TD_POWERSPEC converts a series from the time or spatial domain to the frequency domain in order to facilitate frequency domain analysis. Its calculations serve to estimate the correct power spectrum associated with the series.
Frequency domain analysis converts a signal from the time domain into the frequency domain. The frequency domain representation shows how much of each frequency is present in the signal. It is useful for identifying patterns, trends, and anomalies that may not be apparent in the time domain.
In the frequency domain, a signal is parsed into a series of sine waves of different frequencies and amplitudes. The frequencies are represented using a plot called a power spectrum. The power spectrum shows how much power or energy is present in the signal at each frequency. It is used to identify the dominant frequencies in the signal and to estimate the overall strength of the signal. Fourier transform is the most common method used for frequency domain analysis.
The power spectrum is derived from the Fourier transform by taking the absolute value of the complex Fourier coefficients and squaring them. The resulting values represent the power or energy at each frequency component. The power spectrum is plotted as a function of frequency. The x-axis represents frequency and the y-axis represents power or energy.
The power spectrum provides valuable insights into the characteristics of a signal. For example, it can reveal the dominant frequencies present in the signal, help identify periodicity or cyclical patterns in the signal, filter out unwanted noise or interference in the signal, and compare signals.
Frequency domain analysis is used in signal processing, audio and image compression, and data compression. It is also used in scientific fields such as physics, chemistry, and biology to analyse experimental data and extract meaningful information about the underlying phenomena.
The following procedure is an example of how to use TD_POWERSPEC to run a Significant periodicities statistical test:
- Use TD_ARIMAESTIMATE to generate an ARTFITRESIDUALS layer.
- Use TD_EXTRACT_RESULTS to retrieve residuals from the TD_ARIMAESTIMATE ARTFITRESIDUALS layer.
- Use TD_POWERSPEC with FREQ_STYLE parameter set to K_PERIODICITY to perform spectral analysis on the extracted residuals, and place the results in an ART named PowerSpecResults.
- Use the following command to retrieve top five spectral density magnitudes:
SELECT TOP 5 * FROM PowerSpecResults ORDER BY SPECTRAL_DENSITY_field DESC; - Use the retrieved top five list to form a PERIODICITIES parameter list, and then use TD_SIGNIF_PERIODICITIES to run a significant periodicities test against the list.
- Retrieve results of the TD_SIGNIF_PERIODICITIES test.