A method for separating sinusoidal sweep plus random mixed signals
By sampling and integrating the sinusoidal sweep signal phase as a reference, the difficulty of separating sinusoidal sweep signals from random mixed signals is solved, achieving fast and high-precision signal separation.
Patent Information
- Application Number
- CN202211101532.5
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2022-09-09
- Publication Date
- 2026-02-27
- Estimated Expiration
- 2042-09-09
AI Technical Summary
Separating sinusoidal sweep signals from random mixed signals presents challenges such as difficulty in amplitude identification, low accuracy, and computational complexity.
By setting the phase of the sinusoidal sweep signal as a reference, the mixed signal is sampled at equal phase intervals, time normalization is performed, and the instantaneous amplitude and phase are obtained using the correlation integration method. The sinusoidal sweep signal is then recovered and subtracted from the mixed signal to separate the random signal.
It achieves fast and high-precision separation of sinusoidal frequency sweep and random signals, is applicable to a variety of mixed signal types, is easy to calculate, has high separation accuracy, and is widely adaptable.
Smart Images
Figure CN115526240B_ABST
Abstract
Description
TECHNICAL FIELD
[0001] The present application relates to the field of digital signal processing, and particularly relates to a method for separating a sinusoidal sweep plus random mixed signal. BACKGROUND
[0002] In a sinusoidal sweep plus random combined vibration environment simulation test, the precision of the sinusoidal sweep signal directly affects the control precision of the sinusoidal sweep and the random signal, and the separation of the sinusoidal sweep and the random mixed signal has problems such as difficulty in amplitude identification, low precision, and complex calculation. Therefore, the present application provides a method for separating a mixed signal. SUMMARY
[0003] The present application provides a method for separating a signal, which can quickly and accurately identify the amplitude and phase of the sinusoidal sweep signal in the mixed signal, subtract the sinusoidal sweep signal from the mixed signal, and obtain the random signal, thereby separating the sinusoidal sweep signal and the random signal.
[0004] The present application is implemented as follows:
[0005] A method for separating a sinusoidal sweep plus random mixed signal, characterized in that the method comprises the following steps: step one, providing a sinusoidal sweep plus random mixed time domain signal; step two, sampling the mixed signal once every same phase based on the phase of the sinusoidal sweep signal, and performing time normalization on the obtained sampling signal, that is, reconstructing the sampling signal into a sinusoidal constant frequency plus random mixed signal; step three, obtaining the instantaneous amplitude and instantaneous phase of the signal by using the correlation integral method, thereby recovering the original sinusoidal sweep signal, subtracting the obtained sinusoidal sweep signal from the original sinusoidal sweep plus random mixed signal, and obtaining the random signal, thereby completing the separation of the signal.
[0006] Further, in step one, taking a logarithmic sweep signal as an example, the sinusoidal logarithmic sweep plus random mixed signal is represented as:
[0007]
[0008] In the formula, t is time, y(t) is the mixed signal, is the sinusoidal sweep signal, A(t) is the instantaneous amplitude of the sinusoidal sweep signal, is the instantaneous phase, β is the logarithmic sweep rate, and f s is the starting frequency of the sweep, φ is the initial phase, and r(t) is the random signal.
[0009] Further, step two is specifically as follows:
[0010] Resampling the signal, starting from the first data point, sampling once every interval Δφ phase, where the instantaneous phase of the current sample is The instantaneous phase of the next sample is The relationship between the two instantaneous phases is as follows
[0011]
[0012] From equation (1) and equation (2), we can deduce that:
[0013]
[0014] Where t0 is the current sampling time, t1 is the next sampling time, according to this method from the initial time to calculate the sampling time in turn, at each sampling time point, the original signal is resampled, and the resampled signal is time normalized, which can be reconstructed into a sinusoidal constant frequency mixed signal.
[0015] Further, the third step is specifically:
[0016] Identify the instantaneous amplitude and phase of the sinusoidal constant frequency signal in the reconstructed mixed signal, and let the reconstructed sinusoidal constant frequency mixed signal be expressed as follows:
[0017] y(t') = A(t') sin(ω k t' + φ) + r(t') (4)
[0018] Where t' represents the normalized time sequence after reconstruction, A(t) is the instantaneous phase, ω k is the angular frequency of the sinusoidal constant frequency signal in the reconstructed signal, and r(t') is the reconstructed random signal. The product of equation (4) and the sine function sin(ω k t') is integrated within a period of time [t i ', t t '+T k ], where T k represents the period of sin(ω k t'), and the correlation integral function is:
[0019]
[0020] Similarly, the correlation integral function of the product of equation (4) and the cosine function cos(ω k t') within a period of time [t i ', t t '+T k ] is:
[0021]
[0022] The instantaneous amplitude and phase of the sinusoidal signal with frequency ω i ′,t t ′+T k ] can be obtained from formula (5) and (6) as follows: k
[0023]
[0024] In this way, each period of time is divided into a segment from the starting time to the ending time, and the instantaneous amplitude and phase of the sinusoidal signal in each segment are sequentially obtained;
[0025] The sinusoidal signal with the obtained instantaneous amplitude and phase is recovered as a sinusoidal sweep signal, which is the sinusoidal sweep signal of the original mixed signal. The random signal in the original mixed signal can be separated by subtracting the sinusoidal sweep signal from the original mixed signal.
