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43-411: The TO7 is built around a 1  MHz Motorola 6809 processor. ROM cartridges , designed as MEMO7 , can be introduced through a memory bay. The user interface uses Microsoft BASIC , included in the kit cartridge. The keyboard features a plastic membrane , and further user input is obtained through a lightpen . Cooling is provided by a rear radiator. A standard television can serve as a monitor using

86-908: A x ) {\displaystyle f(ax)} , where a {\displaystyle a} is a non-zero real number such that a x {\displaystyle ax} is within the domain of f {\displaystyle f} , is periodic with period P a {\textstyle {\frac {P}{a}}} . For example, f ( x ) = sin ⁡ ( x ) {\displaystyle f(x)=\sin(x)} has period 2 π {\displaystyle 2\pi } and, therefore, sin ⁡ ( 5 x ) {\displaystyle \sin(5x)} will have period 2 π 5 {\textstyle {\frac {2\pi }{5}}} . Some periodic functions can be described by Fourier series . For instance, for L functions , Carleson's theorem states that they have

129-503: A SCART connector , with the refresh rate being 625-line compatible 50Hz. Audio featured a single channel sound generator with five octaves. A "game expansion" was capable of four channel, six octaves sound. The keyboard has 58 keys and includes arrow keys . Besides cartridges, the machine used cassette tapes for file storage. An upgraded version, the Thomson TO7/70 , was released in 1984 with an introductory price of 3590 FF. It

172-520: A periodic waveform (or simply periodic wave ), is a function that repeats its values at regular intervals or periods . The repeatable part of the function or waveform is called a cycle . For example, the trigonometric functions , which repeat at intervals of 2 π {\displaystyle 2\pi } radians , are periodic functions. Periodic functions are used throughout science to describe oscillations , waves , and other phenomena that exhibit periodicity . Any function that

215-552: A pointwise ( Lebesgue ) almost everywhere convergent Fourier series . Fourier series can only be used for periodic functions, or for functions on a bounded (compact) interval. If f {\displaystyle f} is a periodic function with period P {\displaystyle P} that can be described by a Fourier series, the coefficients of the series can be described by an integral over an interval of length P {\displaystyle P} . Any function that consists only of periodic functions with

258-481: A RGB SCART (Peritel) connector, with a resolution of 320x200 (with 2 colors for each 8 x 1 pixels). The TO7 prototype, called Thomson T9000 , was developed in 1980. The differences regarding the production model are a different startup menu and buggier BIOS . The Thomson TO7 runs on a Motorola 6809 processor clocked at 1 MHz and features 22 KB of RAM (8 KB for the user, 8 KB used as video memory and 8K x 6 bits color memory) and 20KB of ROM (4KB for

301-487: A function f {\displaystyle f} is periodic with period P {\displaystyle P} , then for all x {\displaystyle x} in the domain of f {\displaystyle f} and all positive integers n {\displaystyle n} , If f ( x ) {\displaystyle f(x)} is a function with period P {\displaystyle P} , then f (

344-432: A function is used to mean its fundamental period. A function with period P will repeat on intervals of length P , and these intervals are sometimes also referred to as periods of the function. Geometrically, a periodic function can be defined as a function whose graph exhibits translational symmetry , i.e. a function f is periodic with period P if the graph of f is invariant under translation in

387-447: A function like f : R / Z → R {\displaystyle f:{\mathbb {R} /\mathbb {Z} }\to \mathbb {R} } is a representation of a 1-periodic function. Consider a real waveform consisting of superimposed frequencies, expressed in a set as ratios to a fundamental frequency, f: F = 1 ⁄ f  [f 1 f 2 f 3 ... f N ] where all non-zero elements ≥1 and at least one of

430-548: A more detailed treatment of this and the above frequency ranges, see Electromagnetic spectrum . Gravitational waves are also described in Hertz. Current observations are conducted in the 30–7000 Hz range by laser interferometers like LIGO , and the nanohertz (1–1000 nHz) range by pulsar timing arrays . Future space-based detectors are planned to fill in the gap, with LISA operating from 0.1–10 mHz (with some sensitivity from 10 μHz to 100 mHz), and DECIGO in

