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NAME: cross_spec PURPOSE: This function estimates the power cross-spectrum of two vectors. CATEGORY: Time Series Analysis CALLING SEQUENCE: Result = cross_spec(Y1, Y2) INPUTS: Y1: A floating point vector of the same length as Y2. Y2: A floating point vector of the same length as Y1. OPTIONAL INPUTS: - DELTAT, WIDTH, WINDOW KEYWORD PARAMETERS: AMPLITUDE: Returns the amplitude component of the cross-spectrum. AUTOSPEC1: Returns the auto-spectrum of Y1. AUTOSPEC2: Returns the auto-spectrum of Y2. COHERENCY: Returns the coherency of Y1 and Y2. DELTAT: The time interval between values in the input vectors. DOUBLE: If set the calculations are performed in double precision arithmetic. The default is single precision. FREQ: Returns the frequency values corresponding to the output cross-spectrum. PHASE: Returns the phase component of the cross-spectrum, in radians. Positive values mean that Y1 is leading Y2 at that frequency. WIDTH: The width, of type integer, of the smoothing window to be used by FILTER.pro. If not given then no smoothing is performed. WINDOW: A string containing the name of the smoothing window to be used by FILTER.pro. Smoothing is only performed if WIDTH is given. OUTPUTS: Result: Returns the cross-spectrum. AMPLITUDE, AUTOSPEC1, AUTOSPEC2, COHERENCY, FREQ, PHASE USES: FILTER.pro PROCEDURE: This function uses the FFT function to estimate the spectra. EXAMPLE: Create two time series of a periodic signal of period 23 and phase difference pi/2. Add a pinch of noise. y1 = sin(6.28*findgen(1000)/23.)+0.1*randomn(1, 1000) y2 = sin(6.28*(findgen(1000)/23.-0.25)) $ +0.1*randomn(2, 1000) Estimate the cross-spectrum. result = cross_spec(y1, y2, amplitude=amplitude, phase=phase, freq=freq) The amplitude power spectrum should have a peak at freq=1./23., and the phase at that frequency should be 0.5. CODE: A. Shinbori, 30/09/2011. MODIFICATIONS: A. Shinbori, 30/10/2011 ACKNOWLEDGEMENT: $LastChangedBy: jimm $ $LastChangedDate: 2014-02-11 10:52:58 -0800 (Tue, 11 Feb 2014) $ $LastChangedRevision: 14325 $ $URL $
(See projects/iugonet/tools/statistical_package/coherence_analysis/cross_spectrum/cross_spec.pro)
NAME: dimension PURPOSE: This function returns the dimension of an array. It returns 0 if the input variable is scalar. CATEGORY: Array CALLING SEQUENCE: Result = DIMENSION(Inarray) INPUTS: Inarray: A scalar or array of any type. OUTPUTS: Result: The dimension of Inarray. Returns 0 if scalar. PROCEDURE: This function runs the IDL function SIZE. EXAMPLE: Define a 3*4-element array. x = findgen(3,4) Calculate the dimension of x. result = dimension(x) MODIFICATIONS: A. Shinbori, 30/10/2011 ACKNOWLEDGEMENT: $LastChangedBy: jimm $ $LastChangedDate: 2014-02-11 10:52:58 -0800 (Tue, 11 Feb 2014) $ $LastChangedRevision: 14325 $ $URL $
(See projects/iugonet/tools/statistical_package/coherence_analysis/cross_spectrum/dimension.pro)
NAME: filter PURPOSE: This function returns a smoothed version of the input vector. CATEGORY: Time Series Analysis CALLING SEQUENCE: Result = FILTER( Vector, [Width], [Window] ) INPUTS: Vector: An vector of type floating point and length N. OPTIONAL INPUTS: Width: The width, of type integer, of the smoothing window. Window: A string containing the name of the smoothing window to return. Options are 'boxcar', 'gaussian', 'hanning', 'triangle'. The default is a boxcar window. KEYWORD PARAMETERS: BOXCAR: Sets the smoothing window to a boxcar filter. This is the default. If set to a value, it replaces Width. EDGE_TRUNCATE: Set this keyword to apply the smoothing to all points. If the neighbourhood around a point includes a point outside the array, the nearest edge point is used to compute the smoothed result. If EDGE_TRUNCATE is not set, the points near the end are replaced with NaNs. FILTER: A vector containing the filter window to use. This overrides the window requested in the Window input. This also returns the filter after use. NAN: