CMULTIPLY etc Instructions

CMULTIPLY( options ) cseries1 cseries2 start end newcseries newstart

CADD cseries1 cseries2 start end newcseries newstart

CDIVIDE cseries1 cseries2 start end newcseries newstart

CSUBTRACT cseries1 cseries2 start end newcseries newstart

The last three add, divide, and subtract a pair of complex series, respectively. The most important of the instructions is CMULTIPLY which multiplies one complex series by the complex conjugate of another. Typically, it is applied to Fourier transformed series to construct the periodogram or cross-periodogram.

Parameters

cseries1, cseries2	source series
start, end	range to transform, by default maximum common range of cseries1 and cseries2
newcseries	result series, by default, cseries1
newstart	start for newcseries, by default start

Option (CMULTIPLY only)

SCALE=real expression [unused]

Multiplies newcseries by a scalar. Usually 1./(2\(\pi\)*number of observations) when computing spectral density estimates.

Notes

CMULTIPLY is the instruction generally used to convert a Fourier transform into a spectrum and cross-spectrum. The proper scaling factor for spectral estimates is SCALE=1./(2*%PI*N), where N is the number of actual data points and not the padded length. If you use a taper, you should use the %SCALETAP variable defined by TAPER instead of N.

Examples

cmult(scale=1./(2*%pi*nobs)) 1 1

cmult 1 2 / 3

The first replaces series 1 by its squared absolute value (series 1 times its complex conjugate), divided by \(2\pi \text{NOBS}\). The second sets 3 equal to the product of 1 and the conjugate of 2.