[0026] The beneficial effects of the present application over the prior art are that the signal separation method realizes the separation of the sinusoidal sweep plus random mixed signal, can be applied to the separation of the sinusoidal fixed frequency plus random mixed signal, the sinusoidal logarithmic sweep plus random mixed signal, and the sinusoidal linear sweep plus random mixed signal, is relatively simple to calculate, fast in calculation speed, high in separation precision, and wide in signal range. BRIEF DESCRIPTION OF DRAWINGS
[0027] Figure 1 is a flow chart of sinusoidal sweep plus random mixed signal separation;
[0028] Figure 2 is an acceleration power spectral density graph of the random signal;
[0029] Figure 3 is the instantaneous amplitude and instantaneous phase of the sinusoidal signal identified in the mixed signal;
[0030] Figure 4 is a comparison chart of the sinusoidal sweep plus random mixed signal separation into the sinusoidal sweep and the random signal. DETAILED DESCRIPTION
[0031] To make the purpose, technical solutions and effects of the present application clearer and more explicit, the following examples are used to further describe the present application. It should be noted that the specific implementation described herein is only used to explain the present application and does not limit the present application.
[0032] The present application is implemented as follows: the flow of the present application is shown in Figure 1 Taking the sinusoidal logarithmic sweep plus random mixed signal as an example, a sinusoidal sweep plus random mixed time domain signal is first generated, and a waveform segment thereof is shown in Figure 4 (a) as shown, then the mixed signal is sampled once every interval of the same phase based on the phase of the sinusoidal sweep signal, the obtained sampling signal is time normalized, i.e. reconstructed into a sinusoidal constant frequency plus random mixed signal, then the instantaneous amplitude and instantaneous phase of the signal are obtained using the correlation integral method, i.e. as shown in Figure 3 Figure 4 (b) as shown, the sinusoidal sweep signal obtained is subtracted from the original sinusoidal sweep plus random mixed signal, i.e. the random signal can be obtained, and a waveform segment thereof is as shown in Figure 4 (c) as shown, thus completing the separation of the signals.
[0033] The specific process is as follows: assuming that the sweep range of a sinusoidal sweep signal is 5-100 Hz, the amplitude is 1 g, the initial phase is 0, and the sweep rate is 4 oct / min, assuming that the acceleration power spectral density of a random signal is as shown in FIG. 2, the sinusoidal sweep time domain signal and the random time domain signal are superimposed to obtain a mixed time domain signal, which is expressed as
[0034]
[0035] where t is time, y(t) is the mixed signal, is the sinusoidal sweep signal, is the instantaneous phase, and r(t) is the random signal, and a waveform segment thereof is as shown in Figure 4 (a) as shown,
[0036] Then the signal is resampled, starting from the first data point, and the instantaneous phase is sampled once every interval of , as shown in , the instantaneous phase of the next sampling is , then the relationship between the two instantaneous phases is as follows:
[0037]
[0038] It can be deduced from equation (1) and equation (2) that:
[0039]
[0040] where t0 is the current sampling time, and t1 is the next sampling time, according to this method, the sampling time after the initial time is calculated in sequence, and the original signal is resampled at each sampling time point, and the resampled signal is time normalized, i.e. reconstructed into a sinusoidal constant frequency plus random mixed signal.
[0041] Then the instantaneous amplitude and phase of the sinusoidal constant frequency signal in the reconstructed mixed signal are identified, assuming that the reconstructed sinusoidal constant frequency plus random mixed signal is expressed in the following form:
[0042] y(t′)=sin(ω k t′)+r(t′) (4)
[0043] In the formula, t′ represents the reconstructed and normalized time series, and ω k Let r(t′) be the angular frequency of the sinusoidal fixed-frequency signal in the reconstructed signal, and r(t′) be the reconstructed random signal. Then, let equation (4) be combined with the sinusoidal function si. n (ω k The product of t′) over one period of time [t i ′,t t ′+T k Integrate within the formula, where T k sin(ω) k The period of t′ is expressed by the relevant integral function as follows:
[0044]
[0045] Similarly, equation (4) and the cosine function cos(ω) k The product of t′) over one period of time [t i ′,t t ′+T k The relevant integral function within the brackets is:
[0046]
[0047] From equations (5) and (6), we can obtain the result at time [t]. i ′,t t ′+T k The internal frequency is ω k The instantaneous amplitude and phase of the sinusoidal signal are:
[0048]
[0049] This method divides the time interval from the start time to the end time into segments, each lasting one cycle. The instantaneous amplitude and phase of the sinusoidal fixed-frequency signal within each segment are then calculated sequentially. The instantaneous amplitude and phase of the sinusoidal signal at different frequencies are obtained as follows: Figure 3 As shown.
