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1994issue C041-2

Constructing WAMI power and phase spectra

A spreadsheet can evaluate WAMI power and phase spectra across a grid of cycle frequencies from the length parameters L, M, and N. Fourier sine, cosine, and two-argument arctangent terms turn those parameters into inspectable power and phase maps.

  • WAMI is a three-parameter cycle operator whose frequency behavior is read from constructed power and phase curves, not from a single opaque oscillator reading.
  • Spectral analysis here means evaluating power and phase on a cycle-frequency grid. Fourier analysis builds those spectra from sine and cosine terms and two-argument arctangent phase differences.
  • The length parameters L, M, and N reshape both spectra. A frequency increment of 1.0 is presented as adequate resolution, while an increment of 2.0 extends the higher-frequency portion of the plotted band.
  • Normalized power is a ratio of squared-magnitude terms scaled by its own maximum. Phase is set to 90 degrees at zero frequency, then to degree-converted two-argument arctangent differences of the intermediate vectors.
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Current trackFourier analysis41 readingsSpectral analysis63 readings

A spreadsheet for WAMI spectra

WAMI is a three-parameter cycle operator whose frequency behavior is read from constructed power and phase curves. A spreadsheet can be built to evaluate those WAMI power and phase spectra across a grid of cycle frequencies as functions of the length parameters L, M, and N.

Spectral analysis, in this construction, is inspection of the operator by evaluating power and phase at a grid of cycle frequencies over a stated sampling interval and lookback. Fourier analysis is the construction of those spectra from sine and cosine terms and two-argument arctangent phase differences.

Trial lengths and setup cells

The length parameters are the integers L, M, and N. They enter the trigonometric construction and therefore reshape both spectra. The worked construction uses the trial length values M = 5, L = 4, and N = 5.

Setup cells convert degrees to radians and compute 1/L together with the two coefficients used by later spectral columns.

The frequency grid

The frequency increment is the degree step that sets spectral resolution and the highest frequency shown on the grid. The frequency grid starts at 0 and is stepped by the chosen increment through a band ending at 75 degrees.

A frequency increment of 1.0 is presented as adequate resolution, while an increment of 2.0 extends the higher-frequency portion of the plotted band.

Power and phase from trigonometric terms

Intermediate columns combine sines and cosines of the grid frequency and of multiples set by the length parameters.

One intermediate series is a ratio of squared-magnitude terms. Dividing that series by its own maximum yields the normalized power spectrum: a magnitude response formed from ratios of squared trigonometric terms at each grid frequency.

Phase at zero frequency is set to 90 degrees. Remaining phase values are degree-converted two-argument arctangent differences of the intermediate vectors. That series is the phase spectrum, a phase response expressed in degrees.

Plotting the spectra

The WAMI spectra are obtained by plotting the normalized power series and the phase series against the frequency grid. Once those curves are in view, the operator can be read as a three-parameter instrument whose frequency behavior is visible before it is used as a later forecast baseline.

Educational research material, not investment advice. Historical source context does not establish present-day performance.
11 of 26 in the Fourier analysis track
19941-14 pp.Next on Fourier analysisFourier-tuned momentum filter designEstimate the dominant frequency and the trigger frequency from a Fourier spectrum of detrended history before choosing filter lengths.
All readings on this track · 26 readings
  1. 1982Critiquing Fourier, Elliott, and seasonal commodity models
  2. 1982Evaluating half-hour crossovers with cycle priors and stops
  3. 1984Building moving-window spectral cycle forecasts
  4. 1988Fourier cycles versus calendar seasonal regimes
  5. 1989Constructing analog cycle signatures from price lows
  6. 1990Curve fits fail the forecast test
  7. 1991Auditing moving-average length with Fourier spectra
  8. 1991Closed-form phase for dominant-cycle spectra
  9. 1993Evaluating windowed spectral forecasts of index turning points
  10. 1994Window length for moving-window spectral forecasts
  11. 1994Constructing WAMI power and phase spectra
  12. 1994Fourier-tuned momentum filter design
  13. 1994Aliasing, leakage, and dominant-cycle reads from sampled prices
  14. 1995Constructing indicator lookbacks from Fourier spectra
  15. 1996Constructing phase from a dominant-cycle sine and cosine pair
  16. 1999Sinusoidal pseudo-securities for indicator evaluation
  17. 2000Constructing dominant cycle length from Hilbert phase
  18. 2000Constructing adaptive channel breakouts from a measured cycle period
  19. 2005Embedding forex prices into a singular-spectrum forecast basis
  20. 2005Constructing recurrent forecasts from grouped spectral components
  21. 2007Constructing a dominant cycle from transformed Fourier spectra
  22. 2010Why cycle indicators fail when parameters shift
  23. 2019Constructing futures momentum as open-interest-scaled rate of change
  24. 2019Judging a dominant cycle and a trend filter by sample, lag and the move they keep
  25. 2020Constructing futures turnover time and urgency
  26. 2020Stock power ratio as a growth trend filter
By fieldCycles and spectral analysis129 readingsBy year1994135 readings
All 41 readings tagged Fourier analysis
Also on Fourier analysis5 readings
1982Building FFT spectra to size cycle filters1984Building moving-window spectral cycle forecasts1989Constructing analog cycle signatures from price lows1991Auditing moving-average length with Fourier spectra1991Closed-form phase for dominant-cycle spectra