CN107682096B - A Narrowband Random Signal Generation Method Based on Multilevel Interpolation - Google Patents

Abstract

The invention discloses a narrowband random signal generation method based on multistage interpolation, which comprises the following specific scheme: calculating the series required by multilevel 2-time upsampling according to the highest frequency of the random signal and the maximum relative error allowed by interpolation, designing an FIR filter required by the multilevel 2-time upsampling by adopting a window function method, taking the FIR filter as an initial value of a biological optimization method, searching the FIR filter meeting the requirements of the maximum attenuation allowed by a pass band, the minimum attenuation of a stop band and the lowest order by adopting the biological optimization method, convolving the obtained FIR filter with the random signal, and increasing the signal sampling rate to the required sampling rate by utilizing linear interpolation.

Description

A Narrowband Random Signal Generation Method Based on Multilevel Interpolation

technical field

The present invention relates to the technical field of signal processing, in particular to a method for generating narrow-band random signals based on multi-level interpolation.

Background technique

In order to achieve frequency division multiplexing and improve antenna radiation efficiency, the signals in communication systems are mostly narrow-band random signals. The method of generating narrow-band random signal in the experiment is to upsample the random signal whose frequency is sampling frequency f ₁ to f _s , and then modulate it. Usually f _s is much larger than f ₁ , that is, f _s >> f ₁ , that is, the original sampling frequency needs to be increased by f _s /f ₁ times, and it is very difficult to achieve single-stage implementation, so it is more feasible to use multi-stage upsampling method. accomplish. But the computational complexity of simple multi-level upsampling is very high.

In 2005, Yan Jiaming et al. proposed a linear interpolation method in the document "Research on the Error Calculation Method of Linear Interpolation" ^[5] . The basic idea is: divide the function into n intervals, and calculate the endpoint values of each interval: x ₀ ,x ₁ ,…,x _i ,x _i+1 ,…,x _n , and calculate these endpoints The corresponding function values f(x ₀ ),f(x ₁ ),…,f(x _i ),f(x _i+1 ),…,f(x _n ), when x(x _i <x< When the function value at the point x _i+1 ) is used, the following formula is used to calculate:

The disadvantages of this technical solution are as follows: the division of the function interval affects the accuracy of the linear interpolation, and the larger the interval is, the greater the linear interpolation error. In 2015, Zhao Shen et al. proposed a method of FIR filter interpolation in the document "Research on Real-time Generation and Delay Control of Narrowband Noise in Array Signal Sources" [6]. The basic idea is: under the condition of the original sampling period Ts, insert M-1 zeros between the adjacent data of the original noise signal, and then use the FIR filter to filter the signal, so as to achieve the purpose of increasing the signal sampling rate by M times. The disadvantages of this technical solution are as follows: (1) with the increase of the order of the FIR filter, the calculation amount of this method increases; (2) with the increase of the multiple M that needs to be improved for the sampling rate, the computational complexity of this method is extremely high. Tool increase.

SUMMARY OF THE INVENTION

To reduce the computational complexity of upsampling, simple linear interpolation can be used, but linear interpolation will introduce certain errors. In order to improve the calculation speed of the upsampling operation on the premise of ensuring a certain interpolation accuracy, the present invention proposes a combination of multi-stage 2-fold upsampling and linear interpolation to generate a narrowband random signal. Among them, multi-stage 2 times upsampling is realized by FIR filter. The invention discloses a method for generating a narrow-band random signal based on multi-level interpolation. The specific scheme is as follows:

According to the highest frequency of the random signal and the maximum relative error allowed by interpolation, the number of stages required for multi-level 2-fold upsampling is calculated, and the FIR filter required for each level of 2-fold up-sampling is designed by using the window function method. The initial value of the optimization method is to use the biological optimization method to find the FIR filter that satisfies the maximum attenuation of the passband, the minimum attenuation of the stopband, and the lowest order, and then convolves the obtained FIR filter with a random signal, and then uses linear interpolation to convert the signal. The sampling rate is increased to the required sampling rate;

Specifically include the following steps:

The calculation method of the number of stages L required for multi-stage 2-fold upsampling is as follows:

表示向上取整操作。Among them, f _H and f ₁ are the highest frequency and sampling frequency of the original random signal, δ is the maximum relative error allowed by interpolation,

Indicates a round-up operation.

