Even Odd
- If x is real → → (absolute value is when )
- If x is real and even → → Fourier coefficient are real and even
- If x is real and odd → → Fourier coefficient are purely imaginary and odd
If is Real
2, 3 property is proved using ignoring the complex part of the representation
- Polar form of the Fourier coefficient is , then the trigonometric Fourier representation of is
- Let Cartesian form of the Fourier coefficients is like Fourier coefficient then trigonometric representation of is
- If x is real → → (absolute value is when )
- If x is real and even → → Fourier coefficient are real and even
- If x is real and odd → → Fourier coefficient are purely imaginary and odd