473-499: Is an SI derived unit whose formal expression in terms of SI base units is s , meaning that one hertz is one per second or the reciprocal of one second . It is used only in the case of periodic events. It is named after Heinrich Rudolf Hertz (1857–1894), the first person to provide conclusive proof of the existence of electromagnetic waves . For high frequencies, the unit is commonly expressed in multiples : kilohertz (kHz), megahertz (MHz), gigahertz (GHz), terahertz (THz). Some of

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516-469: Is not periodic is called aperiodic . A function f is said to be periodic if, for some nonzero constant P , it is the case that for all values of x in the domain. A nonzero constant P for which this is the case is called a period of the function. If there exists a least positive constant P with this property, it is called the fundamental period (also primitive period , basic period , or prime period .) Often, "the" period of

559-410: Is periodic with period 2 π {\displaystyle 2\pi } , since for all values of x {\displaystyle x} . This function repeats on intervals of length 2 π {\displaystyle 2\pi } (see the graph to the right). Everyday examples are seen when the variable is time ; for instance the hands of a clock or the phases of

602-473: Is the photon's energy, ν is its frequency, and h is the Planck constant . The hertz is defined as one per second for periodic events. The International Committee for Weights and Measures defined the second as "the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium -133 atom" and then adds: "It follows that

645-670: Is the special case k = 0 {\displaystyle k=0} , and an antiperiodic function is the special case k = π / P {\displaystyle k=\pi /P} . Whenever k P / π {\displaystyle kP/\pi } is rational, the function is also periodic. In signal processing you encounter the problem, that Fourier series represent periodic functions and that Fourier series satisfy convolution theorems (i.e. convolution of Fourier series corresponds to multiplication of represented periodic function and vice versa), but periodic functions cannot be convolved with

688-452: Is usually measured in kilohertz (kHz), megahertz (MHz), or gigahertz (GHz). with the latter known as microwaves . Light is electromagnetic radiation that is even higher in frequency, and has frequencies in the range of tens of terahertz (THz, infrared ) to a few petahertz (PHz, ultraviolet ), with the visible spectrum being 400–790 THz. Electromagnetic radiation with frequencies in the low terahertz range (intermediate between those of

731-398: The x -direction by a distance of P . This definition of periodicity can be extended to other geometric shapes and patterns, as well as be generalized to higher dimensions, such as periodic tessellations of the plane. A sequence can also be viewed as a function defined on the natural numbers , and for a periodic sequence these notions are defined accordingly. The sine function

774-508: The Thomson MO5 and generated by a Motorola MCA1300 gate array capable of 40×25 text display and a resolution of 320 x 200 pixels with 16 colours (limited by 8 x 1 pixel colour attribute areas). The colour palette is 4-bit RGBI , with 8 basic RGB colours and a intensity bit (called P for "Pastel") that controlled saturation ("saturated" or "pastel"). Software developed for the TO-7 can be run on

817-400: The monitor and 16KB on MEMO7 cartridges). As common on home computers designed to be connected to an ordinary TV screen, the 320 x 200 pixels active area doesn't cover the entire screen, and is surrounded by a border. Graphics were limited to 8 colours (generated by combination of RGB primaries ) with proximity constraints (2 colors for each 8 x 1 pixel area). The video output is RGB on

860-464: The moon show periodic behaviour. Periodic motion is motion in which the position(s) of the system are expressible as periodic functions, all with the same period. For a function on the real numbers or on the integers , that means that the entire graph can be formed from copies of one particular portion, repeated at regular intervals. A simple example of a periodic function is the function f {\displaystyle f} that gives

903-401: The " fractional part " of its argument. Its period is 1. In particular, The graph of the function f {\displaystyle f} is the sawtooth wave . The trigonometric functions sine and cosine are common periodic functions, with period 2 π {\displaystyle 2\pi } (see the figure on the right). The subject of Fourier series investigates

