Nyquist–Shannon sampling theorem

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If reached the shutter will travel down. Thereby the internal timer for the asynchronous mode Modus will be set new.

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For stationary Gaussian random signals, this lower bound is usually attained at a sub-Nyquist sampling rate, indicating that sub-Nyquist sampling is optimal for this signal model under optimal quantization. The sampling theorem was implied by the work of Harry Nyquist in , [9] in which he showed that up to 2 B independent pulse samples could be sent through a system of bandwidth B ; but he did not explicitly consider the problem of sampling and reconstruction of continuous signals.

About the same time, Karl Küpfmüller showed a similar result [10] and discussed the sinc-function impulse response of a band-limiting filter, via its integral, the step-response sine integral ; this bandlimiting and reconstruction filter that is so central to the sampling theorem is sometimes referred to as a Küpfmüller filter but seldom so in English.

The sampling theorem, essentially a dual of Nyquist's result, was proved by Claude E. Kotelnikov published similar results in , [11] as did the mathematician E. Whittaker in , [12] J. Whittaker in , [13] and Gabor in "Theory of communication". In , the Eduard Rhein Foundation awarded Kotelnikov their Basic Research Award "for the first theoretically exact formulation of the sampling theorem".

In and , Claude E. Shannon published the two revolutionary articles in which he founded the information theory. Let f t contain no frequencies over W. Others who have independently discovered or played roles in the development of the sampling theorem have been discussed in several historical articles, for example, by Jerri [16] and by Lüke.

Raabe, an assistant to Küpfmüller, proved the theorem in his Ph. Meijering [18] mentions several other discoverers and names in a paragraph and pair of footnotes:.

As pointed out by Higgins [], the sampling theorem should really be considered in two parts, as done above: Both parts of the sampling theorem were given in a somewhat different form by J.

Whittaker [, , ] and before him also by Ogura [, ]. They were probably not aware of the fact that the first part of the theorem had been stated as early as by Borel [25]. However, he appears not to have made the link []. In later years it became known that the sampling theorem had been presented before Shannon to the Russian communication community by Kotel'nikov [].

In more implicit, verbal form, it had also been described in the German literature by Raabe []. Several authors [33, ] have mentioned that Someya [] introduced the theorem in the Japanese literature parallel to Shannon.

In the English literature, Weston [] introduced it independently of Shannon around the same time. However, the paper of Cauchy does not contain such a statement, as has been pointed out by Higgins []. To avoid confusion, perhaps the best thing to do is to refer to it as the sampling theorem, "rather than trying to find a title that does justice to all claimants" [].

Exactly how, when, or why Harry Nyquist had his name attached to the sampling theorem remains obscure. The term Nyquist Sampling Theorem capitalized thus appeared as early as in a book from his former employer, Bell Labs , [19] and appeared again in , [20] and not capitalized in In , Blackman and Tukey cited Nyquist's article as a reference for the sampling theorem of information theory , [23] even though that article does not treat sampling and reconstruction of continuous signals as others did.

Their glossary of terms includes these entries:. This explains Nyquist's name on the critical interval, but not on the theorem. Similarly, Nyquist's name was attached to Nyquist rate in by Harold S.

According to the OED , this may be the origin of the term Nyquist rate. In Black's usage, it is not a sampling rate, but a signaling rate. From Wikipedia, the free encyclopedia. Redirected from Sampling theorem. Proceedings of the Institute of Radio Engineers. Reprint as classic paper in: Nonuniform Sampling, Theory and Practice. Universal minimum-rate sampling and spectrum-blind reconstruction for multiband signals. Compressed Sensing for Analog Signals". Elektrische Nachrichtentechnik in German.

Bell System Technical Journal. Proceedings of the IEEE. Archived from the original on A tutorial review " ". Transmission Systems for Communications.

