We know at least three methods to extract the fundamental component of a power s

Question

We know at least three methods to extract the fundamental component of a power system signal:

(i) Use a linear phase FIR notch filter with the notch frequency at the fundamental frequency
(ii) Use an IIR notch filter with the notch frequency at the fundamental frequency
(iii) If only harmonics are present and the harmonic orders are known, use a cascade of notch
filters with notch frequencies at the harmonics.

Based on these:

Hw2Data.mat Data:

N = 80

f1 = 50

fs = 2000

x1:

x2:

x3:

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 13.7141 8.245079 7.200374 3.946568 5.643464 9.040315 7.219893 4.358713 1.620074 0.698051 2.829165 -1.30882 -8.28888 -5.68097 -3.15211 -5.50614 -0.65908 -0.4074 -15.9618 -23.1037 -13.7141 -8.24508 -7.20037 -3.94657 -5.64346 -9.04032 -7.21989 -4.35871 -1.62007 -0.69805 -2.82917 1.308815 8.288875 5.68097 3.152106 5.506142 0.659079 0.407403 15.96175 23.1037 13.7141 8.245079 7.200374 3.946568 5.643464 9.040315 7.219893 4.358713 1.620074 0.698051 2.829165 -1.30882 -8.28888 -5.68097 -3.15211 -5.50614 -0.65908 -0.4074 -15.9618 -23.1037 -13.7141 -8.24508 -7.20037 -3.94657 -5.64346 -9.04032 -7.21989 -4.35871 -1.62007 -0.69805 -2.82917 1.308815 8.288875 5.68097 3.152106 5.506142 0.659079 0.407403 15.96175 23.1037 Draw a block diagram for each of the methods listed above to extract the funda- mental component. Write a MATLAB function for each of the method listed above and test the function on the given data 'Hw2Data.mat' where there three signals x1, x2 and x3, all with sampling frequency fs-2 kHz and fundamental frequency fl = 50 Hz. From the output, what are the differences among the three options to extract the fundamental component? For function definitions, use function Fund xi -FundExtracI (x) function Fund-X11 = FundExtractII(x) function Fund-X111 = FundExtract111 (X) For output of test sequence, use x1_iFundExtractI (x1) x1-11 = FundExtr x1_1ii -FundExtract III (x1); n = 0:N-1; figure; plot (n, xl_i, n, xl_ii, ' :o', n, xl_iii, ' grid on; actII (x1); s', 'LineWidth', 2);

Explanation / Answer

The notch filter, which highly attenuates a particular frequency component in the input signal while leaving nearby frequency components relatively unchanged, is used in many applications. For example, the elimination of a sinusoidal interference corrupting a signal, such as the 60 Hz power-line interference in the design of a digital instrumentation system, is typically accomplished with a notch filter tuned to the frequency of the interference. Usually very narrow notch characteristic (width) is desired to filter out the single trequency or sinusoidal interference without distorting the signal. The design of infinite-duration impulse response (nR) notch filters has been considered by Carney (1963) and later by Hirano et al (1974). However, the design  

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