2D FFT interpolation - Keeping the amplitude

% input
matrix = [1.41 + 0.31i,-0.480 + 1.47i,-1.67 + 2.23i,-2.38 + 2.02i,-2.07 + 1.47i,-1.11 + 0.34i,-0.0900 - 0.65i,0.700 - 0.79i,1.14 - 0.36i;...
    0.180 - 0.10i,-1.22 + 0.51i,-1.66 + 0.86i,-0.590 + 0.070i,0.410 + 0.070i,0.0300 + 0.99i,-0.300 + 0.67i,0.430 + 0.23i,0.640 + 0.09i;...
    2.11 - 1.18i,0.350 - 1.01i,-0.850 - 0.84i,-0.200 - 1.74i,1.29 - 1.62i,1.59 - 0.16i,1.40 - 0.16i,1.65 - 0.36i,1.53 + 0.13i;...
    0.990 - 2.39i,1.40 - 1.85i,4.22 - 0.01i,6.95 + 1.01i,6.11 + 0.90i,3.04 + 0.17i,1.06 - 0.34i,0.640 - 0.98i,0.900 - 0.71i;...
    1.07 - 2.58i,1.73 - 0.80i,8.23 + 3.39i,16.28 + 7.73i,15.16 + 8.35i,6.40 + 4.22i,0.350 + 0.79i,-0.610 - 0.46i,-0.200 - 0.27i;...
    1.73 - 1.20i,-0.200 + 0.94i,0.170 + 3.56i,3.85 + 5.13i,4.89 + 5.21i,2.14 + 2.96i,0.0300 + 0.12i,0.190 - 0.71i,0.470 + 0.19i;...
    2.48 - 0.46i,1.02 + 1.28i,-1.16 + 2.32i,-1.67 + 1.71i,-0.890 + 0.55i,-0.100 + 0.21i,0.270 - 0.34i,0.710 - 0.57i,0.930 - 0.17i;...
    2.01 + 3.41i,2.02 + 2.68i,-0.130 + 2.40i,-1.26 + 1.97i,-1.21 + 2.15i,0.0600 + 1.64i,1.06 + 0.88i,0.620 + 0.58i,-0.0500 + 0.31i;...
    -0.230 + 7.51i,0.400 + 2.68i,-0.760 + 1.70i,-1.46 + 1.57i,-2.02 + 1.70i,-1.42 + 1.35i,0.00 + 1.16i,-0.330 + 0.86i,-1.19 + 0.56i];


% 2d FFT interpolation
interpol_size = 100;

k = fft2(matrix);
k = fftshift(k);
k_scale = padarray(k,[interpol_size,interpol_size]/2,'both');
k_scale = ifftshift(k_scale);
k_interpol = ifft2(k_scale);

% plot
tiledlayout(1,2)
nexttile
imagesc(abs(matrix))
colorbar
cb = colorbar;
cb.Label.String = "power (10*log10(abs(x))) [dB]";
title('original')
axis square

nexttile
imagesc(10*log10(abs(k_interpol)))
colorbar
cb = colorbar;
cb.Label.String = "power (10*log10(abs(x))) [dB]";
title('2Dfft interpolated')
axis square

I tried to interpolate the original data with a 2d fft, but afterwards unfortunately I don't get the same amplitude values. Altough I expect the values to be equal or bigger than the original based on the sampling theory.

I checked https://ch.mathworks.com/matlabcentral/answers/1900240-effect-of-zero-padding-on-fft-amplitude?s_tid=sug_su , but unfortunately I don't get it do extrapolate the information there into the multidimensional space (in my case 2d).

I know that interpft should work, but this works just in 1d.

Answer 1

[Paul]

Hi canadarunner,

The plot on the left is amplitude and the plot on the right is in dB. Changing the left plot to dB brings the plots closer.

In the same units, would you expect the values in the plot on the left to be larger?

Scaling the interpolated values by the numel(k_interpol)/numel(matrix) would then bring the two plots into alignment. I don't think that's a coincidence, but would have to give more thought to justify doing so.

