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| − | == '''Discrete-Time Fourier Transform Properties with Proofs''' == | + | |
| + | == '''<big> Discrete-Time Fourier Transform Properties with Proofs''' </big>''' == | ||
| + | <br /> | ||
| + | |||
| + | {| class="wikitable sortable" | ||
| + | |- | ||
| + | !Property Name!! Property !! Proof | ||
| + | |- | ||
| + | |Periodicity|| χ(ω + 2π) = χ(ω) || Example | ||
| + | |- | ||
| + | | 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 /> | ||
| + | 2) || Example | ||
| + | |- | ||
| + | | Conjugate & Conjugate Symmetry || Example || Example | ||
| + | |- | ||
| + | | Parversal Relation || Example || Example | ||
| + | |- | ||
| + | | Convolution || Example || Example | ||
| + | |- | ||
| + | | Multiplication || Example || Example | ||
| + | |- | ||
| + | | Duality || Example || Example | ||
| + | |- | ||
| + | | Differentiation in Frequency || Example || Example | ||
| + | |} | ||
Revision as of 20:52, 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) 2) || Example | |
| Conjugate & Conjugate Symmetry | Example | Example |
| Parversal Relation | Example | Example |
| Convolution | Example | Example |
| Multiplication | Example | Example |
| Duality | Example | Example |
| Differentiation in Frequency | Example | Example |
