- #1

- 624

- 11

## Homework Statement

I need to calculate the derivative of a function using discrete Fourier transform (DFT). Below is a simplified version of my code (just for sin function) in python

## Homework Equations

Python:

```
from __future__ import division
import numpy as np
from pylab import *
pi = np.pi
def f(x):
return sin(x)
theta = np.arange(0,2*pi,2*pi/4)
k = np.arange(0,4,1)
x = f(theta)
y = np.fft.fft(x)
derivative = np.fft.ifft(1j*k*y)
print(derivative)
```

## The Attempt at a Solution

So what I do is to sample sin at 4 different points between 0 and 2pi and create with these numbers a vector x. Then I take the DFT of x to get y. What I want is to get the derivative of sin at the chosen points, so to do this I multiply y by k (the wave number, which in this case would be 0,1,2,3) and my the imaginary number 1j (this is because in the Fourier sum I have for each term something of the form e^{ikx}). So in the end I take the inverse DFT of 1j

*k*y and I am supposed to get the derivative of sin. But what I get is this:

[ -1.00000000e+00 -6.12323400e-17j -6.12323400e-17 +2.00000000e+00j

1.00000000e+00 +1.83697020e-16j 6.12323400e-17 -2.00000000e+00j]

when I was supposed to get this:

[1,0,-1,0]

ignoring round-off errors. Can someone tell me what am I doing wrong? Thank you!