Theory of Linear Physical Systems. Theory of Signal Detectability: Composite Deferred Decision Theory. The Measurement of Power Spectra: Die Chemorezeptoren bestehen nicht wie die Paccinischen Körperchen aus einer spezialisierten Nervenendigung, sondern aus einer Sinneszelle, die mit einer Nervenzelle in Verbindung steht.

Die Sinneszellen sind mehr oder weniger auf verschiedene Geschmackszellen spezialisiert:. Durch Kombination dieser vier Grundqualitäten können weitere Geschmacksrichtungen hervorgerufen werden vgl. Wegen ihrer vielfältigen und unerlässlichen Funktionen wäre Leben ohne Lipide nicht möglich.

Viele Elemente kommen in lebenden Zellen in derart geringen Konzentrationen vor, dass es mit den früher Bei ausgeglichener Ernährung bleibt das Körpergewicht konstant. Es wird genau soviel Nahrung Vitamine sind Verbindugnen, die in geringen Konzentrationen für die Aufrec hterhaltung von Stoffwechselfunktionen Vom menschlichen Organismus werden in Form von Gallensäuren täglich etwa 1 g Cholesterin Im Rahmen der speziellen Zytologie Cytologie werden die Elemente besprochen, aus denen Zellen bestehen Gemeinsam mit anorganischem Phosphat stellt Calcium den anorganischen Anteil des Knochens sowie Im Ohr sind Gleichgewichts- und Gehörorgan zum Organum vestibulocochleare zusammengefasst Die Entwicklung vielzelliger Lebewesen aus dem Zusammenschluss von Einzelzellen ist ein ungeheurer Fortschritt Das erste Stadium eines werdenden Menschen befindet sich im Uterus, der Gebärmutter Der weitaus grösste Teil der Energie- gewinnung des Organismus erfolgt innerhalb der Mitochondrien durch Channels should be defined for all multi-channel devices.

Channel entities cannot be defined if the hosting device does not exist Note: FHEM mappes channel 1 to the device if it is not defined explicitely. Therefore it does not need to be defined for single channel devices. An example for a full definition of a 2 channel switch is given below: This device is defined prior to channels to be able to setup references.

LivingroomMainLight is channel 01 dealing with status of light, channel peers and channel assotiated register. If not defined channel 01 is covered by the device entity. LivingRoomBackLight is the second 'channel', channel Its definition is mandatory to operate this function. HM threats each button of remotes, push buttons and similar as channels. It is possible not necessary to define a channel per button.

If all channels are defined access to pairing informatin is possible as well as access to channel related register. Furthermore names make the traces better readable. Usually you issue a hmPairForSec and press the corresponding button on the device to be paired, or issue a hmPairSerial set command if the device is a receiver and you know its serial number.

Autocreate will then create a fhem device and set all necessary attributes. Without pairing the device will not accept messages from fhem. If you cannot use autocreate, then you have to specify: You may detect it by inspecting the fhem log. Currently supported device families: Device messages can only be interpreted correctly if the device type is known.

As an alternative, set the correct subType and model attributes, for a list of possible subType values see "attr hmdevice? The so called "AES-Encryption" is in reality a signing request: Reaction to commands is noticably slower, as 3 messages are sent instead of one before the action is processed by the actor. Every command and its final ack from the device is sent in clear, so an outside observer will know the status of each device.

The firmware implementation is buggy: The HMLAN configurator will answer signing requests by itself, and if it is configured with the 3-byte address of a foreign CCU which is still configurerd with the default password, it is able to answer signing requests correctly. When using a CUL, the perl-module Crypt:: Rijndael needs to be installed. Due to the issues above I do not recommend using Homematic encryption at all. Universal commands available to most hm devices: The old key is determined by the reading aesKeyNbr, which specifies the index of the old key when the reading is divided by 2.

Any new reading will be added usual. May be used to eliminate old data register: This has NO impact to the values in the device. Also commandstack will be cleared. Executed on a channel it will read pair Inforamtion, List0, List1 and List3 of the 1st internal peer.