Set this keyword to ignore NaN values in the input array, provided there is at least one defined value nearby. The default is to return NaNs wherever they occur. NO_NAN: Obsolete version of NAN keyword retained for compatibility but no longer used. START_INDEX: The location of the centre of the window for the first averaged output value, in units of Vector indices. Values must be greater than 0. The default is 0. STEP: An integer defining the step size for window translation, in units of Vector indices. The default is 1. TRIANGLE: Sets the smoothing window to a triangle filter. The default is a boxcar filter. If set to a value, it replaces Width. WRAP_EDGES: If set, the vector is treated as being cyclic and the ends are joined together when smoothing. OUTPUTS: Result: Returns the smoothed version of Vector. USES: dimension.pro filter_window.pro plus.pro PROCEDURE: This function manually convolves the input vector with the filter. EXAMPLE: Create a vector of daily data and a sinusoid for a year. x = randomn( seed, 365 ) + sin( 6.28 * findgen( 365 ) / 365. ) Smooth x with a boxcar filter of 7 days, wrapping the edges together. result = filter( x, 7, 'boxcar', /wrap_edges ) CODE: A. Shinbori, 30/09/2011. MODIFICATIONS: A. Shinbori, 30/10/2011 ACKNOWLEDGEMENT: $LastChangedBy: jimm $ $LastChangedDate: 2014-02-11 10:52:58 -0800 (Tue, 11 Feb 2014) $ $LastChangedRevision: 14325 $ $URL $
(See projects/iugonet/tools/statistical_package/coherence_analysis/cross_spectrum/filter.pro)
NAME: filter_window PURPOSE: This function returns a desired filter window of desired width. CATEGORY: Time Series Analysis CALLING SEQUENCE: Result = filter_window([Width],[Window]) OPTIONAL INPUTS: Width: The width of the filter window, of type integer. Window: A string containing the name of the smoothing window to return. Options are 'boxcar', 'gaussian', 'hanning', 'triangle'. The default is a boxcar window. KEYWORD PARAMETERS: BOXCAR: Sets the output to a boxcar window. This is the default. If set to a value, it replaces Width (obsolete option). DIMENSION: The dimension of the filter, of type integer. The default is 1. TRIANGLE: Sets the output to a triangle window. The default is a boxcar window. If set to a value, it replaces Width (obsolete option). OUTPUTS: Result: Returns the desired filter window. PROCEDURE: This function builds a filter of the desired shape and width, and then normalises it. EXAMPLE: Define a two dimensional boxcar window of width 5. result = filter_window( 5, 'boxcar', dimension=2 ) result should be a 5x5 matrix with 0.04 for all entries. CODE: A. Shinbori, 30/09/2011. MODIFICATIONS: A. Shinbori, 30/10/2011 ACKNOWLEDGEMENT: $LastChangedBy: jimm $ $LastChangedDate: 2014-02-11 10:52:58 -0800 (Tue, 11 Feb 2014) $ $LastChangedRevision: 14325 $ $URL $
(See projects/iugonet/tools/statistical_package/coherence_analysis/cross_spectrum/filter_window.pro)
NAME: plus PURPOSE: This function returns 1 if the input is positive, 0 otherwise. CATEGORY: Mathematics CALLING SEQUENCE: Result = PLUS( Y ) INPUTS: Y: A scalar or array of type integer or floating point. OUTPUTS: Result: Returns 1 if Y is positive, 0 otherwise. PROCEDURE: This function determines whether Y is greater than 0. EXAMPLE: Determine if 3 is positive. result = plus( 3 ) CODE: A. Shinbori, 30/09/2011. MODIFICATIONS: A. Shinbori, 30/10/2011 ACKNOWLEDGEMENT: $LastChangedBy: jimm $ $LastChangedDate: 2014-02-11 10:52:58 -0800 (Tue, 11 Feb 2014) $ $LastChangedRevision: 14325 $ $URL $
(See projects/iugonet/tools/statistical_package/coherence_analysis/cross_spectrum/plus.pro)
PROCEDURE: TEST_CROSS_SPEC.PRO A sample crib sheet that explains how to use the "cross_spec.pro" procedure. You can run this crib sheet. Or alternatively compile and run using the command: .run test_cross_spec Written by: A. Shinbori, May 01, 2013 Last Updated: A. Shinbori, May 01, 2013
(See projects/iugonet/tools/statistical_package/coherence_analysis/cross_spectrum/test_cross_spec.pro)