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Showing papers on "Keying published in 1988"


Journal ArticleDOI
TL;DR: It is shown that for large signal-to-noise ratio, the asymptotic distribution of the phase is of the Tikhonov type and this framework is then used for the synthesis of differentially coherent receiver structures, one for M-ary phase-shift keying (MPSK) and the other for minimum-shiftkeying (MSK).
Abstract: Some results are presented regarding the asymptotic distribution of the phase of a vector perturbed by Gaussian noise. It is shown that for large signal-to-noise ratio, the asymptotic distribution of the phase is of the Tikhonov type. This framework is then used for the synthesis of differentially coherent receiver structures, one for M-ary phase-shift keying (MPSK) and the other for minimum-shift keying (MSK). The first structure bridges the performance gap between coherent and differentially coherent demodulation of MPSK. The MSK receiver uses matched filtering with differential demodulation. >

161 citations


Journal ArticleDOI
TL;DR: The performance of a trellis-coded multilevel differential phase-shift keying (DPSK) modulation over a mobile satellite channel characterized by additive white Gaussian noise (AWGN) and slow Rician fading is presented.
Abstract: The performance of a trellis-coded multilevel differential phase-shift keying (DPSK) modulation over a mobile satellite channel characterized by additive white Gaussian noise (AWGN) and slow Rician fading is presented. Both the optimum and Gaussian (suboptimum) decoding metrics are considered, with performance results given only for the latter. Analytical results (upper bounds on bit error rate) are obtained wherever possible and illustrated by several numerical examples. Also given are simulation results which are more indicative of the exact system performance. Comparisons with results previously obtained for coherent detection of the same coded modulations are presented. >

99 citations


Journal ArticleDOI
TL;DR: In this article, the error rates and sensitivity penalties for multichannel coherent optical communications systems are evaluated for amplitude-shift keying (ASK), phase-shift-keying (PSK), and frequency-shift kening (FSK) modulation, taking into account adjacent channel interference.
Abstract: The error rates and sensitivity penalties for multichannel coherent optical communications systems are evaluated for amplitude-shift keying (ASK), phase-shift keying (PSK), and frequency-shift keying (FSK) modulation, taking into account adjacent channel interference. Both time-domain and frequency-domain analysis are used, the latter being based on a Gaussian approximation. Both techniques yield similar results for sensitivity penalties below 1 dB. For FSK systems, larger values of the modulation index Delta do not necessarily lead to larger channel spacings. ASK and PSK systems both require larger channel spacings than FSK systems with Delta =1. The study was conducted for sources with linewidths narrow enough so that phase noise does not degrade the performance of receivers with matched filter demodulators. >

66 citations


Patent
18 Feb 1988
TL;DR: A data locking system which modifies data in accordance with a renewable key variable derived from the exclusive ORing of a pseudorandom combination number from an external source means with an altered key variable as discussed by the authors.
Abstract: A data locking system which modifies data in accordance with a renewable key variable derived from the exclusive ORing of a pseudorandom combination number from an external source means with an altered key variable.

65 citations


Journal ArticleDOI
TL;DR: M-ary phase-shift keying and differential phase- shift keying (DPSK) on a slow fading Rayleigh channel without diversity is investigated and expressions for the distribution of the phase angle are obtained.
Abstract: M-ary phase-shift keying and differential phase-shift keying (DPSK) on a slow fading Rayleigh channel without diversity is investigated. Expressions for the distribution of the phase angle between a vector with Rayleigh amplitude distribution and a noiseless reference, and between two vectors both with Rayleigh amplitude distribution perturbed by Gaussian noise are obtained. >

52 citations


Journal ArticleDOI
TL;DR: The primary finding was that keypads with square keys resulted in improved speed and a higher degree of accuracy than do keypad with regular keys (either a long horizontal dimension or a longer vertical dimension).
Abstract: This paper reports on a study comparing keying accuracy and speed for eight different numeric keypad configurations on a touch screen. Using touch-sensitive keypads displayed on a computer terminal, operators entered numbers presented to them through a speech synthesizer. Dependent measures collected were keying rates, errors, and the x- and y-dimension standard deviations from the centre point of the key. The primary finding was that keypads with square keys resulted in improved speed and a higher degree of accuracy than do keypads with regular keys (either a long horizontal dimension or a longer vertical dimension). Spread-out versions of the keypads (inter-key spacing = 1·3 cm) did not yield superior performance compared with compressed versions (inter-key spacing = 0·6 cm).

