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Website owner: James Miller

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# Fourier series, integrals, and transforms

Select from the following:
Dirichlet conditions. Sectionally continuous
(or piecewise continuous) function. Fourier series. Even and odd functions.
Half range series. Rate of convergence. Harmonic. Complex Fourier series.
Parseval’s identity. Wave symmetry. Half-wave, Quarter-wave, and Hidden
Symmetries. Orthogonal properties of sine and cosine functions.

Complex frequency spectra. Amplitude, phase spectrum.
Fourier integral theorem. From the Fourier series to the Fourier integral.
Fourier transform. Fourier sine and cosine integrals. Convolution theorem.
Parseval’s identity.

Properties and Fourier transforms of even
and odd functions. Hermitian function. Complex conjugates.

Fourier integral, transform. Magnitude and phase
spectrum. Theorems. Impulse, rectangle, triangle, Heaviside unit
step, sign functions. Convolution. Correlation, autocorrelation.

Theorems involving Impulse function. Complex
Fourier series representation and Fourier transform
of a train of rectangular pulses of width d with period
T.

Properties of the Fourier transform

Pictorial Dictionary of Fourier Transforms

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