Discrete-time Fourier transform
GPTKB entity
Statements (50)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:transformation
|
| gptkbp:abbreviation |
gptkb:DTFT
|
| gptkbp:application |
filter design
system analysis digital signal analysis |
| gptkbp:citation |
gptkb:Alan_V._Oppenheim
gptkb:Ronald_W._Schafer "Discrete-Time Signal Processing" (book) |
| gptkbp:computation |
approximated by Discrete Fourier transform
|
| gptkbp:designer |
Inverse discrete-time Fourier transform
|
| gptkbp:domain |
frequency domain
|
| gptkbp:field |
gptkb:mathematics
gptkb:signal_processing electrical engineering |
| gptkbp:firstDescribed |
mid-20th century
|
| gptkbp:form |
X(e^{jω}) = Σ_{n=-∞}^{∞} x[n] e^{-jωn}
|
| gptkbp:generalizes |
Fourier series
|
| gptkbp:hasUnit |
radians/sample
|
| https://www.w3.org/2000/01/rdf-schema#label |
Discrete-time Fourier transform
|
| gptkbp:input |
discrete-time signal
|
| gptkbp:limitation |
infinite summation required
not directly computable on digital computers not suitable for finite-length signals |
| gptkbp:mapType |
discrete-time signal to frequency domain
|
| gptkbp:output |
frequency spectrum
|
| gptkbp:property |
gptkb:Parseval's_theorem
modulation linearity convolution duality frequency-shifting time-shifting time reversal differentiation in frequency multiplication in time |
| gptkbp:recurrence |
2π
|
| gptkbp:relatedTo |
gptkb:Fourier_transform
gptkb:Z-transform gptkb:Discrete_Fourier_transform |
| gptkbp:usedIn |
digital communications
audio processing image processing spectral analysis speech analysis radar signal processing system identification filter implementation |
| gptkbp:variant |
ω (angular frequency)
|
| gptkbp:bfsParent |
gptkb:Z-Transform
|
| gptkbp:bfsLayer |
6
|