First and Second Derivatives of a Periodic Function Using Discrete Fourier Transforms
First and Second Derivatives of a Periodic Function Using Discrete Fourier Transforms
Consider the family of periodic functions , where . This Demonstration applies the discrete Fourier transform to compute the first and second derivatives of . (The derivative order 0 gives the original function.) The derivatives obtained analytically are shown in dashed red, while the numerical solutions are shown in blue. For a large number of sample points, there is close agreement between the two methods.
f(t)=sin(t)+cos(t)
a
1
ω
1
a
2
ω
2
0≤t≤4π
f(t)