Get rid off white border in spectrum

Hi there, I want to plot the

spectrum of a grayscale image.

Unfortunately there is a white border on the right side

and at the bottom.

My code:

x = 1:1:30;     % vorher>: 0:1:30;
y = 1:1:30;     % vorher: 0:1:30;
[X, Y] = meshgrid(x, y);

% Sinusfunktion für diagonale Linien
fx = 0.1;        % Ortsfrequenz (1/Pixel) 
fy = 0.2;        % Ortsfrequenz (1/Pixel)
p = cos(2*pi*(fx*X + fy*Y)) + 1;

y1 = fft2(p);
freq_x = fftfreq(length(x));
freq_y = fftfreq(length(y));

figure;
imagesc(freq_x, freq_y, log10(1 + abs(fftshift(y1))));
line([0,0], [-0.5,0.5], 'Color', 'r', 'LineWidth',1);
line([-0.5,0.5], [0,0], 'Color', 'r', 'LineWidth',1);
axis image
colormap('gray');

The spectrum currently looks like this:

This is my fftfreq function:

function freqs = fftfreq(n, fs)

end
if nargin < 2
    fs = 1;
end

results = zeros(1, n);
N = fix((n-1)/2) + 1;
results(1:N) = 0:N-1;
results(N+1:end) = (-fix(n/2):-1);
freqs = fftshift(results * (fs / n));

How can I remove the white border?

[VBBV]

Choose min & max range values for the X & Y scales in the axis function instead of default scaling of axis image

x = 1:1:30;     % vorher>: 0:1:30;
y = 1:1:30;     % vorher: 0:1:30;
[X, Y] = meshgrid(x, y);

% Sinusfunktion für diagonale Linien
fx = 0.1;        % Ortsfrequenz (1/Pixel) 
fy = 0.2;        % Ortsfrequenz (1/Pixel)
p = cos(2*pi*(fx*X + fy*Y)) + 1;

y1 = fft2(p);
freq_x = fftfreq(length(x));
freq_y = fftfreq(length(y));

figure;
h = imagesc(freq_x, freq_y, log10(1 + abs(fftshift(y1))))

h = 
  Image with properties:

           CData: [30×30 double]
    CDataMapping: 'scaled'

  Show all properties

line([0,0], [-0.5,0.5], 'Color', 'r', 'LineWidth',1);
line([-0.5,0.5], [0,0], 'Color', 'r', 'LineWidth',1);
axis([min(freq_x) max(freq_x) min(freq_y) max(freq_y) ]);
colormap('gray');

function freqs = fftfreq(n, fs)

if nargin < 2
    fs = 1;
end

results = zeros(1, n);
N = fix((n-1)/2) + 1;
results(1:N) = 0:N-1;
results(N+1:end) = (-fix(n/2):-1);
freqs = fftshift(results * (fs / n));
end

Answer 1

[Dyuman Joshi]

It's not a border, it's the area of figure where there is no data to plot, and the white background is showing.

You can either remove/modify the axis command, and/or update the x and y limits manually

x = 1:1:30;     % vorher>: 0:1:30;
y = 1:1:30;     % vorher: 0:1:30;
[X, Y] = meshgrid(x, y);

% Sinusfunktion für diagonale Linien
fx = 0.1;        % Ortsfrequenz (1/Pixel) 
fy = 0.2;        % Ortsfrequenz (1/Pixel)
p = cos(2*pi*(fx*X + fy*Y)) + 1;

y1 = fft2(p);
freq_x = fftfreq(length(x));
freq_y = fftfreq(length(y));

figure;
imagesc(freq_x, freq_y, log10(1 + abs(fftshift(y1))));
line([0,0], [-0.5,0.5], 'Color', 'r', 'LineWidth',1);
line([-0.5,0.5], [0,0], 'Color', 'r', 'LineWidth',1);
%axis command commented out
%axis image
colormap('gray');

function freqs = fftfreq(n, fs)
if nargin < 2
    fs = 1;
end

results = zeros(1, n);
N = fix((n-1)/2) + 1;
results(1:N) = 0:N-1;
results(N+1:end) = (-fix(n/2):-1);
freqs = fftshift(results * (fs / n));
end

[Dominik Deml]

Okay, but the xticks should still be 0.1 as well as the yticks.

[DGM]

Then just specify the xticks, yticks explicitly. Note that the reason the axes extents get set larger than the image object is because you're creating line objects that extend beyond the image. You can use xline(),yline() instead of plot(), preventing the problem from happening in the first place.

x = 1:1:30;     % vorher>: 0:1:30;
y = 1:1:30;     % vorher: 0:1:30;
[X, Y] = meshgrid(x, y);

% Sinusfunktion für diagonale Linien
fx = 0.1;        % Ortsfrequenz (1/Pixel) 
fy = 0.2;        % Ortsfrequenz (1/Pixel)
p = cos(2*pi*(fx*X + fy*Y)) + 1;
y1 = fft2(p);
freq_x = fftfreq(length(x));
freq_y = fftfreq(length(y));

figure;
imagesc(freq_x, freq_y, log10(1 + abs(fftshift(y1))));
xline(0,'r','linewidth',1);
yline(0,'r','linewidth',1);
axis image
xticks(min(freq_x):0.1:max(freq_x))
yticks(min(freq_y):0.1:max(freq_y))

colormap('gray');

function freqs = fftfreq(n, fs)
	if nargin < 2
		fs = 1;
	end
	results = zeros(1, n);
	N = fix((n-1)/2) + 1;
	results(1:N) = 0:N-1;
	results(N+1:end) = (-fix(n/2):-1);
	freqs = fftshift(results * (fs / n));
end

[Image Analyst]

fft2 operates on the whole image, not just what is visible.

p = cos(2*pi*(fx*X + fy*Y)) + 1;
y1 = fft2(p);

So how will changing the tick marks or axis limits after the above code change y1 at all?

[DGM]

The goal isn't to change y1 at all. This is apparently a matter of axes extents. The range of freq_x and freq_y are both [-0.5 0.4667]. That is the extent of the image object in the current axes. The two red lines span [-0.5 0.5], forcing the axes to be larger than the image object. Like @Dyuman Joshi says, there is no border to crop off.

Answer 2

[Image Analyst]

Try cropping off the last row and column

p = p(1:end-1, 1:end-1)

then call fft2.