Computer session on measurement and analysis of waves and turbulence

6th COSPAR Capacity Building Workshop

Sinaia, Romania, June 4-16, 2007

Ondrej Santolik


2. Time-frequency analysis

A useful way to represent wave measurements are time-frequency power spectrograms. A power spectrogram can be obtained from a measured time series of samples of a given quantity (a waveform) using the Fourier analysis of separate time intervals. We can then represent the power spectra in thin vertically oriented rectangular areas in the time-frequency plane. These rectangles together form a 3D power spectrogram where different levels of the power spectral density correspond to different colors on a predefined color scale. The power spectral density is thus given as a function of time and frequency. For example, if we measure an electric field component in V m-1, the resulting power spectral density will be given in the same units as the separate power spectra, it means in V2m-1Hz-1. Note: Other methods to estimate the power spectral density in the time-frequency plane can be used, and are often very useful (for example, the wavelet analysis) but these are not discussed here.

Instructions:

  1. Download the following IDL procedures:
  2. Read the comments and try to understand the code (the above sequence of files is recommended)
  3. Run the program example_power_spectrogram.pro.
  4. Modify and re-run the program using different frequency resolutions (controlled by the nfft parameter), averaging of the data (nave parameter), and different waveform data sets.

Reading: The ISSI book, Chapters 1.1-1.3