43 citations


Patent
11 Apr 1988
TL;DR: An electrical keying system for a set of incompatible module pairs to prevent powerup of an electrically incompatible module pair in a set was proposed in this paper, where the power-up of the pair was prevented.
Abstract: An electrical keying system for a set of incompatible module pairs to prevent powerup of an electrically incompatible module pair in a set.

30 citations


Patent
29 Apr 1988
TL;DR: A keying system for connector assemblies is defined in this paper, where individual keying means 30,31,32,33 of one of the connector assemblies 8 directly opposing individual keaying means 10,11,12,13 of the other.
Abstract: A keying system 9 for connector assemblies 1,8 comprises, individual keying means 30,31,32,33 of one of the connector assemblies 8 directly opposing individual keying means 10,11,12,13 of the connector assembly 1, either one of the other of said directly opposing individual keying means 30,10; 31,11; 32,12; 33,13 is removed, and a vacancy remaining from a removed individual keying means is occupied with the nonremoved individual keying means upon orientation of the connector assemblies 1,8 in corresponding predeterminate positions with respect to each other.

28 citations


Proceedings ArticleDOI
23 May 1988
TL;DR: A novel feature, useful for the identification of the number of phase states of BPSK and QPSK signals, is seen to provide adequate information identification at SNRs down to 5 dB.
Abstract: The performance of an adaptive technique for the generation of decision functions used in classification of several types of digitally modulated signals-binary amplitude-shift keying (BASK), binary phase-shift keying (BPSK), quaternary phase-shift keying (QPSK), and binary frequency-shift keying (BFSK)-is discussed. A computer simulation is performed to measure the properties of the classifier which is trained with one signal from each class. The method correctly identifies all the signals considered during this experiment. The most interesting result from a small number of trials is considered to be that a novel feature, useful for the identification of the number of phase states of BPSK and QPSK signals, is seen to provide adequate information identification at SNRs down to 5 dB. This feature is the existence of narrowband energy near M times the carrier frequency for M-ary PSK signals. >

26 citations


Journal ArticleDOI
TL;DR: A lower bound on the minimum free Euclidean distance of trellis-coded modulation (TCM) is derived that guarantees the existence of good TCM codes of any complexity and predicts the asymptotic performance of TCM when the complexity of the code becomes large.
Abstract: A lower bound on the minimum free Euclidean distance of trellis-coded modulation (TCM) is derived that guarantees the existence of good TCM codes of any complexity The bound is used to compare trellis codes combined with phase-shift keying, pulse amplitude modulation, and quadratic amplitude-shift keying modulation This random coding bound is the first lower bound on the free distance of trellis codes, is tighter than any upper bound for large constraint lengths, and predicts the asymptotic performance of TCM when the complexity of the code becomes large The bound can be used with any code rate and any modulation scheme and shows that the free distance increases linearly with the constraint length for large values of the constraint length >

17 citations


Proceedings ArticleDOI
J.D. Provence1
07 Jun 1988
TL;DR: An artificial neural network is described for the detection of digital data symbols transmitted over a time-dispersive time-varying channel in the presence of Gaussian noise and results show promising error rates over a wide range of intersymbol-interference durations.
Abstract: An artificial neural network is described for the detection of digital data symbols transmitted over a time-dispersive time-varying channel in the presence of Gaussian noise. The transmitter uses quadrature phase-shift keying modulation. The network computes a maximum-likelihood estimate of the transmitted sequence. Mapping of the maximum-likelihood sequence estimation function onto the artificial neural network structure is described. A neural-network-based receiver structure is presented which can be used for stationary or time-varying channels. Simulation results are presented which show promising error rates over a wide range of intersymbol-interference durations. Unlike the Viterbi algorithm implementation, the neural network does not require a vast amount of memory for storage and the computation time does not increase with increasing channel memory. >

Proceedings ArticleDOI
12 Jun 1988
TL;DR: It is found that coherent detection is superior to differential detection by at least 2.4 dB, which converts to about 30% improvement of spectral efficiency in a two-dimensional frequency reuse system with a fourth-power propagation exponent.
Abstract: The advantage of coherent detection over differential detection for both BPSK (binary phase-shift keying), and QPSK (quaternary phase-shift keying) in a multipath radio channel with either frequency-flat or frequency-selective fading is evaluated. The difference in receiver sensitivity is compared on the basis of three criteria: (1) bit-error rate (VER) averaged over fading samples, (2) BER distribution, and (3) distribution of block error rate. For a quasistatic fading channel, (2) and (3) provide a more meaningful comparison. Both analytical expressions and simulation are used in the comparison. The difference between differential detection of 2- and 4-level PSK is taken into consideration, as is the difference between pure coherent detection and coherent detection that uses differential encoding to resolve phase ambiguity. Both selection diversity and channel coding are considered as techniques for mitigating fading effects. It is found that coherent detection is superior to differential detection by at least 2.4 dB, which converts to about 30% improvement of spectral efficiency in a two-dimensional frequency reuse system with a fourth-power propagation exponent. >


