# demod_cmplx

Perform a complex demodulation on one or more time series.

*Available in version 6.4.0 and later.*

## Prototype

load "$NCARG_ROOT/lib/ncarg/nclscripts/csm/contributed.ncl" function demod_cmplx ( x : numeric, frqdem [1] : numeric, frqcut [1] : numeric, nwt [1] : integer, ndim [1] : integer, opt [1] : logical )

## Arguments

*x*

Array of any dimensionality. The 'time' dimension should be equally spaced.

*frqdem*

The demodulation frequency (cycles per data point). The choice of *frqdem* may
be guided by theory or by a (say) Fourier analysis (e.g., a periodogram) of a series.
The range: 0.0 < *frqdem* < 0.5

*frqcut*

The cutoff frequency. Typically,
*frqcut*=*frqdem* or *frqcut*=*0.50*frqdem* or
*frqcut*=*0.75*frqdem*. Note: *nwt* should be set such that
it passes the desired information.`

*nwt*

A scalar indicating the total number of weights (must be an odd
number; *nwt* >= 3). The more weights, the better the filter,
but there is a greater loss of data.

*ndim*

The dimension of *x* containing the time series.

*opt*

Currently not used. Set to False.

## Return value

A variable of type list containing two arrays of the same sizes, shape and type as *x*.
The two variables (arrays) are the raw demodulated amplitudes and phases. **NOTE:**
The variables within the list can be accessed directly. However, many users find it clearer to
explicitly extract the variables and subsequently delete the returned list variable. See examples.

## Description

The term demodulation refers to extracting (recovering) information about a specific signal
from a series containing information from many signals.
Complex demodulation may be viewed as a local (instantaneous) version of harmonic analysis.
The purpose is to estimate the amplitude [ **A**(t) ] and phase [ **P**(t) ] of a slowly
varying oscillation in the neighborhood of *frqdem*
[*ie*: **A**(t)*cos(2*pi*** frqdem** +

**P**(t)) ]. The resulting series

**must**be further post-processed via a low-pass filter.

As noted in the S-Plus documentation: To better understand the results of complex demodulation several lowpass filters should be tried: the smaller the low pass band, the less instantaneous in time but more specific in frequency is the result.

References:

Bloomfield, P. (1976) Fourier Analysis of Time series: An Introduction Wiley , 1976: Chapter 6 Kessler: U. Washington:Complex DemodulationPMEL:Complex Demodulation

## See Also

**filwgts_lanczos**, **bw_bandpass_filter**,
**wgt_runave_n**, **specx_anal**,
**fourier_info**

## Examples

See worked examples on the
**Spectral Analysis and Complex Demodulation** page.

**Example 1**: Let x(time), frqdem=0.21, frqcut=0.75*frqdem, nwt=71, ndim=0, then

demod_x =demod_cmplx(x, frqdem, frqcut, nwt, ndim, False) ; demod_x[2]delete(demod_x) ; no longer neededprintVarSummary(amp_x)printVarSummary(phase_x)

**Example 2**: Let x(time,lat,lon), frqdem=0.30, frqcut=0.50*frqdem, nwt=101, ndim=0, then

demod_x =demod_cmplx(x, frqdem, frqcut, nwt, ndim, False) ; demod_x[2]delete(demod_x) ; no longer neededprintVarSummary(amp_x)printVarSummary(phase_x)