Furthermore the peerlist will be retrieved for teh given channel. If executed on a device the command will get the above info or all assotated channels. Not included will be the configuration for additional peers. The command is a shortcut for a selection of other commands. Description of the registers is beyond the scope of this documentation. Registers are structured in so called lists each containing a set of registers. CUL-pairing or dimmer thermal limit settings. This is a lot of data!. It controlls actions taken upon receive of a trigger from the peer.

It is mendatory for List 3 and 4 and can be left out for List 0 and 1. If List1 is requested on a device rather then a channel the command will retrieve List1 for all channels assotiated. It may be necessary to refresh the web interface manually to view the results Note4: Nevertheless those are implemented as links as well.

Inhibit can be executed on any actor channel but obviously not on sensors - would not make any sense. Practically it can be used to suspend any notifies as well as peered channel action temporarily without the need to delete them. Block operation set keymatic inhibit on pair Pair the device with a known serialNumber e. If paired, devices will report status information to FHEM. If not paired, the device won't respond to some requests, and certain status information is also not reported. Paring is on device level.

Channels cannot be paired to central separate from the device. See also getPair and unpair. Don't confuse pair to a central with peer channel to channel with peerChan. All peers in the list will be added. As peers are not added in pairs default will be as defined for 'single' by HM for this device. More suffisticated funktionality is provided by peerChan.

Other already installed peers will not be touched. Main purpose of this command is to re-store data to a device. It is recommended to restore register configuration utilising regBulk subsequent. This command will replace the former regRaw. It allows to set register in raw format. Its main purpose is to restore a complete register list to values secured before. Values may be read by getConfig. The resulting readings can be used directly for this command. The peer can be given as channel name or the 4 byte 8 chars HM channel ID.

Only a subset of register can be supproted. Optional parameter [prep exec] allowes to pack the messages and therefore greatly improve data transmission. Usage is to send the commands with paramenter "prep". The data will be accumulated for send. The last command must have the parameter "exec" in order to transmitt the information.

It can be set to '0' other wise. See getRegRaw for full description Supported register for a device can be explored using set regSet?

You need to pair it again to use it with fhem. Rijndael to be able to switch it or deactivate signing from fhem. For multichannel devices it should be issued on an per channel base unpair "Unpair" the device, i. See pair for description. Then number of button being added is 1 to If the command is issued a second time for the same entity additional buttons will be added.

User must provide the appropriate file. In case the device needs to be set to FW update mode manually this is the time the system will wait. It may to be programmed thru channel register. Typically sensor do not send long events. Those are autocrated if applicable. Usually there are 2 virtual channels in addition to the primary channel.

Virtual dimmer channels are inactive by default but can be used in in parallel to the primay channel to control light. Documentation and capabilities for virtual channels is out of scope. Optional for dimmer on-time and ramp time can be choosen, both in seconds with 0.

On-time is analog "on-for-timer". Ramp-time default is 2. Optional ontime and ramptime could be given for dimmer. It may also be entered as end-time in format hh: It is meaningful only for dimmer.

FHEM obeys this behavior by stacking all requests until learn mode is detected. Manual interaction of the user is necessary to activate learn mode. Whether commands are pending is reported on device level with parameter 'protCmdPend'. If all is selected each of the peers will be triggered. An IO device according to eQ3 supports up to 50 virtual buttons. Peering must not be confused with pairing. Pairing refers to assign a device to the central.

Peering refers to virtally connect two channels. Peering allowes direkt interaction between sender and aktor without the necessity of a CCU Peering a sender-channel causes the sender to expect an ack from -each- of its peers after sending a trigger. It will give positive feedback e. LED green only if all peers acknowledged. Peering an aktor-channel will setup a parameter set which defines the action to be taken once a trigger from -this- peer arrived. In other words an aktor will - process trigger from peers only - define the action to be taken dedicated for each peer's trigger An actor channel will setup a default action upon peering - which is actor dependant.

