Fuel measurement-oriented time sequence signal interpolation filter design method

Abstract

The invention discloses a fuel measurement-oriented time sequence signal interpolation filter design method, and belongs to the technical field of digital signal processing. The method is based on a multi-sampling-rate conversion theory, the cut-off frequency and transition band characteristics of an interpolation filter are optimized, filtering parameters are dynamically adjusted in combination with an adaptive algorithm, and high-precision reconstruction of a fuel measurement signal is achieved. The method is characterized in that a rear digital low-pass filter is designed, the aliasing effect is effectively inhibited through a frequency spectrum compression and expansion technology, and the calculation efficiency is improved by utilizing a direct implementation structure. The method is particularly suitable for an aviation fuel measuring system, data redundancy and signal fidelity can be balanced in different sampling rate states, and the measuring precision and stability of the system are remarkably improved.

Description

Technical Field

[0001] This invention belongs to the technical field of digital signal processing for filters, specifically relating to a design method for a time series signal interpolation filter for fuel measurement. Background Technology

[0002] In the modern aviation industry, fuel quality monitoring is crucial for improving aircraft engine efficiency and reducing emissions. Traditional fuel measurement systems typically employ a fixed sampling rate for data acquisition. However, practical applications have revealed significant shortcomings in this method: excessively high sampling frequencies lead to a large amount of redundant data, while excessively low sampling frequencies result in the loss of signal details, thus affecting the system's measurement accuracy and reliability. Therefore, designing a system capable of adapting to multiple sampling rates has become a pressing technical challenge.

[0003] In the field of digital signal processing, multi-rate conversion theory has become an important technique. This theory optimizes data transmission efficiency while maintaining signal quality by adjusting the signal sampling rate. Sequence interpolation, as a fundamental operation, is a key method for achieving integer-fold increases in sampling rate. However, existing interpolation filter designs for fuel measurement systems still suffer from the following problems: traditional filtering algorithms struggle to simultaneously meet the requirements of signal fidelity and computational efficiency under multi-rate conditions; and phase distortion and amplitude distortion during the interpolation process have not been adequately addressed.

[0004] Therefore, based on the above-mentioned problems existing in the prior art, the present invention discloses a design method for a time series signal interpolation filter for fuel measurement. Summary of the Invention

[0005] This invention discloses a design method for a time series signal interpolation filter for fuel measurement. By dynamically adjusting the parameters of the interpolation filter, it can adapt to different sampling rate requirements and solve the problems of data redundancy at high sampling rates and signal loss at low sampling rates in traditional fixed sampling rate methods.

[0006] This invention is achieved through the following technical solution:

[0007] A method for designing a time-series signal interpolation filter for fuel measurement includes the following steps:

[0008] Step 1: Based on the periodic impulse sequence, establish a discrete-time model of the fuel measurement signal;

[0009] Step 2: Increase the sampling frequency of the fuel measurement signal by an integer multiple using upsampling technology to generate a high sampling rate interpolation sequence.

[0010] Step 3: Analyze the spectral characteristics of the interpolated sequence using discrete-time Fourier transform to obtain the phenomena of spectral compression and repetition;

[0011] Step 4: Design a post-digital low-pass filter based on spectral characteristics, and set the cutoff conditions of the post-digital low-pass filter to eliminate spectral imagery and retain the main value range signal.

[0012] Step 5: Perform interpolation filtering based on the post-digital low-pass filter.

[0013] To better realize the present invention, step 2 further includes:

[0014] Step 2.1: Sample the fuel measurement signal at uniform intervals to obtain a sampling sequence;

[0015] Step 2.2: Interpolate the sampling sequence based on the period of the periodic impulse sequence to obtain the interpolated sequence.

[0016] To better implement this invention, the interpolation sequence is further defined as follows:

[0017]

[0018] Where: f(n0) represents the interpolation sequence; This represents the signal sequence after being compressed by a multiple of the period of the periodic impulse sequence; δ M (n) represents a periodic impulse sequence with period M, where M represents the period of the periodic impulse sequence; This indicates that the period T is equal to the uniform interval. The sequence obtained after sampling.

[0019] To better realize this invention, a discrete-time Fourier transform is further performed on the interpolation sequence to obtain the spectrum of the interpolation sequence as follows:

[0020]

[0021] Where: F(e) jω ) represents the spectrum of the interpolation sequence; e -jnω The basis functions represent the discrete-time Fourier transform and are used to calculate the spectrum of a complex exponentially modulated time-domain signal.

[0022] To better realize the present invention, step 4 further includes:

[0023] Step 4.1: Obtain the frequency characteristics of the post-digital low-pass filter;

[0024] Step 4.2: Obtain the spectrum of the output sequence of the post-digital low-pass filter based on the frequency characteristics and the spectrum calculation of the interpolation sequence;

[0025] Step 4.3: Spectral analysis based on the output sequence of the post-digital low-pass filter.

