JP2001045081A - Signal processing method - Google Patents

Abstract

PROBLEM TO BE SOLVED: To apply filtering and complex data processing to sampling data with a very simple processing by applying under-sampling to a signal resulting from modulating a carrier signal with an object signal. SOLUTION: A modulated signal is sampled with a sampling frequency fs where a center frequency f0 of an object signal is related to the frequency fs as fs=4f0/(4k±1) and each of sampling data is distributed into a real part and an imaginary part one by one. The sign of the real part and the imaginary part is inverted at an interval of one and low pass filtering is applied to them. In the low pass filter arithmetic operation where it is carried out by inverting the sign atternately, a filter coefficient of one low pass filter is assigned to the real part and the imaginary part respectively which are multiplied by the input data, the result of multiplications is collected for each real part and imaginary parts to obtain real part data and imaginary part data.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

The present invention relates to a signal processing method for extracting a target signal superimposed on a carrier signal as complex data.

[0002]

2. Description of the Related Art In a radio communication system or the like, data is generally handled as a complex number. In order to obtain complex data from a received signal, a quadrature detection method in which two analog mixers are used, and two types of sine waves having the same frequency as the carrier are multiplied as a reference signal has conventionally been used. FIG. 25 shows a block diagram of a receiving apparatus using the two analog mixers.

The above two types of signals are signals whose phases are shifted by 90 degrees, and usually use cosine and sine signals. At the output of the mixer, which is a multiplier, a signal having a spectrum appears near the frequency of zero and near the frequency twice the frequency of the carrier. By removing the double frequency component with a low-pass filter, it is possible to extract only a baseband signal near zero frequency.

[0004]

However, as long as a mixer which is an analog element is used, the real number channel I (in
-Phase: in-phase component), imaginary channel Q (qua
It becomes very difficult to match the phases and amplitudes of the signals of both channels (i.e., the quadrature component).
In addition, there is a problem of characteristic degradation due to variations in characteristics of analog parts, temperature changes, and aging.

Therefore, it is conceivable to perform A / D conversion at the analog front end stage and demodulate the target signal by digital processing. However, direct sampling at a frequency higher than twice the carrier frequency requires a large amount of data. Undersampling at a frequency lower than twice the carrier frequency is conceivable due to an increase in the hardware scale and the like.

However, since an undersampled discrete-time signal contains many aliasing spectra, it is necessary to perform steep filtering to remove the aliasing spectrum. Also, converting a sampled real-valued signal into complex data requires an extremely complicated exponent operation. In order to process these operations in real time, there is a problem that an extremely high-speed processing device is required.

It is an object of the present invention to provide a signal processing method capable of filtering a signal sampled by undersampling by extremely simple processing and converting the signal into complex data.

A further object of the present invention is to provide a signal processing method capable of filtering a signal sampled at a frequency at least twice the highest frequency of the signal by extremely simple processing and converting the signal into complex data. I do.

[0009]

According to a first aspect of the present invention, there is provided a method for converting sampling data sampled at a sampling frequency f _S such that the center frequency f ₀ of the target signal is mapped to f ₀ = ± f _S / 4. A branching process of sequentially inputting and alternately branching input sampling data into a real part and an imaginary part; a shift processing of inverting the sign of the input sampling data every other in the real part and the imaginary part; a low-pass filter Are alternately multiplied one by one with the shifted sampling data of the real part and the sampling data of the imaginary part, and the multiplication results are totaled for each of the real part and the imaginary part. Complexing processing.

[0010] invention of claim 2 is the invention of claim 1, the sampling data to which the sequentially input, to the carrier frequency f _C, k = 0, 1, 2, as ..., f
_{S = 4f C / (4k +} 1) or f _S = 4f _C / (4k
+3) is characterized by being sampling data sampled at a sampling frequency f _S that becomes +3).

According to a third aspect of the present invention, in the first and second aspects, the low-pass filter has an even filter length.

According to a fourth aspect of the present invention, in the first and second aspects of the invention, the low-pass filter has an odd filter length.

The present invention is to restore a target signal superimposed on a carrier as shown in FIG. 1A as a discrete time signal. This target signal is on the frequency axis
It appears as a spectrum centered on the carrier frequency as shown in FIG. This signal is, for example, f _S = 4f
_When sampling is performed at a sampling frequency f _S that becomes ₀ , a spectrum as shown in FIG. 2A is mapped on the frequency axis. The hatched spectrum is extracted and restored. In this figure, the spectrum mapped to 0 to π is restored.
May be restored.
Further, signals, such as, but spectrum is mapped to the undersampling 0~π at f _S = 4f _0/3 to become such a sampling frequency f _S is inverted, which was restored by reversed again in operation Is also good.

This spectrum can be expressed as f _s =
Since it is sampled at 4f ₀ , the sampling points are four points (+ I, + Q, -I, -Q) as shown on the complex plane in FIG. Can be considered.

Therefore, as shown in FIG. 3A, this is alternately branched into a real part and an imaginary part,
By inverting the sign of every other imaginary part, the real part data and the imaginary part data can be restored. This process, given the frequency axis, and is processing in which the center frequency shown in FIG. 2 (A) shifted to _{π / 2 (f S / 4} ) shifted baseband spectrum. That is, the center frequency f ₀ of the spectrum is shifted to ₀ by this processing.

