| Line 7: | Line 7: | ||
!Property Name!! Property !! Proof | !Property Name!! Property !! Proof | ||
|- | |- | ||
| − | |Periodicity|| | + | |Periodicity|| Χ(ω + 2π) = Χ(ω) || Example |
|- | |- | ||
| − | | Linearity || ax<sub>1</sub>[n] + bx<sub>2</sub>[n] → | + | | Linearity || ax<sub>1</sub>[n] + bx<sub>2</sub>[n] → aΧ<sub>1</sub>(ω) + bΧ<sub>2</sub>(ω) || Example |
|- | |- | ||
| − | | Time Shifting & Frequency Shifting || 1)<br /> | + | | Time Shifting & Frequency Shifting || 1) x[n - n<sub>o</sub>] → e<sup>-jωn<sub>o</sub></sup>X(ω)<br /> |
| − | 2) || Example | + | 2) e<sup>-jω<sub>o</sub>n</sup>x[n] → X[ω - ω<sub>o</sub>]<br /> |
| + | || Example | ||
|- | |- | ||
| − | | Conjugate & Conjugate Symmetry || | + | | Conjugate & Conjugate Symmetry || x[n] → X<sup>*</sup>(-ω) || Example |
|- | |- | ||
| Parversal Relation || Example || Example | | Parversal Relation || Example || Example | ||
Revision as of 21:04, 18 March 2018
Discrete-Time Fourier Transform Properties with Proofs
| Property Name | Property | Proof |
|---|---|---|
| Periodicity | Χ(ω + 2π) = Χ(ω) | Example |
| Linearity | ax1[n] + bx2[n] → aΧ1(ω) + bΧ2(ω) | Example |
| Time Shifting & Frequency Shifting | 1) x[n - no] → e-jωnoX(ω) 2) e-jωonx[n] → X[ω - ωo] |
Example |
| Conjugate & Conjugate Symmetry | x[n] → X*(-ω) | Example |
| Parversal Relation | Example | Example |
| Convolution | Example | Example |
| Multiplication | Example | Example |
| Duality | Example | Example |
| Differentiation in Frequency | Example | Example |