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946-446: The 0.1–10 Hz range. In computers, most central processing units (CPU) are labeled in terms of their clock rate expressed in megahertz ( MHz ) or gigahertz ( GHz ). This specification refers to the frequency of the CPU's master clock signal . This signal is nominally a square wave , which is an electrical voltage that switches between low and high logic levels at regular intervals. As

989-468: The 1970s. In some usage, the "per second" was omitted, so that "megacycles" (Mc) was used as an abbreviation of "megacycles per second" (that is, megahertz (MHz)). Sound is a traveling longitudinal wave , which is an oscillation of pressure . Humans perceive the frequency of a sound as its pitch . Each musical note corresponds to a particular frequency. An infant's ear is able to perceive frequencies ranging from 20 Hz to 20 000  Hz ;

1032-586: The TO-7/70, but the reverse is not possible. At least three games were released for the TO7/70. This microcomputer - or microprocessor -related article is a stub . You can help Misplaced Pages by expanding it . Hertz The hertz (symbol: Hz ) is the unit of frequency in the International System of Units (SI), often described as being equivalent to one event (or cycle ) per second . The hertz

1075-476: The average adult human can hear sounds between 20 Hz and 16 000  Hz . The range of ultrasound , infrasound and other physical vibrations such as molecular and atomic vibrations extends from a few femtohertz into the terahertz range and beyond. Electromagnetic radiation is often described by its frequency—the number of oscillations of the perpendicular electric and magnetic fields per second—expressed in hertz. Radio frequency radiation

1118-519: The complex exponential is made up of cosine and sine waves. This means that Euler's formula (above) has the property such that if L {\displaystyle L} is the period of the function, then A function whose domain is the complex numbers can have two incommensurate periods without being constant. The elliptic functions are such functions. ("Incommensurate" in this context means not real multiples of each other.) Periodic functions can take on values many times. More specifically, if

1161-489: The context of Bloch's theorems and Floquet theory , which govern the solution of various periodic differential equations. In this context, the solution (in one dimension) is typically a function of the form where k {\displaystyle k} is a real or complex number (the Bloch wavevector or Floquet exponent ). Functions of this form are sometimes called Bloch-periodic in this context. A periodic function

1204-440: The event being counted may be a complete cycle); 100 Hz means "one hundred periodic events occur per second", and so on. The unit may be applied to any periodic event—for example, a clock might be said to tick at 1 Hz , or a human heart might be said to beat at 1.2 Hz . The occurrence rate of aperiodic or stochastic events is expressed in reciprocal second or inverse second (1/s or s ) in general or, in

1247-449: The hertz has become the primary unit of measurement accepted by the general populace to determine the performance of a CPU, many experts have criticized this approach, which they claim is an easily manipulable benchmark . Some processors use multiple clock cycles to perform a single operation, while others can perform multiple operations in a single cycle. For personal computers, CPU clock speeds have ranged from approximately 1 MHz in

1290-413: The highest normally usable radio frequencies and long-wave infrared light) is often called terahertz radiation . Even higher frequencies exist, such as that of X-rays and gamma rays , which can be measured in exahertz (EHz). For historical reasons, the frequencies of light and higher frequency electromagnetic radiation are more commonly specified in terms of their wavelengths or photon energies : for

1333-616: The hyperfine splitting in the ground state of the caesium 133 atom is exactly 9 192 631 770  hertz , ν hfs Cs = 9 192 631 770  Hz ." The dimension of the unit hertz is 1/time (T ). Expressed in base SI units, the unit is the reciprocal second (1/s). In English, "hertz" is also used as the plural form. As an SI unit, Hz can be prefixed ; commonly used multiples are kHz (kilohertz, 10  Hz ), MHz (megahertz, 10  Hz ), GHz (gigahertz, 10  Hz ) and THz (terahertz, 10  Hz ). One hertz (i.e. one per second) simply means "one periodic event occurs per second" (where

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1376-545: The idea that an 'arbitrary' periodic function is a sum of trigonometric functions with matching periods. According to the definition above, some exotic functions, for example the Dirichlet function , are also periodic; in the case of Dirichlet function, any nonzero rational number is a period. Using complex variables we have the common period function: Since the cosine and sine functions are both periodic with period 2 π {\displaystyle 2\pi } ,