Journal ArticleDOI
TL;DR: The performance of continuous-phase FSK (frequency-shift keying) systems with rectangular modulation pulse shaping and limiter-discriminator detection is analyzed in the presence of transmission nonlinearities as well as adjacent channel and cochannel interference.
Abstract: The performance of continuous-phase FSK (frequency-shift keying) systems with rectangular modulation pulse shaping and limiter-discriminator detection is analytically evaluated in the presence of transmission nonlinearities as well as adjacent channel and cochannel interference. Consideration of modulation pulses with length tau , shorter than symbol time, T, is investigated. The algorithm developed to evaluate bit-error probability shows that the choice tau /T=1, and even more so in the presence of adjacent channel interference. Moreover, for tau /T=0.5, numerical results are reported that describe system performance under different working conditions and can be used to develop design criteria. >

Patent
04 Oct 1988
TL;DR: In this article, the history of the manual input of an operator from an input means 20 is stored in a storage means 30 when a system 10 is started, and an output means 60 gives the advice to the operator.
Abstract: PURPOSE: To improve learning effect and operation efficiency by storing the history of the keying of an operator and outputting an advice in response to the keying history. CONSTITUTION: The history of the manual input of the operator from an input means 20 is stored in a storage means 30 when a system 10 is started. An inference means 50 refers the keying history of the storage means 30 and a knowledge base 40, and generates the advice advising an efficient operation method for the inefficient operation of the operator. An output means 60 gives the advice to the operator. Namely, the operator does not request information on the operation method, but the output means 60 performs inference from the history of the manual input of the operator and gives the advice to the operator according to need. Thus, the operator can obtain the high learning effect and the operational efficiency of the system can be improved. COPYRIGHT: (C)1990,JPO&Japio

Journal ArticleDOI
TL;DR: Bit-error-rate analysis (BER) analysis of binary DPSK (differential phase-shift keying) data modulation used in conjunction with direct-sequence spread-spectrum is used as a performance measure.
Abstract: The impact of imperfect synchronization on the performance of prediction-error interference rejection filters in noncoherent direct-sequence (DS) spread-spectrum communications is considered. Bit-error-rate analysis (BER) analysis (BER) of binary DPSK (differential phase-shift keying) data modulation used in conjunction with direct-sequence spread-spectrum is used as a performance measure. A first-order noncoherent delay-lock loop is used for the pseudonoise (PN) code tracking. Conditional BER results for the DS/DPSK systems for fixed values of the code tracking error are obtained. The average BER of the system is then evaluated by averaging the conditional BER expressions over the probability density function of the code tracking error. Results include the effects of both a single fading tone and a narrowband Gaussian interferer on the overall system performance. Interferer offset frequency is considered in determining the code tracking loop noise as well as the receiver BER. >

Journal ArticleDOI
TL;DR: Simulation studies indicate that improvements of about 2 dB can be obtained in the coded performance with the proposed adaptive rate system, when compared to a nonadaptive system operating over the same communication medium with identical power and bandwidth resources.
Abstract: The authors present a feedback rate control technique for FH/BFSK (frequency-hop/binary phase-shift keying) signaling over a jammed flat-flat fading channel. An algorithm is developed for tracking the channel fade level, dynamically adjusting the transmitted data rate, and mitigating the effects of partial-band noise jamming. Simulation studies indicate that improvements of about 2 dB can be obtained in the coded performance with the proposed adaptive rate system, when compared to a nonadaptive system operating over the same communication medium with identical power and bandwidth resources. >