% input
matrix = [1.41 + 0.31i,-0.480 + 1.47i,-1.67 + 2.23i,-2.38 + 2.02i,-2.07 + 1.47i,-1.11 + 0.34i,-0.0900 - 0.65i,0.700 - 0.79i,1.14 - 0.36i;...
    0.180 - 0.10i,-1.22 + 0.51i,-1.66 + 0.86i,-0.590 + 0.070i,0.410 + 0.070i,0.0300 + 0.99i,-0.300 + 0.67i,0.430 + 0.23i,0.640 + 0.09i;...
    2.11 - 1.18i,0.350 - 1.01i,-0.850 - 0.84i,-0.200 - 1.74i,1.29 - 1.62i,1.59 - 0.16i,1.40 - 0.16i,1.65 - 0.36i,1.53 + 0.13i;...
    0.990 - 2.39i,1.40 - 1.85i,4.22 - 0.01i,6.95 + 1.01i,6.11 + 0.90i,3.04 + 0.17i,1.06 - 0.34i,0.640 - 0.98i,0.900 - 0.71i;...
    1.07 - 2.58i,1.73 - 0.80i,8.23 + 3.39i,16.28 + 7.73i,15.16 + 8.35i,6.40 + 4.22i,0.350 + 0.79i,-0.610 - 0.46i,-0.200 - 0.27i;...
    1.73 - 1.20i,-0.200 + 0.94i,0.170 + 3.56i,3.85 + 5.13i,4.89 + 5.21i,2.14 + 2.96i,0.0300 + 0.12i,0.190 - 0.71i,0.470 + 0.19i;...
    2.48 - 0.46i,1.02 + 1.28i,-1.16 + 2.32i,-1.67 + 1.71i,-0.890 + 0.55i,-0.100 + 0.21i,0.270 - 0.34i,0.710 - 0.57i,0.930 - 0.17i;...
    2.01 + 3.41i,2.02 + 2.68i,-0.130 + 2.40i,-1.26 + 1.97i,-1.21 + 2.15i,0.0600 + 1.64i,1.06 + 0.88i,0.620 + 0.58i,-0.0500 + 0.31i;...
    -0.230 + 7.51i,0.400 + 2.68i,-0.760 + 1.70i,-1.46 + 1.57i,-2.02 + 1.70i,-1.42 + 1.35i,0.00 + 1.16i,-0.330 + 0.86i,-1.19 + 0.56i];
% 2d FFT interpolation
interpol_size = 100;
k = fft2(matrix);
k = fftshift(k);
k_scale = padarray(k,[interpol_size,interpol_size]/2,'both');
k_scale = ifftshift(k_scale);
k_interpol = ifft2(k_scale);
% plot
tiledlayout(1,2)
nexttile


%imagesc(abs(matrix))
imagesc(10*log10(abs(matrix)))

colorbar
cb = colorbar;
cb.Label.String = "power (10*log10(abs(x))) [dB]";
title('original')
axis square
nexttile
imagesc(10*log10(abs(k_interpol)))
colorbar
cb = colorbar;
cb.Label.String = "power (10*log10(abs(x))) [dB]";
title('2Dfft interpolated')
axis square

[canadarunner]

@Paul - ahh I had the power plot in my original code right, but thank you very much for the scaling! Absolutely what I needed. So my final solution is:

% input
matrix = [1.41 + 0.31i,-0.480 + 1.47i,-1.67 + 2.23i,-2.38 + 2.02i,-2.07 + 1.47i,-1.11 + 0.34i,-0.0900 - 0.65i,0.700 - 0.79i,1.14 - 0.36i;...
    0.180 - 0.10i,-1.22 + 0.51i,-1.66 + 0.86i,-0.590 + 0.070i,0.410 + 0.070i,0.0300 + 0.99i,-0.300 + 0.67i,0.430 + 0.23i,0.640 + 0.09i;...
    2.11 - 1.18i,0.350 - 1.01i,-0.850 - 0.84i,-0.200 - 1.74i,1.29 - 1.62i,1.59 - 0.16i,1.40 - 0.16i,1.65 - 0.36i,1.53 + 0.13i;...
    0.990 - 2.39i,1.40 - 1.85i,4.22 - 0.01i,6.95 + 1.01i,6.11 + 0.90i,3.04 + 0.17i,1.06 - 0.34i,0.640 - 0.98i,0.900 - 0.71i;...
    1.07 - 2.58i,1.73 - 0.80i,8.23 + 3.39i,16.28 + 7.73i,15.16 + 8.35i,6.40 + 4.22i,0.350 + 0.79i,-0.610 - 0.46i,-0.200 - 0.27i;...
    1.73 - 1.20i,-0.200 + 0.94i,0.170 + 3.56i,3.85 + 5.13i,4.89 + 5.21i,2.14 + 2.96i,0.0300 + 0.12i,0.190 - 0.71i,0.470 + 0.19i;...
    2.48 - 0.46i,1.02 + 1.28i,-1.16 + 2.32i,-1.67 + 1.71i,-0.890 + 0.55i,-0.100 + 0.21i,0.270 - 0.34i,0.710 - 0.57i,0.930 - 0.17i;...
    2.01 + 3.41i,2.02 + 2.68i,-0.130 + 2.40i,-1.26 + 1.97i,-1.21 + 2.15i,0.0600 + 1.64i,1.06 + 0.88i,0.620 + 0.58i,-0.0500 + 0.31i;...
    -0.230 + 7.51i,0.400 + 2.68i,-0.760 + 1.70i,-1.46 + 1.57i,-2.02 + 1.70i,-1.42 + 1.35i,0.00 + 1.16i,-0.330 + 0.86i,-1.19 + 0.56i];

% 2d FFT interpolation
interpol_size = 100;
k = fft2(matrix);
k = fftshift(k);
k_scale = padarray(k,[interpol_size,interpol_size]/2,'both');
k_scale = ifftshift(k_scale);
k_interpol = ifft2(k_scale);
k_interpol = k_interpol*numel(k_interpol)/numel(matrix);

% plot
tiledlayout(1,2)
nexttile
%imagesc(abs(matrix))
imagesc(10*log10(abs(matrix)))
colorbar
cb = colorbar;
cb.Label.String = "power (10*log10(abs(x))) [dB]";
title('original')
axis square

nexttile
imagesc(10*log10(abs(k_interpol)))
colorbar
cb = colorbar;
cb.Label.String = "power (10*log10(abs(x))) [dB]";
title('2Dfft interpolated')
axis square
clim([min(10*log10(abs(matrix(:)))),max(10*log10(abs(matrix(:))))])