Functions
void	Daubechies (int p, double *h)

void	splinewl (int p1, int p2, double h1, double h2)

int	splinewl (int p1, int p2, double h, double hm, double g, double gm, int normmode=0, int *points=0)

int	dwtpqmf (double in, int Count, int N, double h, double g, int M, double out)

int	dwtp (double in, int Count, int N, double h, double g, int M, double out)

int	dwtp (double in, int Count, int N, double h, int Mh, double g, int Mg, double out)

int	dwtp (double in, int Count, int N, double h, int sh, int eh, double g, int sg, int eg, double out)

void	idwtp (double in, int Count, int N, double h, double g, int M, double out)

void	idwtp (double in, int Count, int N, double h, int Mh, double g, int Mg, double out)

void	idwtp (double in, int Count, int N, double h, int sh, int eh, double g, int sg, int eg, double out)

void	wavpacqmf (double **spec, double data, int Count, int WID, int wid, int M, double h, double g)

void	wavpac (double **spec, double data, int Count, int WID, int wid, double h, int hs, int he, double g, int gs, int ge)

void	iwavpacqmf (double data, double spec, int Fr, int Wid, int M, double h, double *g)

void	iwavpac (double data, double spec, int Fr, int Wid, double h, int hs, int he, double *g, int gs, int ge)

Detailed Description

wavelet routines

Function Documentation

void Daubechies	(	int	p,
		double *	h
	)

function Daubechies: calculates the Daubechies filter of a given order p

In: filter order p Out: h[2p]: the 2p FIR coefficients

No reutrn value. The calculated filters are minimum phase, which means the energy concentrates at the beginning. This is usually used for reconstruction. On the contrary, for wavelet analysis the filter is mirrored.

int dwtp	(	double *	in,
		int	Count,
		int	N,
		double *	h,
		double *	g,
		int	M,
		double *	out
	)

function dwtp: in this implementation h and g can be different from mirrored reconstruction filters, i.e. the biorthogonal transform. h[0] and g[0] are aligned at the ends of the filters, i.e. h[-M+1:0], g[-M+1:0].

In: in[Count]: waveform data h[-M+1:0], g[-M+1:0]: quadratic mirror filter pair N: maximal time resolution Out: out[N], the wavelet transform, arranged in interleaved format.

Returns maximal atom length (should equal N).

int dwtp	(	double *	in,
		int	Count,
		int	N,
		double *	h,
		int	Mh,
		double *	g,
		int	Mg,
		double *	out
	)

function dwtp: in this implementation h and g can be different size. h[0] and g[0] are aligned at the ends of the filters, i.e. h[-Mh+1:0], g[-Mg+1:0].

In: in[Count]: waveform data h[-Mh+1:0], g[-Mg+1:0]: quadratic mirror filter pair N: maximal time resolution Out: out[N], the wavelet transform, arranged in interleaved format.

Returns maximal atom length (should equal N).

int dwtp	(	double *	in,
		int	Count,
		int	N,
		double *	h,
		int	sh,
		int	eh,
		double *	g,
		int	sg,
		int	eg,
		double *	out
	)

function dwtp: in this implementation h and g can be arbitrarily located: h from $sh to $eh, g from $sg to $eg.

In: in[Count]: waveform data h[sh:eh-1], g[sg:eg-1]: quadratic mirror filter pair N: maximal time resolution Out: out[N], the wavelet transform, arranged in interleaved format.

Returns maximal atom length (should equal N).

int dwtpqmf	(	double *	in,
		int	Count,
		int	N,
		double *	h,
		double *	g,
		int	M,
		double *	out
	)

function dwtpqmf: in this implementation h and g are the same as reconstruction qmf filters. In fact the actual filters used are their mirrors and filter origin are aligned to the ends of the real filters, which turn out to be the starts of h and g.

The inverse transform is idwtp(), the same as inversing dwtp().

In: in[Count]: waveform data h[M], g[M]: quadratic mirror filter pair N: maximal time resolution Count=kN, N=2^lN being the reciprocal of the most detailed frequency scale, i.e. N=1 for no transforming at all, N=2 for dividing into approx. and detail, N=4 for dividing into approx+detail(approx+detial), etc. Count*2/N=2k gives the smallest length to be convolved with h and g. Out: out[N], the wavelet transform, arranged in interleaved format.

Returns maximal atom length (should equal N).

void idwtp	(	double *	in,
		int	Count,
		int	N,
		double *	h,
		double *	g,
		int	M,
		double *	out
	)

function idwtp: periodic wavelet reconstruction by qmf

In: in[Count]: wavelet transform in interleaved format h[M], g[M]: quadratic mirror filter pair N: maximal time resolution Out: out[N], waveform data (detail level 0).

No return value.

void idwtp	(	double *	in,
		int	Count,
		int	N,
		double *	h,
		int	Mh,
		double *	g,
		int	Mg,
		double *	out
	)

function idwtp: in which h and g can have different length.

In: in[Count]: wavelet transform in interleaved format h[Mh], g[Mg]: quadratic mirror filter pair N: maximal time resolution Out: out[N], waveform data (detail level 0).