S1: The FIR filter required for L-level 2-fold up-sampling is designed by using the rectangular window function method, and the FIR filter coefficient g _i (n) of the i-th 2-fold up-sampling is calculated as follows:

Among them, Ni is the order of the _i -th upsampling FIR filter by 2 times. And normalize g _i (n) to h _i (n):

作为初始值，采用生物优化方法求取(4)式中代价函数的最优解，记为

S2: will

As the initial value, the biological optimization method is used to obtain the optimal solution of the cost function in (4), which is denoted as

Among them, the biological optimization method adopted in the present invention is an artificial bee colony algorithm, α is a weighting coefficient, it is recommended to take α>0.6, and M is the Fourier transform length.

的通带衰减α_p和阻带衰减α_s，S3: Calculate the filter obtained by S2

The passband attenuation α _p and stopband attenuation α _s ,

级联的傅里叶变换，且Among them, H(m), m=0,...,M-1, is the obtained L-level 2 times upsampling filter

the cascaded Fourier transform, and

If the pass-band attenuation α _p and stop-band attenuation α _s both meet the requirements, reduce the order of each filter by 2, and repeat steps (2) to (3) until the pass-band attenuation α _p and stop-band attenuation α _s can just meet the requirements, and the order of the filters at all levels is as low as possible;

S4: Convolve the L-level 2x upsampling filter obtained by S1~S3 with the original random signal to increase the sampling frequency by 2 ^L times, and then use linear interpolation to continue to increase the sampling rate of the signal to the required sampling rate f _s .

Due to the adoption of the above technical solutions, the present invention provides a method for generating narrow-band random signals based on multi-level interpolation, which combines the characteristics of high interpolation accuracy of the multi-level upsampling method and low complexity of the linear interpolation method.

Description of drawings

In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the following briefly introduces the accompanying drawings required for the description of the embodiments or the prior art. Obviously, the drawings in the following description are only These are some embodiments described in this application. For those of ordinary skill in the art, other drawings can also be obtained based on these drawings without any creative effort.

Fig. 1 is the flow chart of the method of the present invention.

FIG. 2 is a schematic diagram of an embodiment of the present invention.

Detailed ways

In order to make the technical solutions and advantages of the present invention clearer, the technical solutions in the embodiments of the present invention will be described clearly and completely below with reference to the accompanying drawings in the embodiments of the present invention:

As shown in Figure 1, a narrow-band random signal generation method based on multi-level interpolation is used to calculate the number of stages required for multi-level 2-fold upsampling according to the highest frequency of the random signal and the maximum relative error allowed by the interpolation, and the window function method is used. The FIR filter required for 2x upsampling at all levels is designed as the initial value of the biological optimization method, and the biological optimization method is used to find the FIR filter that satisfies the maximum attenuation of the passband, the minimum attenuation of the stopband and the lowest order. Then convolve the obtained FIR filter with the random signal, and then use linear interpolation to increase the signal sampling rate to the required sampling rate;

Specifically include the following steps:

The calculation method of the number of stages L required for multi-stage 2-fold upsampling is as follows:

表示向上取整操作。Among them, f _H and f ₁ are the highest frequency and sampling frequency of the original random signal, δ is the maximum relative error allowed by interpolation,

Indicates a round-up operation.

S1: The FIR filter required for L-level 2-fold up-sampling is designed by using the rectangular window function method, and the FIR filter coefficient g _i (n) of the i-th 2-fold up-sampling is calculated as follows:

Among them, Ni is the order of the _i -th upsampling FIR filter by 2 times. And normalize g _i (n) to h _i (n):

作为初始值，采用生物优化方法求取(4)式中代价函数的最优解，记为

S2: will

As the initial value, the biological optimization method is used to obtain the optimal solution of the cost function in (4), which is denoted as

Among them, the biological optimization method adopted in the present invention is an artificial bee colony algorithm, α is a weighting coefficient, it is recommended to take α>0.6, and M is the Fourier transform length.

的通带衰减α_p和阻带衰减α_s，S3: Calculate the filter obtained by S2

The passband attenuation α _p and stopband attenuation α _s ,

级联的傅里叶变换，且Among them, H(m), m=0,...,M-1, is the obtained L-level 2 times upsampling filter

the cascaded Fourier transform, and

If the pass-band attenuation α _p and stop-band attenuation α _s both meet the requirements, reduce the order of each filter by 2, and repeat steps (2) to (3) until the pass-band attenuation α _p and stop-band attenuation α _s can just meet the requirements, and the order of the filters at all levels is as low as possible;

S4: Convolve the L-level 2x upsampling filter obtained by S1~S3 with the original random signal to increase the sampling frequency by 2 ^L times, and then use linear interpolation to continue to increase the sampling rate of the signal to the required sampling rate f _s .

