* Digital companding ( using a CCITT J. 17 pre-emphasis curve ) ensures that the encoding and decoding algorithms can track perfectly.

* An equalization filter is not designed to fully pass or block any frequency, but instead to gradually vary the amplitude response as a function of frequency: filters used as pre-emphasis filters, equalizers, or tone controls are good examples.

In high speed digital transmission, pre-emphasis is used to improve signal quality at the output of a data transmission.

In transmitting signals at high data rates, the transmission medium may introduce distortions, so pre-emphasis is used to distort the transmitted signal to correct for this distortion.

In telecommunication, a pre-emphasis network is a network inserted in a system in order to increase the magnitude of one range of frequencies with respect to another.

As the tape is recorded, the relative amplitude of the signal above 1 kHz is used to determine how much pre-emphasis to apply-a low-level signal is boosted by 10 dB ( Dolby B ) or 20 dB ( Dolby C ).

As the signal rises in amplitude, less and less pre-emphasis is applied until at the " Dolby level " (+ 3 VU ), no signal modification is performed.

In telecommunication, de-emphasis is the complement of pre-emphasis, in the antinoise system called emphasis.

for pre-emphasis / de-emphasis RC filters:

Dual-ended systems ( such as Dolby B, Dolby C, Dolby S, dbx Type I and dbx Type II, High Com and High Com II as well as Toshiba's and JVC's ) have a pre-emphasis process applied during recording and then a de-emphasis process applied at playback.

As CD's were intended to work on 14 bit audio, a specification for ' pre-emphasis ' was included to compensate for quantization noise.

In processing electronic audio signals, pre-emphasis refers to a system process designed to increase ( within a frequency band ) the magnitude of some ( usually higher ) frequencies with respect to the magnitude of other ( usually lower ) frequencies in order to improve the overall signal-to-noise ratio by minimizing the adverse effects of such phenomena as attenuation distortion or saturation of recording media in subsequent parts of the system.

To deal with this, both Type I and II use very strong high-frequency pre-emphasis of the audio signal in both the recording path and the control signal path.

This causes the compander to ' back off ' the gain in certain circumstances and reduce the audibility of noise modulation – even with this pre-emphasis, noise modulation can become audible when using very noisy media to begin with, such as the Compact Cassette format.

To filter this noise, the high-frequency response of theatre playback systems was deliberately curtailed … To make matters worse, to increase dialogue intelligibility over such systems, sound mixers were recording soundtracks with so much high-frequency pre-emphasis that high distortion resulted.

It used Dolby B, combined with 25 microsecond pre-emphasis.

If one assumes that the average flux did not change between measurements, a mass-distribution curve is obtained which relates the flux of particles larger than a given radius to the inverse 7/2 power of the radius.

Consider a simple, closed, plane curve C which is a real-analytic image of the unit circle, and which is given by Af.

In the following paper it is shown that in a certain definite sense, exactly an odd number of squares can be inscribed in every such curve which does not contain an infinite number of inscribed squares.

If the vertex is at Af, and if the interior of C is on the left as one moves in the direction of increasing t, then every such corner can be found from the curve obtained by rotating C clockwise through 90-degrees about the vertex.

But Af is just the curve Af translated without rotation through a small arc, for Af is always obtained by rotating C through exactly 90-degrees.

The arc is itself a segment of an analytic curve.

Then in 2 we show that any line involution with the properties that ( A ) It has no complex of invariant lines, and ( B ) Its singular lines form a complex consisting exclusively of the lines which meet a twisted curve, is necessarily of the type discussed in 1.

The order of this congruence is Af, since Af secants of a curve of symbol ( B ) on a quadric surface pass through an arbitrary point.

For the lines of any plane, **yp, meeting Q in a conic C, are transformed into the congruence of secants of the curve C' into which C is transformed in the point involution on Q.

Each generator, **yl, of Af is also exceptional, for each is transformed into the entire congruence of secants of the curve into which that generator is transformed by the point involution on Q.

