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  2. Square wave - Wikipedia

    en.wikipedia.org/wiki/Square_wave

    The square wave in mathematics has many definitions, which are equivalent except at the discontinuities: It can be defined as simply the sign function of a sinusoid: = ⁡ (⁡) = ⁡ (⁡) = ⁡ (⁡) = ⁡ (⁡), which will be 1 when the sinusoid is positive, −1 when the sinusoid is negative, and 0 at the discontinuities.

  3. Optical transfer function - Wikipedia

    en.wikipedia.org/wiki/Optical_transfer_function

    Either transfer function specifies the response to a periodic sine-wave pattern passing through the lens system, as a function of its spatial frequency or period, and its orientation. Formally, the OTF is defined as the Fourier transform of the point spread function (PSF, that is, the impulse response of the optics, the image of a point source).

  4. Wave equation - Wikipedia

    en.wikipedia.org/wiki/Wave_equation

    A so-called eigenmode is a solution that oscillates in time with a well-defined constant angular frequency ω, so that the temporal part of the wave function takes the form e −iωt = cos(ωt) − i sin(ωt), and the amplitude is a function f(x) of the spatial variable x, giving a separation of variables for the wave function: (,) = ().

  5. Gibbs phenomenon - Wikipedia

    en.wikipedia.org/wiki/Gibbs_phenomenon

    Functional approximation of square wave using 5 harmonics Functional approximation of square wave using 25 harmonics Functional approximation of square wave using 125 harmonics. The Gibbs phenomenon is a behavior of the Fourier series of a function with a jump discontinuity and is described as the following:

  6. Fourier series - Wikipedia

    en.wikipedia.org/wiki/Fourier_series

    A square wave (represented as the blue dot) is approximated by its sixth partial sum (represented as the purple dot), formed by summing the first six terms (represented as arrows) of the square wave's Fourier series. Each arrow starts at the vertical sum of all the arrows to its left (i.e. the previous partial sum).

  7. Fourier transform - Wikipedia

    en.wikipedia.org/wiki/Fourier_transform

    This idea makes the spatial Fourier transform very natural in the study of waves, as well as in quantum mechanics, where it is important to be able to represent wave solutions as functions of either position or momentum and sometimes both. In general, functions to which Fourier methods are applicable are complex-valued, and possibly vector-valued.

  8. Sawtooth wave - Wikipedia

    en.wikipedia.org/wiki/Sawtooth_wave

    The sawtooth wave (or saw wave) is a kind of non-sinusoidal waveform. It is so named based on its resemblance to the teeth of a plain-toothed saw with a zero rake angle . A single sawtooth, or an intermittently triggered sawtooth, is called a ramp waveform .

  9. Dirac delta function - Wikipedia

    en.wikipedia.org/wiki/Dirac_delta_function

    Wave functions are assumed to be elements of the Hilbert space L 2 of square-integrable functions, and the total probability of finding a particle within a given interval is the integral of the magnitude of the wave function squared over the interval. A set {|φ n } of wave functions is orthonormal if