[0026] To better realize the present invention, the spectrum of the output sequence of the post-digital low-pass filter in step 4.2 is further defined as follows:

[0027] Y(e jω )=F(e jω )H(e jω );

[0028] Where: Y(e jω F(e) represents the spectrum of the output sequence of the post-digital low-pass filter; jω H(e) represents the spectrum of the interpolation sequence; jω ) represents the frequency response of the post-digital low-pass filter.

[0029] To better realize the present invention, the frequency characteristics obtained in step 4.1 are further as follows:

[0030]

[0031] Where: H(e) jω ) represents the frequency response of the post-digital low-pass filter; M represents the period of the periodic impulse sequence, G 2π / M (ω)=ε(ω+π / M)-ε(ω-π / M), where ε(ω) is the unit step function and δ(ω-2kπ) represents an impulse at every 2kπ frequency, used to construct periodic frequency characteristics.

[0032] To better realize the present invention, the output sequence of the post-digital low-pass filter in step 4.3 is further as follows:

[0033]

[0034] Where: y(n) represents the output sequence of the post-digital low-pass filter; Y(e jω () represents the spectrum of the output sequence of the post-digital low-pass filter; e jnω The basis functions represent the discrete-time Fourier transform.

[0035] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0036] (1) This invention adapts to different sampling rate requirements by dynamically adjusting the parameters of the interpolation filter, thus solving the problems of data redundancy at high sampling rates and signal loss at low sampling rates in the traditional fixed sampling rate method.

[0037] (2) By optimizing the cutoff frequency and transition band characteristics of the filter, this invention significantly reduces phase distortion and amplitude distortion during signal reconstruction, thus ensuring the accuracy of fuel measurement data.

[0038] (3) The present invention adopts a direct implementation structure, which reduces computational complexity and improves system real-time performance while ensuring accuracy;

[0039] (4) This invention achieves flexible switching between pre-filters and post-filters through spectrum compression and expansion technology, thereby enhancing the versatility of system design. Attached Figure Description

[0040] Figure 1 The interpolation filtering flowchart provided by this invention;

[0041] Figure 2 This is the first system based on augmentation sampling provided by the present invention;

[0042] Figure 3 This is the second system based on augmentation sampling provided by the present invention;

[0043] Figure 4 This is a diagram illustrating the direct implementation process of the interpolation filter provided by this invention. Detailed Implementation

[0044] Example 1:

[0045] This embodiment discloses a design method for a time series signal interpolation filter for fuel measurement, specifically as follows:

[0046] The periodic impulse sequence with period M is established as follows:

[0047]

[0048] Where: δ M (n) represents a periodic impulse sequence with period M; n, r, and M are all integers.

[0049] The time series xa(t) in the fuel measurement signal is sampled at uniform intervals T to obtain the sampling sequence x(n) = xa(nT). If we want to increase the sampling frequency by a factor of M, we can interpolate the sampling sequence x(n) as follows:

[0050]

[0051] Where: f(n) represents the interpolation sequence; This represents the signal sequence after being compressed by a multiple of the period of the periodic impulse sequence; δ M (n) represents a periodic impulse sequence with period M, where M represents the period of the periodic impulse sequence; This indicates that the period T is equal to the uniform interval. The sequence obtained after sampling; T / M and n / M are both integers.

[0052] Combining equation (1) and taking the discrete-time Fourier transform of both sides of equation (2), we can obtain the spectrum of the interpolated sequence as follows:

[0053]

[0054] Where: F(e) jω ) represents the spectrum of the interpolation sequence; e -jnω The basis functions represent the discrete-time Fourier transform.

[0055] Substituting n = rM into equation (3), we get:

[0056]

[0057] Equation (4) represents the spectrum F(e) of the interpolation sequence f(n). jω ) is the spectrum X(e) of the sequence x(n). jω The result of compressing by M times. Then, in F(e) jω The principal value interval is [-π, π]. The spectrum repeats M times, and the extra M-1 times are represented as X(e). jω The image of ). When |ω|≤π / M, F(e jω ) is simply equal to X(e) jMω Then, a post-digital low-pass filter is used to achieve this goal, as shown in the attached diagram. Figure 1 As shown, the frequency response of the post-digital low-pass filter is:

[0058]

[0059] Where: C is a constant; It is a unit step function.

[0060] According to formulas (4) and (5), the spectrum of the output sequence of the post-digital low-pass filter can be obtained as follows:

[0061]

[0062] Based on equation (6), we have:

[0063]

[0064] Based on equation (7), we have:

[0065]

[0066] To ensure that y(0) = x(0), we know from equation (8) that we should take C = M, so equation (5) can be simplified to:

[0067]

[0068] Set up an equivalent measurement system based on incremental sampling, such as Figure 2 As shown, we have:

[0069] W1(e jω )=X(e jω )H(e jω (10)

[0070] Considering:

[0071]

[0072] Taking the discrete-time Fourier transform of both sides of equation (11) and combining it with equation (4), we get:

[0073] Y(e jω ) = W1(e jMω (12)

[0074] Substituting equation (10) into equation (12), we get:

[0075] Y(e jω )=X(e jMω )H(e jMω ) = W2(e jω )H(e jMω (13)

[0076] Where: W2(e jω )=X(e jMω );

[0077] According to equation (13), the equivalent measurement system can be obtained as follows: Figure 3 As shown;

[0078] By comparison Figure 3 and Figure 2 It can be seen that if the interpolation filter is changed from a post-position to a pre-position, the frequency response of the measurement system is compressed by a factor of M; conversely, if the interpolation filter is changed from a pre-position to a post-position, the frequency response of the measurement system is expanded by a factor of M. This ensures that under the same input sequence x(n), the measurement system has the same output sequence y(n).

