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Since the sine and cosine transforms use sine and cosine waves instead of complex exponentials and don't require complex numbers or negative frequency, they more closely correspond to Joseph Fourier's original transform equations and are still preferred in some signal processing and statistics applications and may be better suited as an ...
Ptolemy's theorem states that the sum of the products of the lengths of opposite sides is equal to the product of the lengths of the diagonals. When those side-lengths are expressed in terms of the sin and cos values shown in the figure above, this yields the angle sum trigonometric identity for sine: sin(α + β) = sin α cos β + cos α sin β.
Polarization (waves) Coherence (physics), the quality of a wave to display a well defined phase relationship in different regions of its domain of definition; Hilbert transform, a method of changing phase by 90° Reflection phase shift, a phase change that happens when a wave is reflected off of a boundary from fast medium to slow medium
In mathematics, sine and cosine are trigonometric functions of an angle.The sine and cosine of an acute angle are defined in the context of a right triangle: for the specified angle, its sine is the ratio of the length of the side opposite that angle to the length of the longest side of the triangle (the hypotenuse), and the cosine is the ratio of the length of the adjacent leg to that of the ...
To gain some basic intuition for this equation, we consider a propagating (cosine) wave A cos(kx − ωt). We want to see how fast a particular phase of the wave travels. For example, we can choose kx - ωt = 0, the phase of the first crest. This implies kx = ωt, and so v = x / t = ω / k.
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).
Examples of pulse shapes: (a) rectangular pulse, (b) cosine squared (raised cosine) pulse, (c) Dirac pulse, (d) sinc pulse, (e) Gaussian pulse A pulse in signal processing is a rapid, transient change in the amplitude of a signal from a baseline value to a higher or lower value, followed by a rapid return to the baseline value.
A pure tone has the property – unique among real-valued wave shapes – that its wave shape is unchanged by linear time-invariant systems; that is, only the phase and amplitude change between such a system's pure-tone input and its output. Sine and cosine waves can be used as basic building blocks of more