Website owner:  James Miller

Fourier series, integrals, and transforms

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