However, as shown in FIG. 3B, the real part data and the imaginary part data are alternate and shifted by one sampling time. FIG.
When undersampling is performed as shown in (A), a folded spectrum occurs in addition to the target spectrum. In order to remove this unnecessary spectrum, filter operation of a low-pass filter is performed. At this time, the filter operation is performed at intervals according to the shift of the sampling time, thereby eliminating the shift of the sampling time by the interpolation effect of the filter. Can be. That is, as shown in FIG. 4, even if the sampling time is shifted, by multiplying the filter coefficient according to the time, weighting is performed according to the time, and the output from the filter is the center time of the filter length. It can be treated as something.

[0017]

FIG. 5 is a block diagram of a receiving circuit using a direct sampling method for performing A / D conversion by undersampling without down-converting a received signal by a mixer. FIG. 1A shows a reception demodulation circuit of a wireless system, and FIG. 1B shows a reception demodulation circuit of an ultrasonic system.
In FIG. 1A, a high-frequency signal input from an antenna 1 is pre-amplified by amplifiers 2 and 4 and band-limited by a band-pass filter 3 to a narrow frequency band.
A / D conversion is performed by the converter 5. The A / D converted sampling data is input to the DSP 6, and the target signal is restored in the DSP 6. FIG. 2B includes a transducer 1 ′ instead of the antenna 1, but is otherwise the same as the configuration in FIG. As described above, when these block diagrams are compared, they have almost the same configuration except that the configuration of the sensor unit and the used carrier frequency are different, and the processing form is the same. Demodulation of the target signal by such undersampling can be used for radio equipment using narrow band signals, radar, sonar, fish finder, ultrasonic diagnostic equipment, ultrasonic flow meter, etc.
The present invention is applicable to a measuring device that handles a wave such as a sound wave.

{Description of Undersampling} First, conditions under which aliasing does not occur in undersampling will be described. When undersampling is used, a narrow band signal (bandpass signal) in which unnecessary waves other than the target signal are suppressed as much as possible is used to avoid aliasing. In addition, many mapping spectra are generated by undersampling. However, in order to perform digital signal processing by a DSP or the like, it is better to use a mapping spectrum whose frequency is as low as possible, for example, a center frequency of zero (DC). Easy. However, even in such a case, the shift amount from DC can be determined at the time of system design, so that it is possible to reversely shift to DC by the DSP operation. In this embodiment, this shift is performed only by inversion of the sign.

FIG. 6 is a diagram showing how a mapping spectrum is formed by sampling of the A / D converter. In this figure, an input signal is a band-pass signal whose band is limited, and has an input signal bandwidth B, a maximum frequency f _MAX of the input signal, and a sampling frequency f _S. In addition, the spectrum of the original analog signal is shaded.

FIG. 6A shows f_MAX At twice the frequency of
Shows when pulling is performed. FIG. 2B shows f_MAX of
Shows when sampling at a frequency higher than twice
I have. FIG. 4C shows f_MAX = 1.5B signal to f_S = 3
B, ie, f_MAX Twice of
This shows a case where sampling is performed at a frequency. Same figure
(D) processes the signal at the intermediate or narrow band frequency
And f_S> 2f_MAX F_S In the sun
Shows when pulling is performed. The figure (E) shows the intermediate frequency.
7 shows an example of processing when the number is further increased, and f_S 
<F_MAX F_SIndicates when sampling was performed.
You. FIG. 11F shows the same input signal as in FIG. _S = 2.5
B shows a case where sampling is performed. These methods
Then, the mapping spectrum is changed from DC to f_S / 2
However, this mapping spectrum (high and low frequencies) is inverted
ing. The same figure (G) shows the case where the intermediate frequency becomes higher.
In this case, DC is also f_S Depart between / 2
The generated mapping spectrum is inverted. Figure (H) is middle
This shows the case where the inter-frequency becomes higher.
It is f from DC_S The mapping spectrum generated during / 2 is
It is a perfect duplicate of the original spectrum without inversion.

As is apparent from this figure, whether the mapping spectrum generated near DC due to undersampling is inverted or not depends on how many mapping spectra are generated between DC and the original signal area. When the original signal area is included in the count, if the number of times of folding is N, the inversion is performed when N is an even number, and no inversion is performed when N is an odd number.

When f _MAX = N · B, N = 1, 2, 3,..., The minimum sampling frequency f _S = 2B is possible. For example, in FIGS. 9G and 9H, when the original signal area is not included in the count, the number of mapped spectra is 3 and 8, so that they are an inverted spectrum and a non-inverted spectrum, respectively. The inversion and non-inversion can be determined by how the sampling frequency is set for the carrier frequency at the stage of system design. However, when frequency processing is performed by FFT using a DSP or the like, it is easy to invert the spectrum data at the stage of digital signal processing, and inversion / non-inversion of the spectrum hardly causes a problem.

FIG. 7 shows the input signal bandwidth B when the undersampling obtained based on the above is performed.
FIG. 6 is a diagram illustrating a relationship between an input signal maximum frequency f _MAX and a sampling frequency f _S. The solid line in the figure is the condition of the minimum sampling frequency required for undersampling.

