is included in the determination of the second sampling frequency f₀ '.

6. Arrangement for determining the center frequency from a narrowband signal (x (t)),

• - In which a switched capacitor filter ( 1 ) is provided, to which the narrowband signal (x (t)) is present and which is sampled at a sampling frequency f₀,
• a first analog / digital converter is provided, which is used to digitize the output signal (ε (t)) supplied by the switched capacitor filter ( 1 ),
• a second analog / digital converter is provided, which is used to digitize the filter states,
• a computing unit is provided which uses a recursive optimization routine to determine a new sampling frequency f₀ which is present at the output of the computing unit,
• - At which the sampling frequency f₀ is a measure of the center frequency.

7. Arrangement according to claim 6,

• - in which the recursive optimization routine has the Gaussian principle of least squares.