[0050] The instantaneous amplitude and phase of the obtained sinusoidal signal, along with the time information from the fixed-phase resampling, are used to reconstruct a sinusoidal swept frequency signal, the waveform of which is shown below. Figure 4 As shown in (b), this sweep frequency signal is the sinusoidal sweep frequency signal of the original mixed signal. By subtracting this sinusoidal sweep frequency signal from the original mixed signal, the random signal in the original mixed signal can be separated, and its waveform is as follows. Figure 4 As shown in (c).
[0051] The above merely describes the preferred embodiments of the present application, and it should be pointed out that those skilled in the art can make several improvements without departing from the principles of the present application, and these improvements should also be considered as the protection scope of the present application.
Claims
1. A method for separating sinusoidal frequency sweep plus random mixed signals, characterized in that, The method is as follows: Step 1: Given a sinusoidal sweep frequency plus random mixed time-domain signal; Step 2: Using the phase of the sinusoidal sweep signal in the mixed signal as a reference, sample the mixed signal once at equal phase intervals. Perform time normalization on the obtained sampled signals, thus reconstructing a sinusoidal fixed-frequency plus random mixed signal. Specifically, Step 2 involves: Resampling of the signal is performed, starting from the first data point, sampling once every Δφ phase interval. For example, the instantaneous phase of the current sample is... The instantaneous phase of the next sample is The following relationship exists between the two instantaneous phases. From equations (1) and (2), we can deduce that: In the formula, t0 is the current sampling time, and t1 is the next sampling time. Following this method, the subsequent sampling times are calculated sequentially from the initial time. The original signal is resampled at each sampling time point. The resampled signal is then time-normalized to reconstruct a sinusoidal fixed-frequency plus random mixed signal. Step 3: Use the correlation integration method to obtain the instantaneous amplitude and instantaneous phase of the signal, which can recover the original sinusoidal sweep frequency signal. Subtract the obtained sinusoidal sweep frequency signal from the original sinusoidal sweep frequency plus random mixed signal to obtain the random signal. This completes the signal separation.
2. The method for separating sinusoidal sweep frequency plus random mixed signals according to claim 1, characterized in that, In step one, for logarithmic frequency sweep, let the sinusoidal frequency sweep plus random mixed signal be represented as: In the formula, t represents time, and y(t) represents the mixed signal. Let A(t) be a sinusoidal sweep frequency signal, and let A(t) be the instantaneous amplitude of the sinusoidal sweep frequency signal. f is the instantaneous phase, β is the logarithmic sweep rate, and its unit is oct / min. s φ is the starting frequency of the sweep, φ is the initial phase, and r(t) is the random signal.
3. The method for separating sinusoidal sweep frequency plus random mixed signals according to claim 1, characterized in that, Step three specifically refers to: Identify the instantaneous amplitude and phase of the sinusoidal fixed-frequency signal in the reconstructed mixed signal. Suppose the reconstructed sinusoidal fixed-frequency plus random mixed signal is represented in the following form: y(t′)=A(t′)sin(ω k t′+φ)+r(t′) (4) In the formula, t′ represents the reconstructed and normalized time series, and ω k Let A(t′) be the angular frequency of the sinusoidal fixed-frequency signal in the reconstructed signal, A(t′) be the instantaneous amplitude, and r(t′) be the reconstructed random signal. Equation (4) is compared with the sine function sin(ω). k The product of t′) over one period of time [t′ i ,t′ t +T k Integrate within [T] k sin(ω) k The period of t′ is expressed by the relevant integral function as follows: In the formula, equation (4) is related to the cosine function cos(ω). k The product of t′) over one period of time [t′ i ,t′ t +T k The relevant integral function within the brackets is: From equations (5) and (6), we can obtain the result at time [t]. i ′,t t ′+T k The internal frequency is ω k The instantaneous amplitude and phase of the sinusoidal signal are: In this way, the time interval from the start time to the end time is divided into segments, and the instantaneous amplitude and phase of the sinusoidal fixed-frequency signal in the mixed signal are calculated sequentially in each time interval. The instantaneous amplitude and phase of the obtained sinusoidal signal are used to recover the sinusoidal sweep frequency signal. This sweep frequency signal is the sinusoidal sweep frequency signal of the original mixed signal. By subtracting this sinusoidal sweep frequency signal from the original mixed signal, the random signal in the original mixed signal can be separated.