Here, if the input signal sampled at the sampling frequency f _S is treated as a continuous time signal, it can be considered as a periodic signal that repeats this signal at a period f _S on the frequency spectrum. That is, f _S / 2
Spectrum inversion to the spectrum of the non-reversed each appeared and repeated at f _S.

Hereinafter, conditions for selecting an appropriate sampling frequency when a bandpass signal is sampled will be described.

FIG. 8 shows a case where the positive frequency component (mapping spectrum without inversion) of the continuous wave bandpass signal is mapped to 0 ≦ Ω ≦ π. Hereinafter, the lower limit frequency and the upper limit frequency of the frequency band of the input signal (that is, the spectrum of the target signal) are referred to as f _L and f _U , respectively.

The spectrum shown in FIG.
Only a few spectra may be used,
May be considered as a spectrum in which a guard band is added to the spectrum.
FIG. 8A shows the original continuous wave signal. FIG. 8 (B)
Means that the sampling frequency is f _S Is the sampling signal
Frequency spectrum δ_S (F). In this figure
In this case, the lower limit frequency f of the signal band_L Is a sampler
Frequency f_S (F)
_L = Kf_S ). Also, the sampling frequency f_SIs the signal
Bandwidth B = f_U −f_L Is set to twice (f_S = 2
B). Here, k is an integer. From now on, Sampling
Frequency f_S Is uniquely determined.

Then, the upper end frequency f _U of the frequency band and the center frequency f ₀ of the frequency spectrum are expressed as f _U = (k + ／) f _S f ₀ = f _L + B / 2 = (k + ／) f _S Can be expressed. From this relationship, the sampling frequency f _S is

(Equation 1) Is determined.

FIG. 8C shows a frequency spectrum X (Ω) of digital data A / D converted at the sampling frequency f _S. From FIG. 8C, 0 to 2π
Of the original signal, the positive frequency regions f _{L to} f _L of the original signal
_The band occupied by the mapping spectrum corresponding to _U is in the range of 0 to π, and the negative frequency spectrum component occupies the range of π to 2π or -π to 0. Note that the center frequency f ₀ of the frequency spectrum is mapped to Ω = π / 2.

FIG. 9 is a diagram showing the relationship of the frequency spectrum when the positive frequency component of the band-pass signal is mapped to -π ≦ Ω ≦ 0. In this case, the upper limit frequency f _U of the signal band is set to an integral multiple of the sampling frequency f _S (f _U = k · f _S ). Then, f _L = (k − ／) f _S f ₀ = f _L + B / 2 = f _U −B / 2 = (k − ／) f
Can be expressed as _S. From this relationship, the sampling frequency f _S
Is

(Equation 2) Is obtained. In the expression (2), when k = 0, the sampling frequency f _S becomes negative, so that k = 1. Or

(Equation 3) May also be expressed.

In FIG. 9, the positive frequency component of the bandpass signal is mapped to -π ≦ Ω ≦ 0, and the negative frequency component of X (f) is mapped to the region of 0 ≦ Ω ≦ + π. That is, the signal mapped in the region of 0 ≦ Ω ≦ + π has a spectrum in which the high and low frequency components of the frequency component are inverted with respect to the original spectrum.

The examples shown in FIGS. 8 and 9 are special cases in which the lower limit frequency f _L and the upper limit frequency f _U of the signal frequency band each become an integral multiple of the sampling frequency.
As for the undersampling in the example, as described above, it is possible to determine whether the spectrum is inverted or not based on how many mapping spectra are folded between the DC and the original signal. In the case of FIG. 8, since an even number of duplicates occur between the DC and the original signal, no spectral inversion occurs. In the case of FIG. 9, an odd number of copies are folded between DC and the original signal, so that spectrum inversion occurs.

Thus, the examples of FIGS. 8 and 9 are a special case where the conditions among the lower limit frequency f _L , the upper limit frequency f _U and the sampling frequency f _S are satisfied. The following considers a more general case where such conditions are not met. FIG.
FIG. 4 is a diagram illustrating an example of a frequency spectrum shape when undersampling is performed at a general sampling frequency f _S that does not satisfy the above conditions. When the above condition is not satisfied, adjacent mapping spectra are spaced apart without being in contact as shown in FIG. However, even in this case, as shown in FIG. 11, an area (an area indicated by a broken line in the figure) divided by a frequency of an integer multiple (k · f _S ) of the sampling frequency f _S is a frequency to which a guard band is added. Considering the band, it can be considered exactly as in the case of FIG. Also, depending on the position of the reflected mapping spectrum, the processing can be performed in the same manner as in FIG. in this way,
It is not necessary to distinguish between the case where the lower limit frequency f _L or the upper limit frequency f _U is an integral multiple of the sampling frequency f _S and the case shown in FIG.

If the sampling frequency f _S is too low, the mapped positive frequency spectral component and negative spectral component overlap as shown in FIG. 12, and aliasing occurs. That is, in order to avoid aliasing, the sampling frequency f is twice or more the signal bandwidth B.
_S is required.

As described above, in the case of FIGS. 8 and 9 where the lower limit frequency f _L and the upper limit frequency f _U of the signal frequency band are integral multiples of the sampling frequency f _S , the case of FIG. The spectrum can be restored near the band (DC). Based on this, general conditions necessary for restoring the original signal will be clarified from the lower limit frequency f _L , upper limit frequency f _U , and sampling frequency f _S of the signal frequency band. However, the frequency bandwidth B =
and f _U -f _L.

