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Use of the complex dynamic cross-spectrum for i...

Use of the complex dynamic cross-spectrum for indentifying sporadic radio emissions

Vladimir Kolyadin
LOFAR Transients Key Project Meeting, Meudon, December 2011

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June 23, 2012
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  1. The using of complex dynamic cross-spectra for identification of sporadic

    radio emission Vladimir L. Koliadin The Institute of Radio Astronomy of NASU, Kharkov, Ukraine W N S NS "West" "North" "South" 0.9km 0.9km 0.9km W N S NS "West" "North" "South" 0.9km 0.9km 0.9km 00 00 11 11 000 111 000 111 00 11 00 11 W2 W1 N2 N1 S1 S2
  2. Very short baseline interferometry (VSBI) • Idea: we form local

    interferometers within the antenna system of UTR-2 • Goal: to get and use information about the phase difference between antennas • Background: the phase difference carries information about the direction of arrival
  3. Some variants of local interferometers W N S NS "West"

    "North" "South" 0.9km 0.9km 0.9km W N S NS "West" "North" "South" 0.9km 0.9km 0.9km 0 0 1 1 000 111 000 111 000 111 000 111 W2 W1 N2 N1 S1 S2
  4. DSPZ - Digital spectral analyzer (RI NASU) DSPZ u1 (t)

    u2 (t) P1 (f, t) P2 (f, t) Re ˙ R12 (f, t) Im ˙ R12 (f, t)
  5. ˙ R(f, t) = P1 (f, t) ˙ R∗ 12

    (f, t) ˙ R12 (f, t) P2 (f, t) = R11 (f, t) ˙ R∗ 12 (f, t) ˙ R12 (f, t) R22 (f, t)
  6. ˙ S1i (f, t) = FFT(u1i (t)), t ∈ Ti

    ; ˙ S2i (f, t) = FFT(u2i (t)), t ∈ Ti ; ˙ Rmn (f, t) = 1 N K i=1 ˙ Smi (f, t) ˙ S∗ ni (f, t), m, n = 1, 2
  7. Dynamic spectra: at DSPZ output • P1 (f, t) =

    R11 (f, t) - power dynamic spectrum of the 1st antenna • P2 (f, t) = R22 (f, t) - power dynamic spectrum of the 2nd antenna • A12 (f, t) = | ˙ R12 (f, t)| - cross-power dynamic spectrum • Φ12 (f, t) = arg ˙ R12 (f, t) - phase dynamic spectrum
  8. Parameters of DSPZ Frequency range: 0 . . . 33MHz

    Frequency resolution: ∆f = 4kHz Frequency channels: K = 8192 Temporal resolution: ∆t = 0.001 . . . 0.1sec
  9. Two pairs of local interferometers 00 00 11 11 00

    11 00 11 000 111 000 111 W2 W1 N2 N1 S1 S2 ments