[0079] The unit impulse response of the post-digital low-pass filter is denoted by h(n). Let the length of h(n) be N, satisfying that N / M is a positive integer, then:

[0080]

[0081] According to equation (14), we get the following: Figure 1 The direct structure of the interpolation filter shown is equivalent to that of... Figure 4The structure shown.

[0082] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any way. Any simple modifications or equivalent changes made to the above embodiments based on the technical essence of the present invention shall fall within the protection scope of the present invention.

Claims

1. A method for designing a time-series signal interpolation filter for fuel measurement, characterized in that, Includes the following steps: Step 1: Based on the periodic impulse sequence, establish a discrete-time model of the fuel measurement signal; Step 2: Increase the sampling frequency of the fuel measurement signal by an integer multiple using upsampling technology to generate a high sampling rate interpolation sequence. Step 3: Analyze the spectral characteristics of the interpolated sequence using discrete-time Fourier transform to obtain the phenomena of spectral compression and repetition; Step 4: Design a post-digital low-pass filter based on spectral characteristics, and set the cutoff conditions of the post-digital low-pass filter to eliminate spectral imagery and retain the main value range signal. Step 5: Perform interpolation filtering based on the post-digital low-pass filter.

2. The method for designing a time-series signal interpolation filter for fuel measurement according to claim 1, characterized in that, Step 2 includes: Step 2.1: Sample the fuel measurement signal at uniform intervals to obtain a sampling sequence; Step 2.2: Interpolate the sampling sequence based on the period of the periodic impulse sequence to obtain the interpolated sequence.

3. The method for designing a time-series signal interpolation filter for fuel measurement according to claim 2, characterized in that, The interpolation sequence is: Where: f(n) represents the interpolation sequence; This represents the signal sequence after being compressed by a multiple of the period of the periodic impulse sequence; δ M (n) represents a periodic impulse sequence with period M, where M represents the period of the periodic impulse sequence; This indicates that the period T is equal to the uniform interval. The sequence obtained after sampling.

4. The method for designing a time-series signal interpolation filter for fuel measurement according to claim 3, characterized in that, Taking the discrete-time Fourier transform of the interpolated sequence, the spectrum of the interpolated sequence is obtained as follows: Where: F(e) jω ) represents the spectrum of the interpolation sequence; e -jnω The basis functions represent the discrete-time Fourier transform and are used to calculate the spectrum of complex exponentially modulated time-domain signals.

5. The method for designing a time-series signal interpolation filter for fuel measurement according to claim 4, characterized in that, Step 4 includes: Step 4.1: Obtain the frequency characteristics of the post-digital low-pass filter; Step 4.2: Obtain the spectrum of the output sequence of the post-digital low-pass filter based on the frequency characteristics and the spectrum calculation of the interpolation sequence; Step 4.3: Spectral Calculation Based on the Output Sequence of the Post-Digital Low-Pass Filter The output sequence of the post-digital low-pass filter.

6. The method for designing a time-series signal interpolation filter for fuel measurement according to claim 5, characterized in that, The spectrum of the output sequence of the post-digital low-pass filter in step 4.2 is as follows: Y(e jω )=F(e jω )H(e jω ); Where: Y(e) jω F(e) represents the spectrum of the output sequence of the post-digital low-pass filter; jω H(e) represents the spectrum of the interpolation sequence; jω ) represents the frequency response of the post-digital low-pass filter.

7. The method for designing a time-series signal interpolation filter for fuel measurement according to claim 6, characterized in that, The frequency characteristics obtained in step 4.1 are as follows: Where: H(e) jω ) represents the frequency response of the post-digital low-pass filter; M represents the period of the periodic impulse sequence, G 2π / M (ω)=ε(ω+π / M)-ε(ω-π / M), where ε(ω) is the unit step function and δ(ω-2kπ) represents an impulse at every 2kπ frequency, used to construct periodic frequency characteristics.

8. The method for designing a time-series signal interpolation filter for fuel measurement according to claim 7, characterized in that, The output sequence of the post-digital low-pass filter in step 4.3 is as follows: Where: y(n) represents the output sequence of the post-digital low-pass filter; Y(e jω () represents the spectrum of the output sequence of the post-digital low-pass filter; e jnω The basis functions represent the discrete-time Fourier transform.

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