It may also depend whether one or 2 buttons are peered in one command. A swich may setup oen button for 'on' and the other for 'off' if 2 button are peered. If only one button is peered the funktion will likely be 'toggle'. The funtion can be modified by programming the register aktor dependant. Even though the command is executed on a remote or push-button it will as well take effect on the actuator directly.

Both sides' peering is virtually independant and has different impact on sender and receiver side. Peering of one actuator-channel to multiple sender-channel as well as one sender-channel to multiple Actuator-channel is possible.

If 'single' is choosen buttons are counted from 1. It needs to be set, should be 0 [single dual]: With a dimmer this means one button for dim-up and one for dim-down. It is useful for e. Nevertheless also dimmer can be learned to only one button. This gives the user the option to redo the peering on the remote channel while the settings in the actor will not be removed. Defaults to self channelNo. How long shall the button be pressed?

Number of repetition of the messages is defined. If peered to a device it periodically sends the temperature until "off" is given. If peered to a device it periodically sends the temperature and humidity until both are "off". All these commands work right now only if you have more then one smoekDetector, and you peered them to form a group.

For issuing the commands you have to use the master of this group, and currently you have to guess which of the detectors is the master. You need to peer all team-members to the master. Don't forget to also peerChan the master itself to the team - i. To this purpose issue this set command first or a number of them , and then choose from the teach-in menu of the 4Dis the "Central" to transmit the data.

Up to 24 intervals can be specified for each week day, the resolution is 10 Minutes. The last time spec must always be The tempList for one or more devices can be stored in a file. User can compare the tempList in the file with the data read from the device.

Restore will write the tempList to the device. Default opeartion is verify. Default file is tempList. Default templateName is the name of the actor Default for file and templateName can be set with attribut tempListTmpl Example for templist file.

Implicitely teh weekplan of TC will be used. Possible parameter will be set to the current register value of the device - i. Parameter may be changed after assigning the template by using the tplPara command. The command is avalilable if HMinfo is defined and a tamplate fitting the combination is available.

Note that the register of the device need to be available see getConfig command. In case of dedicated template for long and short trigger separat commands will be available. A command s available for each parameter of each assigned template.

Add the time it ends and the number of days it shall last. This is especially helpful if device is operated in wakeup mode. If the command is executed on a device it will set all LEDs to the specified color. For Expert all LEDs can be set individual by providing a 8-digit hex number to the device. A sequence of colors can be given separating the color entries by ','.

White spaces must not be used in the list. List is to be entered separated by ','. Multople symbols can be acticated at the same time, concatinating them comma separated.

Don't use spaces here. Possiblesymbols are [bulb switch window door blind scene phone bell clock arrowUp arrowDown] Example: Symbols scene,phone,bell and clock are active. If this is set the 3 parameter of a line can be adapted. The text is assotiated with the text defined for the buttons. Alternaly a free text of up to 12 char can be used color is one white, red, orange, yellow, green, blue icon is one off, on, open, closed, error, ok, noIcon Example: If help is given a help on the command is given.

Options for all parameter will be given. If empty the value as per reading will be transmittet - i. When set attr chan param reWriteDisplayxx the 3 lines will be rewritten to the latest value after xx seconds.

Sets the delay in seconds after the lock automatically locked again. Up to 36entries can be applied. The repeater can handle up to 36 entries. Data will be taken from attribut repPeers. Reading repPeer is formated: Number src dst broadcast verify number: Only needed for experimentation. The first command will be immediately sent, the next one after the previous one is acked by the target. Data is stored in a format to be executed from fhem command prompt.

The file is located in the fhem home directory aside of fhem. Data will be stored cumulative - i. It is up to the user to avoid duplicate storage of the same entity. Explicitely this is the peer-list and the register.

With the register also the peering is included. The file is readable and editable by the user. Additionaly timestamps are stored to help user to validate. It is up to the user to read the data from the HM-hardware prior to execution. See recommended flow below. This command will not store any FHEM attributes o device definitions. This continues to remain in fhem.