[0036] Figure 13, the spectrum being mapped to the same frequency range as the spectrum of the original continuous-wave input bandpass signal (positive frequency spectrum components to an impulse of k = 0) and the spectral 0 _+, the m-th impulse (K
= Negative frequency spectral components are mapped by m) it is, appears in the spectrum 0 ₊ the right (higher frequency side) on the frequency axis, (m-1) -th impulse (k = m-
The negative frequency spectral component mapped by 1) is
It is a diagram showing a case in which appears in the spectrum 0 ₊ the left (lower frequency side). M written in the spectrum part in the figure
_- is a mapping spectrum of negative frequency spectrum by impulses at the position of k = m. m-1 _- is k = m
It is a mapping spectrum of a negative frequency spectrum by -1. Here, all are treated as continuous time signals.

In the same figure, the m-th impulse
The frequency spectrum shift shown in FIG.
The zero frequency of the original spectrum
・ F _S Go to This gives the original negative frequency −f
_U Is m · f_S −f_U Go to However, if m = 0
The original spectrum from the impulse at zero frequency
M to correspond to the mapping to the same frequency position as
= 0 is excluded. From this, the original sampling
A folded mapping spectrum on both sides of the frequency spectrum
M must be an integer greater than or equal to 1 to appear
I understand. And there is an upper limit to m.
Will be described later.

The sampling frequency f _S is because it is required value of at least twice the frequency bandwidth B of the spectrum, the conditions f _S ≧ 2B ... (1) is satisfied. Then, from FIG. 13 (C), (m- 1) f S -f L ≦ f L ... (2) and _{f U ≦ m · f S -f} U ... (3) are satisfied simultaneously. Further, the frequency bandwidth B = f _U −f _L
From the above, the condition of f _U / B = 1 + f _L / B ≧ 1 (4) is obtained, and f _S / B ≧ 2 is obtained from the expression (1).

Then, from the equations (2) and (3),

(Equation 4) Is obtained. In addition, by using the relational expression of f _U = f ₀ + B / 2, Expression (4) can be rewritten as a relation between the center frequency f _{0 of the} spectrum and the sampling frequency f _S.

(Equation 5) Is obtained. However, when m = 1, the f _S upper limit frequency is infinite.

Next, the minimum sampling frequency required for storing the bandpass signal is examined. Minimum sampling frequency, the sampling frequency f _S from the relationship of FIG. 13
, The upper limit frequency f _U of the signal frequency band and the lower end frequency mf _S −f _{U of the} spectrum to be mapped match as shown in FIG. That is, if the sampling frequency is lowered below this, aliasing occurs, so that it can be seen that the sampling frequency at which the equation (4) is satisfied is the desired minimum value.

That is, from the equation (4), the minimum sampling frequency f _S is given by f _S = (2 / m) f _U (5) where m = 1, 2, 3,. However,
m is not not take any of the natural numbers, the spectrum 0 ₊
There is a maximum value for setting so that the mapping of the negative-side spectrum occurs right next to the higher frequency side.
From (5), m = 2f _U / f _S is obtained, (1) _{m = 2f U / f S ≦} f U / B ... (13) from the equation obtained. From this, it can be seen that the maximum integer value of m is [f _U / B], and that m can take values of 1, 2, 3,..., [F _U / B]. Here, [X] represents a maximum integer not exceeding X. As a result, the minimum sampling frequency f _S
Is obtained when m is the maximum value, and is given by f _S = (2 / m) f _U and m = [f _U / B]. At this time, if f _U / B is an integer, the minimum sampling frequency is 2B. In this case, f
_L / B is also an integer.

The value satisfying the inequality sign of the equation (4) is shown in FIG.
A shaded area of 5 is obtained. Also, the above minimum sampling
The frequency is shown by a thick solid line in the figure. In the figure,
From equation (5), the minimum sampling period for each integer value of m
Wave number f_S Is determined, for example, m = 1
When f_U When / B is in the range of 2-3, f of m = 2 _S 
The value of / B is smaller. Even if m becomes large,
The engagement is similar, f_UDetermined by m when / B = m + 1 or more
F_S Is determined by (m + 1) rather than the value of / B
F_S Zigzag shape where the value of / B is smaller
It becomes the relationship.

From the above, the desired sampling frequency f _S
It can be seen that it is sufficient to select a value on the thick solid line in FIG. 15 or in a shaded area. However, from the viewpoint of efficiency, it is desirable to select the sampling frequency f _S as low as possible. Therefore, the necessary minimum sampling frequency which is a value on a thick solid line may be selected.

{Description of Complex Sampling Method}
A process in which undersampling is performed so that the non-inverted spectrum of the target signal is mapped to the baseband region using the required minimum sampling frequency described above will be described. First, consider an analog bandpass signal x (t) having a plurality of envelopes z (t).

[0045]

(Equation 6) Here, z (t) is the center frequency of zero and the total frequency bandwidth B
It is assumed that the signal is a complex signal having a frequency spectrum of (−B / 2 ≦ f ≦ + B / 2). That is, x (t) is the target signal z (t)
Carrier signal modulated by
₀ (= 2πf ₀ ), which is a modulated analog signal having the entire bandwidth B.

