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Tracking Digital Notch Filter Design and Application

With the design simple, and convenient, real-time and other properties,[link widoczny dla zalogowanych], can effectively eliminate the signal interference signals of unknown frequency. Second, the adaptive tracking digital notch filter design 1. Digital notch filters the basic principles of digital notch filter can trap the signal in addition to the specific frequency components, the corresponding frequency known as the notch frequency, while the other frequency components will not be affected. Generally the requirements of digital notch filters for two _1.2J,[link widoczny dla zalogowanych], one of its transfer function should be zero on the unit circle, so that it traps the notch depth is infinite; the second is the transfer function of the zeros and poles must be match, so in addition to the frequency of the notch, the rest of the excess pad! frequency components will not be affected. Meet the above requirements digital notch filter transfer function H (z) has the following form of mirror symmetry [,]: Japanese (I -): (1) l + a1pz + P where, z as a complex variable, P is close to 1 but a constant slightly less than 1, the introduction of P guarantees that at (z) each have a zero near the corresponding pole, and the zeros and poles in the same radius of the line, but a little close to the origin of the pole, P value also determines the size of the width of the notch frequency _lJ. From (1) shows that,[link widoczny dla zalogowanych], when z == e, r, the digital notch filter notch frequency fo for the J:-arc-cos (-al / 2) (2) ,0 --- z, type , for the sampling period. 2. Tracking Digital notch filter design without loss of generality, assume that the expression for the interference signal: r (t) = rmsin (2 ~ rft +) + rt (t) (3) where, r for the interference signal Peak (V); plant for the interference signal frequency (Hz); for the initial phase (rad); rt (t) for other random interference. Let (t) through the digital notch filter, according to equation (1) transfer function, the output is e (t), then there is e (t) = (t) + a1 (t A 1) + (t-2) A alpe (t-1) a Pe (t-2) (4) Order J (a1) = Σe (t) (5) Clearly, the J (a.) Minimize a. Corresponds to the signal frequency (see equation 2). lll stiff which 'adaptive least square method to obtain the mouth. , The algorithm is expressed as [3]: fe (t) = (t) + port 1 (t a 1) (t A 1) + I (? a 2) to port 1 (I 1) P (?) { e (? A 1) a P (?) e (? a 2) IP (t) = P (t A 1) / ((t) +, (t) e (t) a dictionary of I (t) = port I (t A 1) + P (t), (t) P (t) where (t) = de (t) / da = (t-1) a P (t) e (t-1) a 1 ( t-1) P (t) 1 (t-1) a (t) (t a 2) (t) =,[link widoczny dla zalogowanych], lo2 (t A 1) + (1 + o) p (?) Pop (? A 1) + (1 A Po) p (∞) (6) (t) for the adaptive forgetting factor; to make sine wave frequencies fall within the notch to P (t) instead of P so that they are adaptive (0) = 0.95, o = 0.99p (0) = 0.75, Po = 0.99,[link widoczny dla zalogowanych], P (∞) = 0.995 port 1 (0) = 0, (0) = (a 1) = 0, P (0) = 1043. system structure shown in Figure 1, adaptive tracking digital notch filter interference signals received with the same frequency reference signal r (t), by (6) obtained with the interference signal frequency corresponding parameter port. using digital notch filter ports constitute the H (z), can be trapped in addition to the signal interference signals, where P 0.8 according to the actual situation preferable to 0.95. Clearly, the adaptive tracking digital notch wave filter can automatically track the frequency of interference signals, so even if the frequency of interference signal fluctuates, the digital notch filter H (z) the corresponding frequency interference can also signal to eliminate it. * 6 Figure 1 c, test results (t), where r50 +0.1 t0s ≤ t <2s factory = {50.22s ≤ ? <3s ,50.2-0 .1 t3s ≤ t <4s55535l49 {;} L4745_.1 a II a 'a 2Iijr-IO234 time / s' Figure 2 Figure 3 from a vibration (piezoelectric) sensor to obtain the signal, the signal frequency by 50Hz interference pollution. use this method to process the signal, reference signal r (t) frequency signal is taken as the same frequency with the AC power signal, the results of treatment shown in Figure 4. can be seen that the processed signal to the expected requirements. 5 of Guangdong, a 500.5 0 time / s Figure 3I1l Hitomi ■ ridicule sleep

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