Computer session on measurement and analysis of waves and turbulence
6th COSPAR Capacity Building Workshop 
Sinaia, Romania, June 4-16, 2007
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:
- Download the following IDL procedures:
- Read the comments and try to understand the code (the above sequence of files is recommended)
- Run the program example_power_spectrogram.pro.
- 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