Discrete-Time Fourier Transform (DTFT)
GPTKB entity
Statements (40)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:transformation
|
| gptkbp:aliasing |
can occur due to sampling
|
| gptkbp:alternativeName |
gptkb:DTFT
discrete-time Fourier analysis |
| gptkbp:application |
gptkb:radar
communications image processing audio signal processing speech analysis |
| gptkbp:appliesTo |
discrete-time signals
|
| gptkbp:approximation |
gptkb:Discrete_Fourier_Transform_(DFT)
|
| gptkbp:designer |
Inverse Discrete-Time Fourier Transform
|
| gptkbp:domain |
frequency domain
|
| gptkbp:field |
gptkb:mathematics
gptkb:signal_processing |
| gptkbp:form |
X(e^{jω}) = Σ_{n=-∞}^{∞} x[n] e^{-jωn}
|
| gptkbp:hasUnit |
radians per sample
|
| https://www.w3.org/2000/01/rdf-schema#label |
Discrete-Time Fourier Transform (DTFT)
|
| gptkbp:input |
sequence of complex numbers
|
| gptkbp:introduced |
gptkb:Norbert_Wiener
|
| gptkbp:introducedIn |
1932
|
| gptkbp:inverseFormula |
x[n] = (1/2π) ∫_{-π}^{π} X(e^{jω}) e^{jωn} dω
|
| gptkbp:limitation |
not directly computable for finite-length signals
|
| gptkbp:mapType |
discrete-time signal to frequency domain representation
|
| gptkbp:output |
periodic function of frequency
|
| gptkbp:property |
gptkb:Parseval's_theorem
linearity convolution frequency-shifting time-shifting |
| gptkbp:range |
complex numbers
|
| gptkbp:recurrence |
2π
|
| gptkbp:relatedTo |
gptkb:Fourier_Transform
gptkb:Z-transform gptkb:Discrete_Fourier_Transform_(DFT) |
| gptkbp:usedFor |
filter design
system analysis frequency analysis of discrete signals |
| gptkbp:bfsParent |
gptkb:Discrete_Fourier_Transform_(DFT)
|
| gptkbp:bfsLayer |
6
|