For example, in the case of wireless communication, the complex signal z
A signal obtained by amplitude-modulating the carrier frequency ω ₀ with a voice signal or digital data represented by (t) corresponds to x (t). The operation of reproducing the audio signal or the digital data z (t) as the target signal from the modulated signal x (t) is demodulation. In the case of active sonar, the ultrasonic signal output at the transmission frequency ω ₀ is reflected by the target, and the reflected echo signal on which the Doppler frequency component is superimposed corresponds to x (t). And this Doppler frequency component itself is a complex envelope z
(t), and the operation of extracting this is demodulation.

The reproduction of the complex envelope z (t) is performed by adding the band-pass signal x (t) to

(Equation 7) Can be performed as follows by demodulation processing of multiplying by

[0048]

(Equation 8) Here, * represents a complex conjugate number. The double frequency component of the second term in the last row generated by Expression (8), which is a demodulation process to the baseband, can be removed by passing this signal through a low-pass filter. As a result, the target complex signal z (t) can be obtained.

First, the band-pass signal x (t) shown in the equation (6) is pre-amplified and then the sampling frequency f _S
When sampling is performed by an A / D converter driven at (= 1 / T _S ), the following digital signal is obtained.

[0050]

(Equation 9) In this sampling unit, the center frequency ω ₀ (= 2πf ₀ ) of the spectrum is converted into a continuous frequency to f
_The sampling frequency f _S mapped to _S / 4 is set. That is,

(Equation 10) Set to. Then

[Equation 11] Because

(Equation 12) Holds. Substituting these relationships into equation (9) gives

(Equation 13) Is obtained. Thereafter, the sampling frequency f _S = 1 /
The analog signals x (nTs) and z (nTs) sampled at Ts are represented as x [n] and z [n] as digital data. Then, the above equation (13) becomes:

[Equation 14] Becomes Here, when Expression (12) is transformed,

(Equation 15) Because

(Equation 16) Is the same as modulating the signal of z [n] at the discrete angular frequency π / 2. That is, z along the discrete frequency axis
This corresponds to the fact that the discrete frequency spectrum of [n] is parallel-shifted by π / 2 toward the plus side. The frequency spectrum of z (t) having the center frequency f ₀ = 0 is mapped to a discrete frequency spectrum having a center angular frequency π / 2 by digitization by undersampling. FIG.
Next, how the frequency spectrum is mapped on the discrete frequency axis by the undersampling process will be described.

Assuming that the original analog complex envelope signal z (t) is

[Equation 17] And digital signal z [n] after sampling at sampling frequency f _S = 1 / T _S

(Equation 18) Then, the original analog signal x (t) becomes

[Equation 19] When sampling at a sampling frequency f _S = 1 / T _S ,

(Equation 20) Is obtained.

Here, the analog complex envelope signal z
(t)

(Equation 21) Is decomposed into a mounting part x _C (t) and an imaginary part x _S (t). Each sampled signal z (n · T _S ), x _C (n
T _s ) and x _s (n · T _s ) are represented as z [n], a real part x _C [n], and an imaginary part x _S [n] as digital signals.

Next, a process of demodulating a digital signal having a discrete frequency spectrum with a central angular frequency of π / 2 obtained by undersampling into a baseband signal is performed. In the demodulation processing, the discrete frequency spectrum may be shifted by π / 2 to the minus side.

(Equation 22) Is used as a discrete complex exponential function c [n]. That is, since the equation (14) is multiplied by the equation (22) to shift the frequency,

(Equation 23) Is obtained. From equation (23), it can be seen that a complex envelope signal z [n] can be obtained by multiplying the digital data x [n] obtained after the undersampling by a discrete complex exponential function c [n] and demodulating it.

Here, the even-numbered sampled data is represented by n = 2m, and the odd-numbered data is represented by n = 2m + 1. First, n
= 2m (m = 0, ± 1, ± 2, ± 3, ...)

(Equation 24) Therefore, Equation (23) is

(Equation 25) become. Similarly, considering the odd-numbered sample where n = 2m + 1,

(Equation 26) Because

[Equation 27] Holds.

As described above, the center frequency ω ₀ (= 2πf)
_{By 0)} to set the sampling frequency f _S is mapped to f _S / 4, the discrete complex envelope z real part, imaginary part, respectively (the number 25 of the [n]) expression, be determined by the equation (27) Can be.

From these relational expressions, a discrete complex envelope signal z which is a baseband signal having a center frequency of zero is obtained from the sampled digital real number data x [n].
You can find the real and imaginary parts of [n], respectively.

[Equation 28] Can be expressed as However, the expression (28) shows that the sample times of the real part and the imaginary part are 2 m and 2 m, respectively.
+1. That is, the value of the real part is intended sampling time of the analog signal is 2 mT _S, the value of the imaginary part is the sampling time of the analog signal (2m +
1) It is of T _S , each being different. In order to process the demodulated data, it is desirable that both the real part and the imaginary part are sampled at the same time. Therefore, data at the same time is generated by interpolating one or both of the real part and the imaginary part of Expression (28). This process is performed simultaneously with the filtering process for removing unnecessary spectra.