Furthermore the secured data will not automatically be reloaded to the HM-hardware. It is up to the user to perform a restore. As with other commands also 'configSave' is best executed on a device rather then on a channel. If executed on a device also the assotiated channel data will be secured. Recommended work-order for device 'HMdev': The data is taken from the storage in FHEM and not read directly outof the device.

If register content is not present please use getConfig, getReg in advance. Registername can be used alternaly if decoded by FHEM. If rgistername is used list is ignored and can be set to 0. It an be set to dummy if not used. It does the same as reg but strips off units regList returns a list of register that are decoded by FHEM for this device. Note that there could be more register implemented for a device.

Stored will be the data as available in fhem. It is necessary to read the information from the device prior to the save. The command supports device-level action. Storage to the file will be cumulative. If an entity is stored multiple times to the same file data will be appended. User can identify time of storage in the file if necessary.

Content of the file can be used to restore device configuration. It will restore all peers and all register to the entity. The attribute is applicable for devices only. It will modify the readings upon entering dead of the device. Upon leaving state 'dead' the selected readings will be set to 'notDead'. It is expected that useful values will be filled by the normally operating device. Other valvues will be ignored state: Periodic numerical readings will be set to 0 which influences graphics attr myDevice readingOnDead state,channels reading state of the device and all its channels will be set to 'dead'.

The attribut may be useful in case a device is being checked that does not send messages regularely - e. This actiondetect will be autocreated for each device with build in cyclic status report.

Due to performance considerations the report latency is set to sec 10min. It can be controlled by the attribute "actCycle" of "ActionDetector". Once entered to the supervision the HM device has 2 attributes: This function can be enabled for devices with non-cyclic messages as well. It is up to the user to enter a reasonable cycletime. Therefore the update of the readings and the display will be delayed depending on the size of the database.

Recommendations and constrains upon usage: Do not use it separate on each channel of a multi-channel device to avoid duplicate execution usage on devices which only react to 'config' mode is not recommended since executen will not start until config is triggered by the user usage on devices which support wakeup-mode is usefull. But consider that execution is delayed until the device "wakes up".

User does not need to wait for the device to wake up. Note that also the register burstRx needs to be set in the device. This attibute controls the presentation of device parameter in the readings.

It can be overruled if expert attibute is also applied to the channel device. Make sure to check out attribut showInternalValues in the global values as well. Nevertheless - by definition - showInternalValues overrules expert. IOgrp can be given to devices and shall point to a virtual CCU. Optional a prefered IO - perfIO can be given. In case this IO is operational it will be selected regardless of rssi values.

It defines the dimmable range to be used with this dimmer-channel. It is meant to support e. Impacted are commands on, up, down, toggle and pct. This simply results from the calculation and reflects physical level is above or below the given range. In case of virtual dimmer channels available present the attribut needs to be set for each channel User should be careful to set min level other then '0' Example: Doing that it converts the device and its channel to the new model.

Reason for this attribute is an eQ3 bug as some devices are delivered with wrong Module IDs. They are not supposed to be set by hand, and are necessary in order to correctly interpret device messages or to be able to send them. Devices which donly support config mode no repeat ist allowed. For devices with wakeup mode the device will wait for next wakeup. Lonng delay might be considered in this case.

See available parameter for details rawToReadable Used to convert raw KFM values to readable data, based on measured values. If switched '1' each RSSI entry will be written to a reading. User may use this to log and generate a graph of RSSI level. If not given the detault template is taken from file tempList.

So adjusting this might fix problems for example when weather messages of virtual devices are not received reliably available parameter for attribut "param" HM-Sen-RD-O offAtPon heat channel only: If this parameter is not given the entity will toggle its state between On and Off with each trigger msgReduce: Numbers from 0 no skip up to 9 can be given.

This will apply to readings and set commands. It does not apply to any register. This results eventually in state on-till which allowes better icon handling. This event relies on complete reading of channels configuration, otherwise Data can be incomplete or incorrect. Begin of previous Rain - timestamp of the reading is the end of rain.

