Multitaper Spectral Analysis and Wavelet Denoising Applied to Helioseismic Data

Solar Oscillation Frequency Changes on Time Scales of Nine Days

“…We examine time series of nine-days length which were processed with a multi-taper spectral analysis (Komm et al, 1999) to produce power spectra for each spherical harmonic degree ( ℓ ) and order ( m ) up to ℓ = 100. The mode frequencies characterized by n, ℓ, and m were estimated by fitting the individual peaks (Anderson, Duvall, and Jefferies, 1990).…”

“…Here, P j is the Legendre polynomial of order j, a j are the splitting coefficients, and we take j max to be nine. Since the optimal number of tapers depends on the length of the time series (Komm et al, 1999), we use three generalized-sine tapers for the nine-day time series as opposed to five for the standard GONG procedure which measures frequencies from time series of 108 days duration. It should be noted that not all modes are fitted successfully at every epoch due to the stochastic nature of the modes.…”

“…However, there is still no consensus regarding the physical mechanism that gives rise to these changes (Kuhn, 2001). One deficiency is the lack of measurements for modes at high frequency and high degree (Rhodes, Reiter, and Schou, 2003) and little information about the correlation on short time scales.…”

Observational techniques to measure solar and stellar oscillations

“…It can also be demonstrated that the variance of the MT spectrum is reduced by a factor ∼ 1/N 3 (Komm et al 1999). Several functions can be used as tapers (e.g.…”

“…Slepian tapers, Slepian 1978), but they are difficult to calculate. Indeed a simpler approach is to use as tapers sinusoidal functions in which the first taper is similar to a Hanning window (Komm et al 1999). In Fig.…”