No return value.

void idwtp	(	double *	in,
		int	Count,
		int	N,
		double *	h,
		int	sh,
		int	eh,
		double *	g,
		int	sg,
		int	eg,
		double *	out
	)

function idwtp: in which h and g can be arbitrarily located: h from $sh to $eh, g from $sg to $eg

In: in[Count]: wavelet transform in interleaved format h[sh:eh-1], g[sg:eg-1]: quadratic mirror filter pair N: maximal time resolution Out: out[N], waveform data (detail level 0).

No return value.

void iwavpac	(	double *	data,
		double **	spec,
		int	Fr,
		int	Wid,
		double *	h,
		int	hs,
		int	he,
		double *	g,
		int	gs,
		int	ge
	)

function iwavpac: inverse transform of wavpac

In: spec[Fr][Wid] h[hs:he-1], g[gs:ge-1], reconstruction filter pair Out: data[Fr*Wid]

No return value.

void iwavpacqmf	(	double *	data,
		double **	spec,
		int	Fr,
		int	Wid,
		int	M,
		double *	h,
		double *	g
	)

function iwavpacqmf: inverse transform of wavpacqmf

In: spec[Fr][Wid], Fr>M*2 h[M], g[M], quadratic mirror filter pair Out: data[Fr*Wid]

No return value.

void splinewl	(	int	p1,
		int	p2,
		double *	h,
		double *	hm
	)

function splinewl: computes spline biorthogonal wavelet filters. This version of splinewl calcualtes the positive-time half of h and hm coefficients only.

p1 and p2 must have the same parity. If p1 is even, p1 coefficients will be returned in h1; if p1 is odd, p1-1 coefficients will be returned in h1.

Actual length of h is p1+1, of hm is p1+2p2-1. only a half of each is kept. p even: h[0:p1/2] <- [p1/2:p1], hm[0:p1/2+p2-1] <- [p1/2+p2-1:p1+2p2-2] p odd: h[0:(p1-1)/2] <- [(p1+1)/2:p1], hm[0:(p1-3)/2+p2] <- [(p1-1)/2+p2:p1+2p2-2] i.e. h[0:hp1] <- [p1-hp1:p1], hm[0:hp1+p2-1] <- [p1-hp1-1+p2:p1+2p2-2]

In: p1, p2: specify vanishing moments of h and hm Out: h[] and hm[] as specified above.

No return value.

int splinewl	(	int	p1,
		int	p2,
		double *	h,
		double *	hm,
		double *	g,
		double *	gm,
		int	normmode,
		int *	points
	)

function splinewl: calculates the analysis and reconstruction filter pairs of spline biorthogonal wavelet (h, g) and (hm, gm). h has the size p1+1, hm has the size p1+2p2-1.

If p1+1 is odd, then all four filters are symmetric; if not, then h and hm are symmetric, while g and gm are anti-symmetric.

The concatenation of filters h with hm (or g with gm) introduces a time shift of p1+p2-1, which is the return value multiplied by -1.

If normmode==1, the results are normalized so that ||h||^2=||g||^2=1; if normmode==2, the results are normalized so that ||hm||^2=||gm||^2=1, if normmode==3, the results are normalized so that ||h||^2==||g||^2=||hm||^2=||gm||^2.

If a points buffer is specified, the function returns the starting and ending positions (inclusive) of h, hm, g, and gm, in the order of (hs, he, hms, hme, gs, ge, gms, gme), as ps[0]~ps[7].

In: p1 and p2, specify vanishing moments of h and hm, respectively. normmode: mode for normalization Out: h[p1+1], g[p1+1], hm[p1+2p2-1], gm[p1+2p2-1], points[8] (optional)

Returns -p1-p2+1.

void wavpac	(	double ***	spec,
		double *	data,
		int	Count,
		int	WID,
		int	wid,
		double *	h,
		int	hs,
		int	he,
		double *	g,
		int	gs,
		int	ge
	)

function wavpac: calculate pseudo local cosine transforms using wavelet packet,

In: data[Count], Count=fr*WID, waveform data WID: largest scale, equals 2^ORDER wid: smallest scale, euqals 2^order h[hs:he-1], g[gs:ge-1]: filter pair Out: spec[0][fr][WID], spec[1][2*fr][WID/2], ..., spec[ORDER-order-1][FR][wid]

No return value.

void wavpacqmf	(	double ***	spec,
		double *	data,
		int	Count,
		int	WID,
		int	wid,
		int	M,
		double *	h,
		double *	g
	)

function wavpacqmf: calculate pseudo local cosine transforms using wavelet packet

In: data[Count], Count=fr*WID, waveform data WID: largest scale, equals 2^ORDER wid: smallest scale, euqals 2^order h[M], g[M]: quadratic mirror filter pair, fr>2*M Out: spec[0][fr][WID], spec[1][2*fr][WID/2], ..., spec[ORDER-order-1][FR][wid]

No return value.

HSM and tools

Functions

Detailed Description

Function Documentation