Example:

The magnitude spectrum of the 3-stage 2-times upsampling filter is shown in Figure 2. The 2-times upsampling designed by the 120, 30 and 20-order rectangular window obtains the pass-band attenuation and stop-band attenuation of the filters at all levels of 1dB and 60dB, respectively. . The 3-stage 2-times upsampling filter obtained by the method of the present invention needs 112, 28 and 18 stages, and the passband attenuation and stopband attenuation of the filters at all levels can still be guaranteed. Reduced computation for multi-level upsampling.

It is assumed that the frequency of the original sinusoidal signal is f _H =4KHz, the amplitude is A=1, and the sampling frequency is f ₁ =360KHz. In order to obtain the narrowband signal, the method proposed in this paper is used to increase the sampling frequency of the original sinusoidal signal to f _s =0.18GHz, and the maximum relative error δ is guaranteed to be 10 ^-3 , 10 ^-4 , 10 ^-5 and 10 ^-6 respectively. When the narrowband random signal is generated by the linear interpolation method, the maximum relative error is 5.96×10 ^-4 . When the multi-level 2 times up-sampling method is used to generate a narrow-band random signal, the time-consuming is 20.41 seconds. It can be seen from Table 1 that the method for generating narrow-band random signals by combining multi-level 2-fold upsampling and linear interpolation proposed by the present invention has a maximum relative error much smaller than the linear interpolation method, and its calculation speed is much faster than that of multi-level 2-fold upsampling. method.

Table 1 Maximum relative error and time consumption of the present invention

The method has the characteristics of high interpolation accuracy of multi-level upsampling method and low complexity of linear interpolation method, and can be used in the application of real-time narrowband signal generation that requires high interpolation accuracy.

The above description is only a preferred embodiment of the present invention, but the protection scope of the present invention is not limited to this. The equivalent replacement or change of the inventive concept thereof shall be included within the protection scope of the present invention.

Claims (1)

1. A narrowband signal generation method based on multi-stage interpolation is characterized in that: calculating the number of stages required by multilevel 2-time upsampling according to the highest frequency of a random signal and the maximum relative error allowed by interpolation, designing an FIR filter required by the multilevel 2-time upsampling by adopting a window function method, taking the FIR filter as an initial value of a biological optimization method, searching the FIR filter meeting the requirements of the maximum attenuation allowed by a pass band, the minimum attenuation of a stop band and the lowest order by adopting the biological optimization method, convolving the obtained FIR filter with the random signal, and increasing the signal sampling rate to the required sampling rate by utilizing linear interpolation;

the calculation method of the required number of stages L for multistage 2-time upsampling is as follows:

wherein f is_HAnd f₁The highest frequency and sampling frequency of the original random signal, the maximum relative error allowed for interpolation,

represents a rounding up operation;

the calculation method of the FIR filter required by each stage of 2 times of up-sampling is as follows:

s1, designing the FIR filter needed by L-level 2 times up-sampling by adopting a rectangular window function method, wherein the coefficient g of the FIR filter of the ith-level 2 times up-sampling_i(n) is calculated as follows:

wherein N is_iUp-sampling the order of the FIR filter 2 times for the ith stage and dividing g_i(n) normalization to h_i(n)：

S2: h is to be_i(n)，

As an initial value, the optimal solution of the cost function in the formula is obtained by adopting a biological optimization method and is recorded as

Wherein α is a weighting coefficient, α >0.6, and M is a Fourier transform length;

s3: calculating the resulting filter of S2

Pass band attenuation α_pAnd stop band attenuation α_s，

Wherein h (M), M0, …, M-1 is L-level 2-fold upsampling filter obtained

A cascaded Fourier transform is performed by a Fourier transform,

if pass band attenuation α_pAnd stop band attenuation α_sWhen the requirements are met, the order of each stage of filter is reduced by 2 orders, and the steps S2-S3 are repeated until the passband attenuation α is reached_pAnd stop band attenuation α_sThe requirement can be met just right, and the order of each stage of filter is as low as possible;

s4, convolving the L-level 2-time upsampling filter obtained by S1-S3 with the original random signal to improve the sampling frequency by 2^LMultiplying, then using linear interpolation to increase the sampling rate of the signal to the required sampling rate f_s。

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