| [574] | 1 | % 'FFT2_detrend': calculate the 2D spectrum of the input scalar after removing the linear trend
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| 2 |
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| 3 | %------------------------------------------------------------------------
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| 4 | %%%% Use the general syntax for transform fields with a single input %%%%
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| [510] | 5 | % OUTPUT:
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| [574] | 6 | % DataOut: output field structure
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| 7 |
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| [510] | 8 | %INPUT:
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| [574] | 9 | % DataIn: first input field structure
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| 10 | %------------------------------------------------------------------------
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| [510] | 11 | function DataOut=FFT2_detrend(DataIn)
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| [574] | 12 | %------------------------------------------------------------------------
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| [510] | 13 | DataOut=[];
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| 14 | if strcmp(DataIn,'*')
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| 15 | DataOut.InputFieldType='scalar';
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| 16 | return
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| 17 | end
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| 18 | %%%%%%%%%%%%%%%%%%%%%%%%%
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| [532] | 19 | [CellInfo,NbDim,errormsg]=find_field_cells(DataIn);
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| [510] | 20 | if ~isempty(errormsg)
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| 21 | DataOut.Txt=errormsg;
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| 22 | return
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| 23 | end
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| 24 | DataOut.ListVarName={};
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| 25 | DataOut.VarDimName={};
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| [532] | 26 | for ilist=1:numel(CellInfo)
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| 27 | if NbDim(ilist)==2 && numel(CellInfo{ilist}.CoordIndex)==2 % field with structured coordinates
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| [510] | 28 | %process coordinates
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| [532] | 29 | CoordName=DataIn.ListVarName(CellInfo{ilist}.CoordIndex);
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| [510] | 30 | x1 = DataIn.(CoordName{2}); y1 = DataIn.(CoordName{1});
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| 31 | [x y] = meshgrid(x1,y1);
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| 32 | coeff(1,1) = sum(sum(x.^2)); coeff(1,2) = sum(sum(x.*y)); coeff(1,3) = sum(sum(x));
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| 33 | coeff(2,1) = sum(sum(x.*y)); coeff(2,2) = sum(sum(y.^2)); coeff(2,3) = sum(sum(y));
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| 34 | coeff(3,1) = sum(sum(x)); coeff(3,2) = sum(sum(y)); coeff(3,3) = length(x1)*length(y1);
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| 35 | delta_x = x1(2) - x1(1); delta_y = y1(2) - y1(1);
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| 36 | Nx = length(x1); Ny = length(y1);
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| 37 | Nxa = 1:Nx; Nya = 1:Ny;
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| 38 | ssx = find(Nxa<Nx/2); ssy = find(Nya<Ny/2);
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| 39 | Nxa(Nx-ssx+1) = -Nxa(ssx)+1; Nya(Ny-ssy+1) = -Nya(ssy)+1;
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| 40 | [Nxa Ix] = sort(Nxa); [Nya Iy] = sort(Nya);
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| 41 | kx1 = (2*pi/delta_x/Nx)*(Nxa-1); ky1 = (2*pi/delta_y/Ny)*(Nya-1);
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| 42 | ss = find(ky1>=0); ky1 = ky1(ss);
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| 43 | [kx ky] = meshgrid(kx1,ky1);
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| 44 | DataOut.(CoordName{2}) = kx1; DataOut.(CoordName{1}) = ky1;
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| 45 | if isfield(DataIn,'CoordUnit')
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| 46 | DataOut.CoordUnit=[DataIn.CoordUnit '^{-1}'];
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| 47 | DataOut.ListGlobalAttribute={'CoordUnit'};
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| 48 | end
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| 49 | %process scalar
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| [532] | 50 | ivar=CellInfo{ilist}.VarIndex_scalar(1);
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| [510] | 51 | VarName=DataIn.ListVarName{ivar};
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| 52 | z=DataIn.(VarName);
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| 53 | rhs(1) = sum(sum(x.*z)); rhs(2) = sum(sum(y.*z)); rhs(3) = sum(sum(z));
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| 54 | lin_coeff = inv(coeff)*rhs';
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| 55 | lin_trend = lin_coeff(1)*x + lin_coeff(2)*y + lin_coeff(3);
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| 56 | z2 = z - lin_trend;
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| 57 | spec2 = abs(fft2(z2)).^2;
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| 58 | spec2 = spec2(Iy,Ix);
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| 59 | spec2 = spec2(ss,:);
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| 60 | %DataOut.(VarName) = log(spec2);
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| 61 | DataOut.(VarName) = spec2;
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| 62 | spec_sum=sum(sum(spec2));
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| [532] | 63 | kx_mean=sum(sum(spec2.*kx))/spec_sum;
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| 64 | ky_mean=sum(sum(spec2.*ky))/spec_sum;
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| 65 | theta=atand(ky_mean/kx_mean);
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| 66 | lambda=2*pi/(sqrt(kx_mean*kx_mean+ky_mean*ky_mean));
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| [510] | 67 |
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| 68 | DataOut.ListVarName=[CoordName {VarName}];%list of variables
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| 69 | DataOut.VarDimName=[CoordName {CoordName}];%list of dimensions for variables
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| 70 | break
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| 71 | end
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| 72 | end
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| 73 |
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| 74 |
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| 75 |
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