I have two functions f[x,y] and g[x,y] calculated on a grid {x,y}. Then I perform numerical Fourier transforms,

FTf=Fourier[dataf]; FTg=Fourier[datag] 

I am looking for convolution $w=f*g$. To calculate it, I do

listw=InverseFourier[FTf*FTg] 

and finally I would like to plot density of $w$. To do it, I reshape listw and then construct list data={{x1,y1,w1},...} and finally

ListDensityPlot[data] 

Everything seems ok but the final plot is quite strange. Is everything ok with my derivation?

To be specific, the following code presents the simpler version:

f[x_, y_] := Exp[-(x^2 + y^2)]; g[x_, y_] := Exp[-4*(x^2 + y^2)]; fdata = Table[f[x, y], {x, -1, 1, 0.1}, {y, -1, 1, 0.1}]; gdata = Table[g[x, y], {x, -1, 1, 0.1}, {y, -1, 1, 0.1}]; FTf = Fourier[fdata]; FTg = Fourier[gdata]; listw = InverseFourier[FTf*FTg]; wvalues = Abs[ArrayReshape[listw, 21^2]]; xypairs = Flatten[Table[{x, y}, {x, -1, 1, 0.1}, {y, -1, 1, 0.1}], 1]; data = ArrayReshape[Transpose[{xypairs, wvalues}], {21^2, 3}]; ListDensityPlot[data] 

which produces plot:

For simple functions, I can calculate FT explicitly:

FTf1 = FourierTransform[f[x, y], {x, y}, {w1, w2}]; FTf2 = FourierTransform[g[x, y], {x, y}, {w1, w2}]; wfunction = InverseFourierTransform[FTf1*FTf2, {w1, w2}, {x, y}] 

and then can density plot wfunction[x_,y_]:

I have two functions f[x,y] and g[x,y] calculated on a grid {x,y}. Then I perform numerical Fourier transforms,

FTf=Fourier[dataf]; FTg=Fourier[datag] 

I am looking for convolution $w=f*g$. To calculate it, I do

listw=InverseFourier[FTf*FTg] 

and finally I would like to plot density of $w$. To do it, I reshape listw and then construct list data={{x1,y1,w1},...} and finally

ListDensityPlot[data] 

Everything seems ok but the final plot is quite strange. Is everything ok with my derivation?

To be specific, the following code presents the simpler version:

f[x_, y_] := Exp[-(x^2 + y^2)]; g[x_, y_] := Exp[-4*(x^2 + y^2)]; fdata = Table[f[x, y], {x, -1, 1, 0.1}, {y, -1, 1, 0.1}]; gdata = Table[g[x, y], {x, -1, 1, 0.1}, {y, -1, 1, 0.1}]; FTf = Fourier[fdata]; FTg = Fourier[gdata]; listw = InverseFourier[FTf*FTg]; wvalues = Abs[ArrayReshape[listw, 21^2]]; xypairs = Flatten[Table[{x, y}, {x, -1, 1, 0.1}, {y, -1, 1, 0.1}], 1]; data = ArrayReshape[Transpose[{xypairs, wvalues}], {21^2, 3}]; ListDensityPlot[data] 

which produces plot:

For simple functions, I can calculate FT explicitly:

FTf1 = FourierTransform[f[x, y], {x, y}, {w1, w2}]; FTf2 = FourierTransform[g[x, y], {x, y}, {w1, w2}]; wfunction = InverseFourierTransform[FTf1*FTf2, {w1, w2}, {x, y}] 

and then can density plot wfunction[x_,y_]:

I have two functions f[x,y] and g[x,y] calculated on a grid {x,y}. Then I perform numerical Fourier transforms,

FTf=Fourier[dataf]; FTg=Fourier[datag] 

I am looking for convolution $w=f*g$. To calculate it, I do

listw=InverseFourier[FTf*FTg] 

and finally I would like to plot density of $w$. To do it, I reshape listw and then construct list data={{x1,y1,w1},...} and finally

ListDensityPlot[data] 

Everything seems ok but the final plot is quite strange. Is everything ok with my derivation?

I have two functions f[x,y] and g[x,y] calculated on a grid {x,y}. Then I perform numerical Fourier transforms,

FTf=Fourier[dataf]; FTg=Fourier[datag] 

I am looking for convolution $w=f*g$. To calculate it, I do

listw=InverseFourier[FTf*FTg] 

and finally I would like to plot density of $w$. To do it, I reshape listw and then construct list data={{x1,y1,w1},...} and finally

ListDensityPlot[data] 

Everything seems ok but the final plot is quite strange. Is everything ok with my derivation?

To be specific, the following code presents the simpler version:

f[x_, y_] := Exp[-(x^2 + y^2)]; g[x_, y_] := Exp[-4*(x^2 + y^2)]; fdata = Table[f[x, y], {x, -1, 1, 0.1}, {y, -1, 1, 0.1}]; gdata = Table[g[x, y], {x, -1, 1, 0.1}, {y, -1, 1, 0.1}]; FTf = Fourier[fdata]; FTg = Fourier[gdata]; listw = InverseFourier[FTf*FTg]; wvalues = Abs[ArrayReshape[listw, 21^2]]; xypairs = Flatten[Table[{x, y}, {x, -1, 1, 0.1}, {y, -1, 1, 0.1}], 1]; data = ArrayReshape[Transpose[{xypairs, wvalues}], {21^2, 3}]; ListDensityPlot[data] 

which produces plot:

For simple functions, I can calculate FT explicitly:

FTf1 = FourierTransform[f[x, y], {x, y}, {w1, w2}]; FTf2 = FourierTransform[g[x, y], {x, y}, {w1, w2}]; wfunction = InverseFourierTransform[FTf1*FTf2, {w1, w2}, {x, y}] 

and then can density plot wfunction[x_,y_]: