Functions of correlation function of dct,dft and dwt in MATLAB

1. Realization of Matlab with discrete Fourier transform

The Matlab function FFT, fft2 and fftn can implement one-dimensional, two-and N-dimensional DFT algorithms respectively, while functions Ifft, ifft2 and ifftn are used to calculate the inverse DFT. These functions are called in the following format:

A=fft (X,n,dim)

where x represents the input image, n represents the sampling interval, and if x is less than the value, then Matlab will fill the x 0, otherwise it will be truncated so that it is N; DIM indicates a discrete Fourier transform.

A=FFT2 (X,mrows,ncols)

where Mrows and NCOLS specify an x size of 0 padding for x.

A=FFTN (X,size)

Where SIZE is a vector, each element will specify the length of the X corresponding dimension after 0 padding.

The call formats of the functions Ifft, ifft2, and ifftn are identical to the corresponding discrete Fourier transform functions.

Example: two-dimensional Fourier spectrum of images

% read in original image

I=imread (' lena.bmp ');

Imshow (I)

% seeking discrete Fourier spectrum

J=fftshift (fft2 (I));

Figure

Imshow (log (ABS (J)), [8,10])

2. Matlab implementation of discrete cosine transform

2.1. dCT2 function

Function: Two-dimensional DCT transform

Format: B=idct2 (A)

B=idct2 (A,m,n)

B=idct2 (A,[m,n])

Description: B=idct2 (a) calculates the DCT inverse of a, B, the same size as B, B=idct2 (A,m,n) and B=idct2 (A,[m,n]) by a complement of 0 or clipping, so that the size of B is MXN.

2.3. dctmtx function

function: Calculate the DCT transformation matrix

Format: D=DCTMTX (n)

Description: D=DCTMTX (n) returns a NXN DCT transformation matrix with the output matrix D as a double type.

3. Matlab implementation of Image wavelet transform

3.1 Matlab implementation of a dimensional wavelet transform

(1) DWT function

function: one-dimensional discrete wavelet transform

Format: [CA,CD]=DWT (X, ' wname ')

[Ca,cd]=dwt (X,lo_d,hi_d)

Note: [Ca,cd]=dwt (X, ' Wname ') uses the specified wavelet function ' wname ' to decompose the signal X, and the CA and CD are approximate components and detail components respectively; [CA,CD]=DWT (X,lo_d,hi_d) uses the specified filter group lo_d, Hi_ D the signal is decomposed.

(2) IDWT function

function: one-dimensional discrete wavelet inverse transform

Format: X=IDWT (CA,CD, ' wname ')

X=IDWT (Ca,cd,lo_r,hi_r)

X=IDWT (CA,CD, ' wname ', L)

X=IDWT (ca,cd,lo_r,hi_r,l)

Description: X=IDWT (CA,CD, ' wname ') reconstructed the original signal X by the wavelet inverse transform by the approximate component CA and the detail component CD.

' Wname ' is the selected wavelet function

X=IDWT (Ca,cd,lo_r,hi_r) reconstructs the original signal X with the specified reconstruction filter lo_r and hi_r by wavelet inverse transform.

X=IDWT (CA,CD, ' wname ', L) and X=IDWT (ca,cd,lo_r,hi_r,l) Specify the L point near the center of the return signal X.

3.2 Matlab implementation of two-dimensional wavelet transform

Functions of two-dimensional wavelet transform

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Function name function function

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Dwt2 Two-dimensional discrete wavelet transform

Multi-layer wavelet decomposition of wavedec2 two-dimensional signal

Idwt2 Two-dimensional discrete wavelet inverse transformation

Multi-layer wavelet reconstruction of waverec2 two-dimensional signal

Wrcoef2 reconstruction of a layer by multi-layer wavelet decomposition

UPCOEF2 reconstruction of approximate component or detail component by multi-layer wavelet decomposition

Detcoef2 extracting the detail component of wavelet decomposition of two-dimensional signal

Appcoef2 extracting approximate component of wavelet decomposition of two-dimensional signal

Single-layer reconstruction of upwlev2 two-dimensional wavelet decomposition

Dwtpet2 Two-dimensional periodic wavelet transform

Idwtper2 Two-dimensional periodic wavelet inverse transformation

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(1) Wcodemat function

function: pseudo-color coding of data matrix

Format: Y=wcodemat (X,nb,opt,absol)

Y=wcodemat (x,nb,opt)

Y=wcodemat (X,NB)

Y=wcodemat (X)

Note: Y=wcodemat (X,NB,OPT,ABSOL) returns the encoding matrix Y of the data matrix X, the maximum value of NB pseudo-code, that is, the encoding range is 0~NB, the default value nb=16;

OPT Specifies the encoding method (the default value is ' mat '), i.e.:

opt= ' Row ', encoded by line

Opt= ' col ', coded by column

Opt= ' mat ', encoded by the entire matrix

Absol is the control parameter of the function (the default value is ' 1 '), i.e.:

Absol=0, the encoding matrix is returned

Absol=1, returns the absolute value of the data Matrix ABS (X)

(2) Dwt2 function

Function: two-dimensional discrete wavelet transform

Format: [Ca,ch,cv,cd]=dwt2 (X, ' wname ')

[Ca,ch,cv,cd]=dwt2 (X,lo_d,hi_d)

Description: [Ca,ch,cv,cd]=dwt2 (X, ' Wname ') uses the specified wavelet function ' Wname ' to two-dimensional discrete wavelet transform of two-dimension signal X, CA,CH,CV,CD are approximate component, horizontal detail component, vertical detail component and diagonal detail component respectively; [CA, CH,CV,CD]=DWT2 (x,lo_d,hi_d) uses the specified decomposition low-pass and high-pass filter lo_d and hi_d decomposition signal X.

(3) WAVEDEC2 function

Function: Multi-layer wavelet decomposition of two-dimensional signal

Format: [C,s]=wavedec2 (X,n, ' wname ')

[C,s]=wavedec2 (X,n,lo_d,hi_d)

Description: [C,s]=wavedec2 (X,n, ' Wname ') uses the wavelet function ' Wname ' to perform N-layer decomposition of the two-dimensional signal X; [C,S]=WAVEDEC2 (X,n,lo_d,hi_d) uses the specified decomposition low-pass and high-pass filters Lo_d and Hi_d Decomposition signal X.

(4) Idwt2 function

Function: two-dimensional discrete wavelet inverse transform

Format: X=idwt2 (CA,CH,CV,CD, ' wname ')

X=IDWT2 (Ca,ch,cv,cd,lo_r,hi_r)

X=idwt2 (CA,CH,CV,CD, ' wname ', S)