PSERIES (Jan93) grasp.grtools PSERIES (Jan93) NAME pseries -- Calculate the Power Spectra of a GONG time series image. USAGE pseries input output PARAMETERS input Input image list. output Output image list. type_output = "gong" Output data type. "fft" Complex FFT: (band1 = real part, band2 = imaginary part). "power" Power/Phase: (band1 = power, band2 = phase). "gong" Power/Phase in GONG power spectrum format. window = "none" Type of window to be used on the data before transforming. Five of the most commonly used windows are available. (N = number of points) "bartlett" |j - 0.5*N| w(j) = 1 - |---------| | 0.5*N | "hamming" w(j) = 0.54 - 0.46*cos(2*pi*j/(N-1)) "hanning" w(j) = 0.5 * [1. - cos(2*pi*j/"(N-1))] "parzen" |j - 0.5*(N-1)| w(j) = 1 - |-------------| | 0.5*(N+1) | "welch" 2 /j - 0.5*(N-1)\ w(j) = 1 - < ------------- > \ 0.5*(N+1) / gapfill = yes Use gap-filled data. DESCRIPTION PSERIES computes the 1-dimensional FFT of the input image line(s) and writes the result to the corresponding line(s) of the output image according to type_output. The task assumes that the input image data is the complex time series of spherical harmonic coefficients stored in GONG format. That is, a 3-d image where band 1 contains the REAL part and band 2 contains the IMAGINARY part. The task expects to find the following header keywords in addition to a GONG MWCS: L_VALUE - The spherical harmonic degree L of the input image. MTYPE - "even" or "all" If type_output = "fft" or "power", the output image will be either the complex FFT or power spectrum, with no special reformatting. If type_output = "gong", the output image will be reformatted to GONG power spectra: 3-d images where band1 = power, band2 = phase. The columns will be the frequency bins, and each line will hold the power spectrum of a specific spherical harmonic "m": line[1] => m=-L, line[naxis2] => m=L, for even m's only. The input image lines are windowed according to window and zero-padded to the next power of two (if necessary) prior to transforming. If gapfill = YES, the task will use all the data (i.e., assuming that some type of gap filling algorithm has been previously applied to the time series). If gapfill = NO, then each line of the input image will be multiplied by the observing window (stored in the last line of that image) to set any gap filled data to zero before the FFT is done. EXAMPLES 1. To calculate the GONG power spectrum of an image: gr> pseries imageA imageB 2. To calculate the power spectrum but not have the standard GONG output format: gr> pseries imageA imageB type=power TIME REQUIREMENTS The following timings are for a Sun 3/60 (with disk) using 68881 binaries, and a Sun 4/370. The task was used to FFT a 512x127x2 GONG image (i.e., an l=250 time series of 8.5 hours duration). Image Size CPU Time (seconds) ------------------------------------------------ Sun 3/60 Sun 4/370 512x127x2 35.5 5.01 BUGS No renormalization is done if a window is used. SEE ALSO pseries, ptox, xtop