FIG. 17 is a block diagram for executing the demodulation method in the DSP of FIG. In this block diagram, the distribution unit 11 distributes the sampled discrete real number data x [n] to a real number part and an imaginary number part alternately according to whether the data is an even number or an odd number. In each of the real and imaginary parts, multipliers 12 and 13 are provided.
Restores the real data and the imaginary data by inverting the sign of the data every other (multiplying by -1) according to the data number m. Then, unnecessary data is removed by inputting the data to the low-pass filters 14 and 15, and the real number data and the imaginary number data are interpolated into data at the same sampling time. Since the data is distributed one by one to the real part and the imaginary part, the transfer rate of the real data x [n] is equal to the sampling frequency f _S , but the transfer rate after conversion to the complex data is f _S / 2. . Also, the frequency domain of the complex data _{-f S / 4~f S / 4 (} -
B / 2 to B / 2).

The above is a case where the processing is performed with the even-numbered sample being n = 2m and the odd-numbered sample being n = 2m + 1. Hereinafter, the even-numbered sample is n = 2m and the odd-numbered sample is n = 2m− The case of processing as 1 will be described.

First, for the even-numbered sample in the above equation (23), n = 2 m is set in the same manner as in the above case.
The real part of [n] can be determined. Also, since the odd-numbered samples are set to n = m-1,

(Equation 29) From

[Equation 30] become. Therefore, the odd-numbered sample is defined as n = 2m−
When it is set to 1, the real part and the imaginary part of the discrete complex envelope z [n] can be obtained by Expressions (25) and (30), respectively. As a result, the real part and the imaginary part of the discrete complex envelope z [n], which is the baseband signal having the center frequency of zero, are obtained from the sampled digital real number data x [n].

(Equation 31) Is represented by

This (Equation 31) is also expressed as “odd 2m +
Since the sampling times of the real part and the imaginary part are different as in the case of “1”, the sampling times are aligned by interpolation using a low-pass filter, as described above.

FIG. 18 is a block diagram for executing the demodulation method in the DSP of FIG. The processing in this block diagram is the same as that shown in FIG. 17 except that the order of the distribution of discrete real number data x [n] into real and imaginary parts is different.

{Design of Low-Pass Filter} How the low-pass filter shown in FIGS. 17 and 18 is configured will be described. First, a description will be given of a low-pass filter that aligns the sampling times of both the real number data and the imaginary number data by interpolation such that both data are shifted back and forth by half the sampling period T _S / 2. In the case of FIG. 17, the real number data is advanced by T _S / 2, and the imaginary number data is delayed by T _S / 2. In the case of FIG. 18, the real number data is delayed by T _S / 2, and the imaginary number data is advanced by T _S / 2.

First, the interpolation (interpolation)
think of. To perform interpolation, first insert the zero data every second for each of the real part data string and imaginary part data string, the data rate is made real data of the sampling frequency f _S, the imaginary data. The actual real number data corresponds to the imaginary part 0 data, and the actual imaginary number data corresponds to the real number part 0 data. Next, the real part data sequence and the imaginary part data sequence are input to a low-pass filter. The low-pass filter (interpolator) is used even length of the FIR filter _{(T S = 1 / f S} ). Hereinafter, this procedure will be described in detail.

FIG. 19 shows an interpolation procedure when one zero data is inserted. As an example, a case where the filter length is an even number L = 8 is shown.

FIG. 19A shows a case where the even number (n = 2m) of the input signal x [n] shown in FIG. 17 is distributed to real number data and the odd number (n = 2m + 1) is distributed to imaginary number data. 18B shows the input signal x [n] shown in FIG.
Are distributed to imaginary data and odd-numbered (n = 2m-1) to real data. Due to this distribution, the data rate as a complex number is reduced to の of the sampling frequency f _S. However, since zero data for interpolation is inserted into these data, the data rate as complex data is 2
Back in multiples of f _S. However, as shown in FIG. 19, the multiplication result between the zero data to be inserted and the filter coefficient is zero, and does not affect the filter operation result. For this reason,
It is possible to eliminate zero data and their corresponding filter coefficients. FIG. 20 shows the relationship between the filter coefficients obtained by removing the filter coefficients corresponding to the zero data inserted as described above, and real numbers and imaginary numbers. Thus, it can be seen that the data rate eventually decreases to の of the sampling frequency f _S even if 0 data is inserted.

FIG. 21 is a diagram showing the structure of the filter coefficients of the final low-pass filter. The interpolator low-pass filter h [n], n = 0, 1, 2, 3,..., (L
-2) and (L-1) are the even-numbered (n) of the input signal x [n].
= 2m, n = 0, 2, 4,..., (L-2)) as real data, and odd-numbered (n = 2m + 1, n = 1, 3, 5,.
When (L-1)) is distributed to imaginary data, the even-numbered coefficients (n = 0, 2, 4,...) Of the original even-length filter are changed to odd-numbered coefficients (n = 1, 3, 5) for real numbers. , ...) are divided for imaginary numbers.

The even-numbered (n = 2) of the input signal x [n]
m) is distributed to real data and the odd-numbered (n = 2m-1) is distributed to imaginary data, the odd-numbered coefficients (n = 1, 3, 5,...) of the original even-length filter are used for real numbers , Even coefficients (n = 0, 2, 4,...) Are divided for imaginary numbers.