This curve is of symbol Af since it meets **yl, and hence every line of Af in the Af invariant points on **yl and since it obviously meets every line of Af in a single point.

Hence C' is a Af curve on Q.

By ( 1 ), the image of this pencil is a ruled surface of order Af which is met by the plane of the pencil in a curve, C, of order Af.

To avoid this contradiction it is necessary that C be composite, with the secant of **zg and a curve of order Af as components.

We now observe that the case in which **zg is a Af curve on a quadric is impossible if the complex of singular lines consists exclusively of the lines which meet Aj.

This contradicts the preceding observations, and so, under the assumption of this paper, we must reject the possibility that **zg is a Af curve on a quadric surface.

Continuing with the case in which **zg is a Af curve on a quadric Q, we first observe that the second regulus of Q consists precisely of the lines which join the two free intersections of **zg and the planes through any one of the multiple secants.

We assume that average total unit cost in the relevant region of operation is constant with respect to quantity produced ( the average cost curve is horizontal, and therefore is identical with the marginal cost curve ), and is the same for every firm ( and therefore for the industry ).

Fermat always started with an algebraic equation and then described the geometric curve which satisfied it, while Descartes starts with geometric curves and produces their equations as one of several properties of the curves.

* Some curves that seem simple, such as the circle, cannot be described exactly by a Bézier or piecewise Bézier curve ; though a four-piece cubic Bézier curve can approximate a circle ( see Bézier spline ), with a maximum radial error of less than one part in a thousand, when each inner control point ( or offline point ) is the distance horizontally or vertically from an outer control point on a unit circle.

Although the details of each particular elliptic curve scheme are described in the article referenced above some common implementation considerations are discussed here.

The idea of self-similar curves was taken further by Paul Pierre Lévy, who, in his 1938 paper Plane or Space Curves and Surfaces Consisting of Parts Similar to the Whole described a new fractal curve, the Lévy C curve.

This magnetization as a function of the external field is described by a hysteresis curve.

The learning curve described by Ebbinghaus refers to how fast one learns information.

Besides product homogeneity and absence of collusion, the notion more generally associated with perfect competition is the negligibility of the size of agents, which makes them believe that they can sell as much of the good as they wish at the equilibrium price but nothing at a higher price ( in particular, firms are described as each one of them facing a horizontal demand curve ).

In 1958 Bing proved a weak version of the Poincaré conjecture: if every simple closed curve of a compact 3-manifold is contained in a 3-ball, then the manifold is homeomorphic to the 3-sphere .< ref > Bing also described some of the pitfalls in trying to prove the Poincaré conjecture.

The concept is notable because, in the version of Keynesian macroeconomic theory which was dominant between the end of WWII and the late-1970s, inflation and recession were regarded as mutually exclusive, the relationship between the two being described by the Phillips curve.

As described above, the demand curve is generally downward-sloping, there may be rare examples of goods that have upward-sloping demand curves.

A movement along the curve is described as a " change in the quantity demanded " to distinguish it from a " change in demand ," that is, a shift of the curve.

For accurate temperature measurements, the resistance / temperature curve of the device must be described in more detail.

The Koch snowflake ( also known as the Koch star and Koch island ) is a mathematical curve and one of the earliest fractal curves to have been described.

The Koch curve originally described by Koch is constructed with only one of the three sides of the original triangle.

In three-dimensions, the third order behavior of a curve is described by a related notion of torsion, which measures the extent to which a curve tends to perform a corkscrew in space.

Bunning's first game as a major league pitcher was on July 20, 1955, with the Detroit Tigers, after having toiled in the minor leagues 1950 – 1954 and part of the 1955 season, when the Tigers club described him as having " an excellent curve ball, a confusing delivery and a sneaky fast ball ".

This enabled a curve to be described using an equation rather than an elaborate geometrical construction.

This process has been proposed that the life cycle of innovations can be described using the's-curve ' or diffusion curve.

However, Phillips ' original curve described the behavior of money wages.

The traditional Phillips curve story starts with a wage Phillips Curve, of the sort described by A. W.