As the structure of this signal is not understood, no checksum is verified, so it is likely to receive bogus messages. Your definition should look like E. Any received IR-Code will be stored as a Button attribute for this devices. The name of these attributes is dependent on the two attributes learncount and learnprefix. The IR-command can be specified as buttonname according to Button.

If a buttonname is specified, the corresponding IR-Code will be sent out. Flags between E will produce IR-Repetitions. You can type the IR-Code as plain as above, or with a heading "I" as learnt for the buttons. ON Switching on the reception of IR signals. This is not recommended as many remote controls do repeat their signals. This is the recommended modus operandi. IR-Codes are learnt as Button-Attributes. The name for a learnt Button - IR-Code is compiled out of three elements: This is done according to the following syntax: Button IA Button IA To make sure that something happens when this IR-code is received later on one has to modify the attribute and to add commands as attribute values.

This is done by defining group-attributes that contain only parts of the IR-Code. By manually modifying this attribute new button sequences can be arranged. A button-attribute-name is constructed by: It will be automatically created by autocreate, just make sure that you set the right rfmode like attr CUL0 rfmode MAX.

The rf address must not be in use by any other MAX device. You also have to set the other device into pairing mode manually. For Thermostats, this is pressing the "Boost" button for 3 seconds, for example. Make sure you associate the target device s with fakeShutterContact beforehand.

Make sure you associate the target device with fakeWallThermostat beforehand. In theory every SlowRF protocol should work, as the hook is implemented in the culfw output routine: There are still some restrictions: Since there is no ack or a resend mechanism, it should be primarily used to forward "unimportant" data, it was developed for forwading KS packets.

As the configured base id is not 00, it will activate RF reception on boot, and will start sending messages to the base CUL.

Now you have to define this RFR cul as a fhem device: Both parameters have two characters, each representing a one byte hex number. Get Same as for the CUL. Define The received devices created automatically. The ID of the defive are the first two Hex values of the package as dezimal. The humidity if available battery: The Channelnumber if available trend: The temperature trend if available israining: Statement rain between two measurements if available rain: The rain value, a consecutive number until the battery is changed if available winddir: The current wind direction windgrad: The current wind direction in degrees windspeed: The current wind speed windgust: It is important, however, that a device is only received by the defined IO Device, e.

Valid values are 1 through 8. It is important, however, that a device is only received by the CUL defined, e.

Currently the CUL is supported with its versions: If the fhem-device is none, than the inserted device must already be in the flash-mode.

Box image from fhem. A calendar device periodically gathers calendar events from the source calendar at the given URL or from a file. The file must be in ICal format. If the URL starts with https: SSL must be installed use cpan -i IO:: Note for users of Google Calendar: SSL is not installed on your system, you can replace it by http: Check with your browser first if unsure.

Note for users of Netxtcloud Calendar: The optional parameter interval is the time between subsequent updates in seconds. It defaults to 1 hour. The next automatic retrieval is scheduled to occur interval seconds later. You can give none, one or several of the format , timeFormat , filter , series and limit parameters and it makes even sense to give the filter parameter several times.

The format parameter determines the overall formatting of the calendar event. The following format specifications are available: If the format parameter is omitted, the custom format string from the defaultFormat attribute is used. The last occurance wins if the format parameter is given several times. The web page strftime. If the timeFormat parameter is omitted, the time format specification from the defaultTimeFormat attribute is used.

Single quotes ' or double quotes " can be used to enclose the format specification. The last occurance wins if the parameter is given several times. All filters must apply for a calendar event to be displayed. The parameter is cumulative: Single quotes ' can be used instead. This applies per series. To limit the total amount of events displayed see the limit parameter below. The limit parameter limits the number of events displayed.

Only properties that have been kept during processing of the source are shown. The list of calendar events created from each VEVENT entry is shown as well as the list of calendar events that have been omitted. The specification is explained there. The time is specified relative to the current time t.

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