As described above, the odd number (2) of the input signal x [n]
(A) and (B) have opposite coefficient patterns depending on the distribution according to the method of taking (m + 1) or (2m-1).
If the original filter length is L (even number), both the real and imaginary filter lengths are L / 2.

In the above description, the sampling times are aligned by shifting both the real part data and the imaginary part data by a half sampling period. However, it is not the only method to make the sampling times uniform, but the real part and the imaginary part Any setting may be used as long as the data sampling times are the same.

A method of using the data of the real part as it is and shifting the data of the imaginary part by one sample period to align the sampling times of the data of the real part and the imaginary part will be described. (Number 28), (Expression 31) data of the imaginary part to the sampling time 2 mT _S as shown in equation no. To generate this 2 mT _S data, where 2
2, an odd-length low-pass filter is used. This figure shows a case where 0 data is inserted to set the data rate to f _S. The filter coefficients of the odd-length low-pass filter are alternately distributed to the real part and the imaginary part. Is output.

Since the data corresponding to the odd-numbered coefficient is 0 on the real-number part, only the even-numbered coefficient is operated, and the data is output as 2m data corresponding to the central sampling time. On the other hand, since the data corresponding to the even-numbered coefficient is 0 on the imaginary part, only the odd-numbered coefficient is calculated, and the data is output as 2m data which is intermediate between 2m-1 and 2m + 1.

FIG. 23 is a diagram showing actual low-pass filter coefficients. In practice, this coefficient may be multiplied by the input real number data and imaginary number data without inserting 0 data.

{In the case of inverted spectrum} Whether the frequency spectrum of discrete data appearing near the baseband (0 to π) is inverted by undersampling is determined by
It is determined by the relationship among the input signal bandwidth B, the input signal opposing frequency f _MAX (center frequency f ₀ ), and the sampling frequency f _S. Although the case where the spectrum is not inverted has been described as it is, the processing and the filter configuration when the spectrum is inverted by undersampling will be described below.

First, sampling of the analog bandpass signal x (t) is performed. In this case, the processing up to equation (9) is the same as the case where the spectrum is not inverted. Here, the sampling frequency f _{S at} which the frequency spectrum center frequency ω ₀ (= 2πf ₀ ) of the analog signal before sampling is converted to a continuous frequency and mapped to 3f _S / 4 is set. That is, the sampling frequency f _S
To

(Equation 32) And Then

[Equation 33] Because

(Equation 34) Holds. Substituting these relationships into equation (9) gives:

(Equation 35) Is obtained. Rewriting equation (35) as a digital signal,

[Equation 36] Becomes

Here, as in the above equation (12),
4) By transforming the equation,

(37) Because

(38) Converts the signal of z [n] to a discrete angular frequency of 3π / 2 (or -π
/ 2). In other words, this corresponds to the fact that the discrete frequency spectrum of z [n] is shifted in parallel by 3π / 2 along the discrete frequency axis. Alternatively, this corresponds to that the discrete frequency spectrum of z [n] is shifted by π / 2 to the minus side. The frequency spectrum of z (t) having the center frequency f ₀ = 0 is mapped to a discrete frequency spectrum having a center angular frequency of 3π / 2 by digitization by undersampling. Or, it is the same even if it is considered that the image is mapped to the central angular frequency -π / 2. FIG. 24 shows how a frequency spectrum is mapped on a discrete angular frequency axis by undersampling.

Suppose that the original analog complex envelope signal z (t) is

[Equation 39] And the digital signal z [n] after sampling is

(Equation 40) Then, the original analog signal x (t) becomes

[Equation 41] And after sampling

(Equation 42) Is obtained.

Next, a process of demodulating a digital signal having a discrete frequency spectrum with a central angular frequency of 3π / 2 obtained by undersampling into a baseband signal is performed. The demodulation process can be performed by shifting the discrete frequency spectrum to the negative side by 3π / 2.

[Equation 43] Is used as a discrete complex exponential function c [n]. (Equation 3
By multiplying equation (6) by equation (43),

[Equation 44] Is obtained.

First, n = 2m (m = 0, ± 1, ± 2, ± 2
3,...), And processing is performed with the odd-numbered sample set as n = 2 + 1. First, considering an even-numbered sample where n = 2m,

[Equation 45] Therefore, Equation (44) is

[Equation 46] become.

Similarly, considering an odd-numbered sample where n = 2m + 1,

[Equation 47] Because

[Equation 48] Holds.

From this, it can be seen that the real part and the imaginary part of the discrete complex envelope z [n] can be obtained by the relational expressions of Expressions (46) and (48), respectively.

From these relational expressions, a discrete complex envelope signal z which is a baseband signal having a center frequency of zero is obtained from the sampled digital real number data x [n].
You can find the real and imaginary parts of [n], respectively.

[Equation 49] Can be expressed as

The real part and the imaginary part of the equation (49) are also shifted by one sample period. In this case, the interpolation can be performed by the configuration shown in FIG. 17 as in the case where the spectrum is not inverted.

When the even-numbered sample is processed as n = 2m and the odd-numbered sample is processed as n = 2m-1, the odd-numbered sample is processed in the same manner as in the above-described non-inversion.

[Equation 50] Becomes That is, the real part and the imaginary part of the discrete complex envelope z [n] can be obtained by the relational expressions of Expressions (25) and (50), respectively.