1419-454: The late 1970s ( Atari , Commodore , Apple computers ) to up to 6 GHz in IBM Power microprocessors . Various computer buses , such as the front-side bus connecting the CPU and northbridge , also operate at various frequencies in the megahertz range. Higher frequencies than the International System of Units provides prefixes for are believed to occur naturally in the frequencies of

1462-701: The quantum-mechanical vibrations of massive particles, although these are not directly observable and must be inferred through other phenomena. By convention, these are typically not expressed in hertz, but in terms of the equivalent energy, which is proportional to the frequency by the factor of the Planck constant . The CJK Compatibility block in Unicode contains characters for common SI units for frequency. These are intended for compatibility with East Asian character encodings, and not for use in new documents (which would be expected to use Latin letters, e.g. "MHz"). Periodic waveform A periodic function also called

1505-544: The rules for capitalisation of a common noun ; i.e., hertz becomes capitalised at the beginning of a sentence and in titles but is otherwise in lower case. The hertz is named after the German physicist Heinrich Hertz (1857–1894), who made important scientific contributions to the study of electromagnetism . The name was established by the International Electrotechnical Commission (IEC) in 1935. It

1548-410: The same period is also periodic (with period equal or smaller), including: One subset of periodic functions is that of antiperiodic functions . This is a function f {\displaystyle f} such that f ( x + P ) = − f ( x ) {\displaystyle f(x+P)=-f(x)} for all x {\displaystyle x} . For example,

1591-411: The sine and cosine functions are π {\displaystyle \pi } -antiperiodic and 2 π {\displaystyle 2\pi } -periodic. While a P {\displaystyle P} -antiperiodic function is a 2 P {\displaystyle 2P} -periodic function, the converse is not necessarily true. A further generalization appears in

1634-413: The specific case of radioactivity , in becquerels . Whereas 1 Hz (one per second) specifically refers to one cycle (or periodic event) per second, 1 Bq (also one per second) specifically refers to one radionuclide event per second on average. Even though frequency, angular velocity , angular frequency and radioactivity all have the dimension T , of these only frequency is expressed using

1677-480: The unit hertz. Thus a disc rotating at 60 revolutions per minute (rpm) is said to have an angular velocity of 2 π  rad/s and a frequency of rotation of 1 Hz . The correspondence between a frequency f with the unit hertz and an angular velocity ω with the unit radians per second is The hertz is named after Heinrich Hertz . As with every SI unit named for a person, its symbol starts with an upper case letter (Hz), but when written in full, it follows

1720-403: The unit's most common uses are in the description of periodic waveforms and musical tones , particularly those used in radio - and audio-related applications. It is also used to describe the clock speeds at which computers and other electronics are driven. The units are sometimes also used as a representation of the energy of a photon , via the Planck relation E  =  hν , where E

1763-416: The usual definition, since the involved integrals diverge. A possible way out is to define a periodic function on a bounded but periodic domain. To this end you can use the notion of a quotient space : That is, each element in R / Z {\displaystyle {\mathbb {R} /\mathbb {Z} }} is an equivalence class of real numbers that share the same fractional part . Thus

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1806-482: Was adopted by the General Conference on Weights and Measures (CGPM) ( Conférence générale des poids et mesures ) in 1960, replacing the previous name for the unit, "cycles per second" (cps), along with its related multiples, primarily "kilocycles per second" (kc/s) and "megacycles per second" (Mc/s), and occasionally "kilomegacycles per second" (kMc/s). The term "cycles per second" was largely replaced by "hertz" by

1849-552: Was used as an educational tool in French schools under the Computing for All plan, where the TO7/70 could be used as a used a " nano-machine" terminal for the "Nanoréseau" educational network. Among improvements RAM was increased to 64 KB - "70" on the version name stands for 64+6 (64KB RAM + 6KB ROM). The 6809 processor was replaced by a Motorola 6809E and the color palette was extended from 8 to 16 colors. Graphics were similar to

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