matlab中，如何用wavefun画dbN、Morlet、MexicanHat、sym小波基图？

更改小波基的名称，dbN，symN和coifN是正交小波基，是有尺度函数的，只更改N就行，如

[phi,psi,x] = wavefun('sym4',10)%建议使用10次以上迭代计算，比较精确

subplot(211),plot(x,phi)%尺度函数

subplot(212),plot(x,psi)%小波函数

Morlet(Morl)、MexicanHat(mexh)是没有尺度函数定义的小波基，只能显示其小波函数，

[psi,x] = wavefun('Morl',10)

subplot(212),plot(x,psi)%小波函数

参看matlab对wavefun的帮助文档即可，对各种类型的小波基的格式有很详细的说明。

程序如下：

function [nn, L] = nntrain(nn, train_x, train_y, opts, val_x, val_y)

%NNTRAIN trains a neural net

% [nn, L] = nnff(nn, x, y, opts) trains the neural network nn with input x and

% output y for opts.numepochs epochs, with minibatches of size

% opts.batchsize. Returns a neural network nn with updated activations,

% errors, weights and biases, (nn.a, nn.e, nn.W, nn.b) and L, the sum

% squared error for each training minibatch.

assert(isfloat(train_x), 'train_x must be a float')

assert(nargin == 4 || nargin == 6,'number ofinput arguments must be 4 or 6')

loss.train.e = []

loss.train.e_frac = []

loss.val.e = []

loss.val.e_frac= []

opts.validation = 0

if nargin == 6

opts.validation = 1

end

fhandle = []

if isfield(opts,'plot') &&opts.plot == 1

fhandle = figure()

end

m = size(train_x, 1)

batchsize = opts.batchsize

numepochs = opts.numepochs

numbatches = m / batchsize

assert(rem(numbatches, 1) == 0, 'numbatches must be a integer')

L = zeros(numepochs*numbatches,1)

n = 1

for i = 1 : numepochs

tic

kk = randperm(m)

for l = 1 : numbatches

batch_x = train_x(kk((l - 1) * batchsize + 1 : l * batchsize), :)

%Add noise to input (for use in denoising autoencoder)

if(nn.inputZeroMaskedFraction ~= 0)

batch_x = batch_x.*(rand(size(batch_x))>nn.inputZeroMaskedFraction)

end

batch_y = train_y(kk((l - 1) * batchsize + 1 : l * batchsize), :)

nn = nnff(nn, batch_x, batch_y)

nn = nnbp(nn)

nn = nnapplygrads(nn)

L(n) = nn.L

n = n + 1

end

t = toc

if ishandle(fhandle)

if opts.validation == 1

loss = nneval(nn, loss, train_x, train_y, val_x, val_y)

else

loss = nneval(nn, loss, train_x, train_y)

end

nnupdatefigures(nn, fhandle, loss, opts, i)

end

disp(['epoch ' num2str(i) '/' num2str(opts.numepochs) '. Took ' num2str(t) ' seconds' '. Mean squared error on training set is ' num2str(mean(L((n-numbatches):(n-1))))])

nn.learningRate = nn.learningRate * nn.scaling_learningRate

end

end

Matlab之小波滤波函数 :

1 wfilters函数

[Lo_D,Hi_D,Lo_R,Hi_R] = wfilters('wname') computes four filters associated with the orthogonal or biorthogonal wavelet named in the string 'wname'. The four output filters are

Lo_D, the decomposition low-pass filter Hi_D, the decomposition high-pass filter Lo_R, the reconstruction low-pass filter

Hi_R, the reconstruction high-pass filter

2 biorfilt函数

The biorfilt command returns either four or eight filters associated with biorthogonal wavelets.

3 orthfilt函数

[Lo_D,Hi_D,Lo_R,Hi_R] = orthfilt(W) computes the four filters associated with the scaling filter W corresponding to a wavelet

4 biorwaef函数

[RF,DF] = biorwavf(W) returns two scaling filters associated with the biorthogonal wavelet specified by the string W.

5 coifwavf函数

F = coifwavf(W) returns the scaling filter associated with the Coiflet wavelet specified by the string W where W = 'coifN'. Possible values for N are 1, 2, 3, 4, or 5

6 dbaux函数

W = dbaux(N,SUMW) is the order N Daubechies scaling filter such that sum(W) = SUMW. Possible values for N are 1, 2, 3, ...

W = dbaux(N) is equivalent to W = dbaux(N,1) W = dbaux(N,0) is equivalent to W = dbaux(N,1)

7 dbwavf函数

F = dbwavf(W) returns the scaling filter associated with Daubechies wavelet specified by the string W where W = 'dbN'. Possible values for N are 1, 2, 3, ..., 45.

8 mexihat函数

[PSI,X] = mexihat(LB,UB,N) returns values of the Mexican hat wavelet on an N point regular grid, X, in the interval [LB,UB].

Output arguments are the wavelet function PSI computed on the grid X. This wavelet has [-5 5] as effective support.

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