What is the right way to detect edges using gradient filter

I have to apply a the gradient filter to detect edges but i dont know how and when i must convert the image in a proper way to have the correct results.

the image to be filtered is on a grayscale and of type uint8, when i perform the convolution by my own function, what must i convert before and after ?

i get an image with edges but i dont know if it is correct ?

cam = imread("cameraman.pgm");

filtre_x = [ 0 0 0 ; -1 0 1 ; 0 0 0 ];

filtre_y = [ 0 -1 0 ; 0 0 0 ; 0 1 0 ];

Gx = convolution(filtre_x,cam);

Gy = convolution(filtre_y,cam);

magnitude = sqrt( Gx.^2 + Gy.^2 );

imshow(cam);

imshow(magnitude);

here is my function

function img_filtre = convolution(filtre,img)

img = im2double(img);

Taille = size(img);

M = Taille(1); % nombre de ligne

N = Taille(2); % nombre de colonne

img_temp = zeros(M,N);

img_temp = img;

temp = 0;

for i=1:M-2

for j=1:N-2

temp = filtre .* img(i:i+2,j:j+2);

img_temp( i+1 , j+1 ) = sum(temp(:));

end

end

img_filtre = (img_temp); % retourner l'image filtrée

end