WLANA

WLANA - general wavelet analysis

A general wavelet analysis SPAtom (Project: MBBM/VA - WLLib).

Usage:

SPU WLANA WAVE HOPSIZE ITYPE MAXSIZE FTYPE FCNT FPAR1 FPAR2 WTYPE F0 ACUT ORDER USEDS OTYPE AMAX AREF

Inputs:

WAVE

The input signal wave item (mono)

HOPSIZE

The distance between frames in samples

ITYPE

The input frame alignment (values: BEGIN, CENTER)

MAXSIZE

The maximum signal queue length

FTYPE

The frequency bin definition type (values: RANGEQ, RANGED, DELTA, QUOTIENT, VECTOR)

FCNT

The number of bins. The default is 1.

FPAR1, FPAR2

The frequency bin definition parameters

WTYPE

The type of wavelet function. The following values are supported:

MORLET|GAUSSGENERAL|LAPLACE|GAUSSNDERIV|MEXICANHAT|GOUPILLAUD|MORLETII

F0

The number of sin/cos cycles per window. It should be in the range 2<F0<7. This parameter has no meaning for wavelet types GAUSSNDERIV and MEXICANHAT. The default is 5.

ACUT

The filter length relative to the Gaussian function. The value should be in the range 1<ACUT<3. The default is 3.

ORDER

Only used for GAUSSGENERAL and GAUSSNDERIV wavelets.The default is 2. For GAUSSGENERAL wavelets, ORDER is the exponent (power) and must be >= 1 and in the range 1<ORDER<4. For GAUSSNDERIV wavelets, ORDER is the derivation order and must be >=1 and is converted to the nearest integer.

USEDS

The use downsampling (values: YES, NO). If turned on,

OTYPE

The type of output spectrum (values: REALIMAG|LINAMPPHASE|LOGAMPPHASE)

AMAX

An amplitude value > 0. The default is 1.

AREF

A reference amplitude > 0. The default is 1.

Outputs:

Y1

The real part or amplitude

Y2

The imaginary part or phase

F

The frequency bins

LMAX

The maximum frame length in samples

I

The number of processed frames

N

The maximum number of frames

SR

The sampling rate in Hz

Function:

Downsampling

If enabled, the wavelet spectrum is computed from the highest to the lowest bin (nFBins-1, .., 0) and on each bin i where f[i] fulfills the switch criterion defined below, a 1:2 downsampling is applied to the signal.

switch criterion:

where:

f[i] - frequency of bin i

dSRate - sampling rate

dDFStep - normalized downsampling step switch frequency

D - current number of downsampling steps, starts with 0 (= no downsampling) and is incremented by 1 for each downsampling step

A FIR filter is used for anti-aliasing. The length of this filter depends on the cutoff frequency (parameter dDFCut). The downsampling frequency parameters are normalized frequencies (= scaled by 1/dSRate).

Each downsampling step increases the frame length in the following way:

where:

LD - maximum frame length for step D (=nDown..1); Note: LnDown is the length of the wavelet for the lowest frequency bin at the highest downsampling step

L0 - is the required frame length for the original sampling rate

M - number of filter coefficients (half filter length)