Discrete Time Fourier Series

URI: https://gptkb.org/entity/Discrete_Time_Fourier_Series
GPTKB entity
Statements (50)
Predicate Object
gptkbp:instanceOf gptkb:mathematical_concept
gptkbp:abbreviation gptkb:DTFS
gptkbp:application Digital signal processing
Image processing
Communications
Audio analysis
System analysis
gptkbp:appliesTo Periodic discrete-time signals
gptkbp:basisFor Complex exponentials
gptkbp:category Digital signal processing
Fourier analysis
Mathematical series
gptkbp:coefficientFormula X[k] = (1/N) sum_{n=0}^{N-1} x[n] e^{-j(2π/N)kn}
gptkbp:domain Discrete time
gptkbp:field gptkb:Mathematics
gptkb:signal_processing
gptkbp:form x[n] = sum_{k=0}^{N-1} X[k] e^{j(2π/N)kn}
gptkbp:generalizes Fourier Series for continuous time
gptkbp:hasComponent Fourier coefficients
Basis functions
Period N
https://www.w3.org/2000/01/rdf-schema#label Discrete Time Fourier Series
gptkbp:introduced gptkb:Jean-Baptiste_Joseph_Fourier
gptkbp:inverseFormula x[n] = sum_{k=0}^{N-1} X[k] e^{j(2π/N)kn}
gptkbp:isDiscreteVersionOf gptkb:Fourier_Series
gptkbp:period N
gptkbp:property gptkb:Parseval's_theorem
Linearity
Time shift
Convolution property
Frequency shift
Symmetry properties
gptkbp:recurrence Periodic signals
gptkbp:relatedConcept gptkb:Laplace_transform
gptkb:Z-transform
Sampling theorem
gptkbp:relatedTo gptkb:Fourier_Transform
gptkb:Discrete_Fourier_Transform
gptkb:Fourier_Series
gptkbp:represents Sum of complex exponentials
gptkbp:usedFor Frequency analysis
Signal decomposition
gptkbp:usedIn gptkb:Mathematics
gptkb:Physics
Engineering
Telecommunications
Computer science
Control systems
gptkbp:bfsParent gptkb:DTFS
gptkbp:bfsLayer 8