Theorem 1 (Convolution Theorem) – If f (t) and g (t) are periodic functions with period T that satisfy the Dirichlet conditions, the Fourier coefficients γ k of the convolution product f ∗ g, are ...

Abstract: The linear canonical transform (LCT) plays an important role in many fields of optics and signal processing. Many properties for this transform are already known, however, the convolution ...

The fractional Fourier transform (FRFT), which is a generalization of the Fourier transform, has many applications in several areas, including signal processing and optics. Almeida (see ibid., vol.4, ...

Convolution and correlation are useful for applications such as filtering, modulation, detection, and pattern recognition. Add your perspective Help others by sharing more (125 characters min.) Cancel ...

As a corollary, we also construct stochastic processes whose sample paths have nontrivial, deterministic, and linear Φ-variation for each function Φ from our class. The proof of our main result relies ...