Finite Differences

• $f^{\prime }(x)=\frac{df}{dx}\to \frac{\Delta f}{\Delta x}$
• 
• Forward differences $f^{\prime }(x)=\frac{f(x_{i+1})-f(x_i)}{\Delta x}$
• Non Isotropic
• Backward differences $f^{\prime }(x)=\frac{f(x_i)-f(x_{i-1})}{\Delta x}$
• Non Isotropic
• Central differences $f^{\prime }(x)=\frac{f(x_{i+1})-f(x_{i-1})}{2\Delta x}$
• High pass filter
• Non isotropic