Fourier TransformΒΆ
Complex form or exponential form of Fourier Integral
assume that
converges
-
Comparison
-
compare to Laplace transform
-
compare to Fourier Series Fourier Transform can be regarded as Fourier series whose
.
-
Amplitude SpectrumΒΆ
The amplitude spectrum of
Fourier & Inverse Fourier TransformΒΆ
-
Fourier transform
-
inverse Fourier transform
Fourier Sine TransformΒΆ
-
Fourier sine transform
-
inverse Fourier sine transform
Fourier Cosine TransformΒΆ
- Fourier cosine transform
- inverse Fourier cosine transform
Fourier Transform propertiesΒΆ
LinearityΒΆ
Time ShiftingΒΆ
-
Inverse Time Shifting
Frequency ShiftingΒΆ
-
Inverse Frequency Shifting
ScalingΒΆ
- Inverse Scaling
Time ReversalΒΆ
SymmetryΒΆ
modulationΒΆ
particular exampleΒΆ
prof. Laplace Transform
Frequency DifferentiationΒΆ
Transforms of DerivativesΒΆ
-
for Fourier transform
-
for Fourier sine transform
-
for Fourier cosine transform
Transform of IntegralΒΆ
ConvolutionΒΆ
- Definition
- Property
- Theorem
Dirac Delta FunctionΒΆ
-
Definition
Fourier TransformΒΆ
FilteringΒΆ
Discrete Fourier TransformΒΆ
Let
LinearityΒΆ
PeriodicityΒΆ
Inverse N-point DFTΒΆ
Complex Fourier CoefficientsΒΆ
note that the coefficient of complex Fourier
Sampled Fourier SeriesΒΆ
in which
Solving the BVPΒΆ
- BVP (Boundary Value Problem)
There are three possible condition below
-
Fourier transform -
and Fourier sine transform -
and Fourier cosine transform
Method of Separation of VariableΒΆ
kernel : assume that 1.
2.