As a result, the real part and the imaginary part of the discrete complex envelope z [n], which is a baseband signal having a center frequency of zero, are obtained from the sampled digital real number data x [n].

(Equation 51) Is represented by Even under this condition, the sampling time of the real part and the sampling time of the imaginary part are shifted by one each.
8, the sampling time can be made uniform.

As described above, by using the same low-pass filter as in the case where the spectrum is inverted but not inverted, and interpolating with this low-pass filter, it is possible to obtain complex number data at the same time for both the real part and the imaginary part.

[0086]

As described above, according to the present invention, the sampling data whose center frequency f ₀ becomes f ₀ = ± f _S / 4 by sampling at the sampling frequency f _S is branched, and the sign is inverted. Since the spectrum can be shifted to the baseband and the data can be complexed by an extremely simple operation of performing a filter operation of half the actual amount, direct undersampling and the like can be performed with a simple configuration. ,
There is an advantage that real-time processing such as wireless communication is facilitated.

[Brief description of the drawings]

FIG. 1 is a diagram showing a carrier signal on which a target signal to which the present invention is applied is superimposed.

FIG. 2 is a diagram illustrating a spectrum and the like when a carrier signal on which the target signal is superimposed is sampled at a sampling frequency f _S (= 4f ₀ ).

FIG. 3 is a diagram illustrating a process of converting the sampling data into complex data.

FIG. 4 is a diagram showing a process for matching sampling times of real number data and imaginary number data of the complex data by interpolation.

FIG. 5 is a block diagram of a communication device and a sonar device to which the present invention is applied;

FIG. 6 is a diagram showing a generation pattern of a mapping spectrum when undersampling is performed.

FIG. 7 is a diagram illustrating a condition of a minimum sampling frequency when undersampling is performed.

FIG. 8 is a diagram illustrating a frequency spectrum of a band-pass signal and a mapping spectrum when the frequency spectrum is sampled so as not to be inverted.

FIG. 9 is a diagram showing a frequency spectrum of a band-pass signal and a mapping spectrum when sampling is performed so as to invert the frequency spectrum.

FIG. 10 is a diagram showing a mapping spectrum when a bandpass signal is sampled under different conditions.

FIG. 11 is a diagram illustrating a process of adding a guard band to a bandwidth.

FIG. 12 is a diagram illustrating the occurrence of aliasing when the sampling frequency is smaller than the bandwidth.

FIG. 13 is a diagram showing a relationship between a frequency spectrum before sampling and a group of mapping spectra after undersampling.

FIG. 14 is a diagram showing a spectrum distribution when the sampling frequency is set to the lowest sampling frequency.

FIG. 15 is a diagram showing conditions of a sampling frequency required according to a bandwidth and a maximum frequency of a signal.

FIG. 16 is a diagram showing a distribution of a mapping spectrum generated by undersampling.

FIG. 17 is a block diagram of a signal processing unit (DSP) that performs complexization, low-pass filtering, and interpolation of sampling data.

FIG. 18 is a block diagram of a signal processing unit (DSP) that performs complexization, low-pass filtering, and interpolation of sampling data.

FIG. 19 illustrates a case where 0 is interpolated when both real and imaginary parts are interpolated.
FIG. 9 is a diagram illustrating an example of a low-pass filter when data is inserted.

FIG. 20 is a diagram illustrating an example of a low-pass filter when 0 data is omitted.

FIG. 21 is a diagram showing filter coefficients on the real and imaginary sides.

FIG. 22 is a diagram illustrating an example of a low-pass filter when zero data is inserted when only the imaginary part is interpolated.

FIG. 23 is a diagram illustrating an example of a low-pass filter when 0 data is omitted.

FIG. 24 is a diagram showing a distribution of a mapped spectrum generated by undersampling for inverting a spectrum.

FIG. 25 is a diagram showing a configuration of a sonar device for complexing a received signal using a conventional analog mixer.

[Explanation of symbols]

 DESCRIPTION OF SYMBOLS 1 ... Antenna, 1 '... Transducer, 2 ... High frequency preamplifier, 3 ... Bandpass filter, 4 ... High frequency amplifier, 5 ... A / D converter (for undersampling), 6 ... DSP, 11 ... Distribution part, 12, 13 ... Multipliers, 14,15 ... Low-pass filter

Claims (4)

[Claims] 1. The center frequency f ₀ of a target signal is f ₀ = ±
a branching process for sequentially inputting sampling data sampled at a sampling frequency f _S mapped to f _S / 4 and alternately branching the input sampling data into a real part and an imaginary part; In the shift processing of inverting the sign of the input sampling data every other, the filter coefficient of the low-pass filter is alternately multiplied by one with the shifted sampling data of the real part and the sampling data of the imaginary part, A signal processing method comprising: a complexization process of summing multiplication results for each real part and imaginary part to obtain real part data and imaginary part data. 2. The sampling data sequentially inputted.
Is the carrier frequency f _C , K = 0,1,2, ...
As f_S = 4f_C / (4k + 1) or f _S = 4f
_C / Sampling frequency f such that (4k + 3)_S 
Claims are sampling data sampled at
2. The signal processing method according to 1. 3. The signal processing method according to claim 1, wherein the low-pass filter has an even filter length. 4. The signal processing method according to claim 1, wherein the low-pass filter has an odd filter length.