Journal ArticleDOI
TL;DR: It is shown that the structure of block codes, when used in conjunction with on-off keying signaling, renders these codes fairly inefficient with respect to obtaining reasonable CMG on the optical channel, and the authors propose using pulse-position modulation with more than one pulse per word to obtain reasonableCMG while consuming small amounts of bandwidth.
Abstract: Coding for avalanche photodiode (APD)-based direct-detection optical channels is investigated using a simple channel model that clearly points out the difference between the signal-dependent optical noise channel model and additive white Gaussian noise channel model. Coding and modulation are viewed as a single entity and the coding/modulation gain (CMG) is used to analyze and construct good codes for APD-based optical receivers. It is shown that the structure of block codes, when used in conjunction with on-off keying signaling, renders these codes fairly inefficient with respect to obtaining reasonable CMG on the optical channel. In contrast, codes (or modulations) that use fewer channel ones (pulses) than information ones per block can offer substantial CMG on the optical channel. For bandwidth-constrained applications, the authors propose using pulse-position modulation with more than one pulse per word to obtain reasonable CMG while consuming small amounts of bandwidth. >

Proceedings ArticleDOI
23 Oct 1988
TL;DR: The author presents the uncoded and coded performance results of MFSK and DPSK on a generalized fading-channel model, the slow nonselective Nakagami-m fading channel, and it is shown that the effective diversity of the system is in the product of two parameters.
Abstract: The author presents the uncoded and coded performance results of MFSK (M-ary frequency-shift keying) and DPSK (differentially coherent binary phase-shift keying) on a generalized fading-channel model, the slow nonselective Nakagami-m fading channel. Simple expressions are given for asymptotic slopes of probability of bit error for a large signal-to-noise ratio, and it is shown that the effective diversity of the system is in the product of two parameters, one for the code and one for the channel. It is concluded that the results obtained are potentially useful in the performance assessment of several current MFSK and DPSK systems that are required to operate on channels with a wide variety of fading or scintillation conditions. >

Proceedings ArticleDOI
12 Jun 1988
TL;DR: It was found that over a channel with flat slow Rayleigh fading, an 8-PSK (phase modulation keying) coded-modulation technique achieves almost the same diversity gain as a system studied earlier that used rate-2/3 code with 4- PSK modulation.
Abstract: The performance of non-frequency-selective (flat) slow Rayleigh fading channels has been studied for bandlimited channels using a technique similar to trellis coded modulation, using a similar technique. A group of very simple block codes is used. Coding is used to implement diversity selection. It was found that over a channel with flat slow Rayleigh fading, an 8-PSK (phase modulation keying) coded-modulation technique achieves almost the same diversity gain (at least 15 dB at 10/sup -3/ word error rate) as a system studied earlier that used rate-2/3 code with 4-PSK modulation. However, the former is without bandwidth expansion, while the latter entails 50% bandwidth expansion. >

Patent
29 Sep 1988
TL;DR: In this article, a cyclic-keyed circuit for a danger-indicating installation with several indicators (4, 5) is presented, where each indicator is connected across a two-wire indicating line (2, 3) to a central means having evaluation electronics (20) and associates the signals supplied by indicators with clearly defined states on the indicators.
Abstract: of EP01582171. Circuit arrangement for a danger-indicating installation with several indicators (4, 5), which are connected across a two-wire indicating line (2, 3) to a central means having evaluation electronics (20) and which associates the signals supplied by indicators (4, 5) with clearly defined states on the indicators, with a signal level applied to the indicators by the evaluation electronics (20) via indicating line (2, 3) and which is cyclicly keyed, with in each case one counter (43) providing in the indicators (4, 5) and which counts the logic states corresponding to this signal level keying and in the case of identity of the count with an address value in each case preset on each indicator supplies a signal characterizing its state across indicating line (2, 3) to evaluation electronics (20), all the counters (43) being resettable by a resetting signal, characterized in that the resetting signal for the counters (43) of indicators (4, 5) is in the form of a further signal level keying and that the signal characterizing the state, e.g. alarm of fault, of the individual indicator (4, 5) is supplied as a clearly defined, but different signal level to evaluation electronics (20) by the selected indicator (4, 5) within the time interval up to the selection of the next indicator.

Proceedings ArticleDOI
12 Jun 1988
TL;DR: It is shown through simulations that performance close to the optimal receiver can be obtained while realizing significant computational savings.
Abstract: The decoding of signals in infinite intersymbol interference caused by severe filtering is considered. A state-variable representation of a linear system is used to define the decoder tree. Tree decoding is then performed by the M-algorithm. It is shown through simulations that performance close to the optimal receiver can be obtained while realizing significant computational savings. Binary phase-shift keying with rectangular baseband pulse shaping and continuous phase/frequency-shift-keyed signals are considered. The channel is modeled as a narrowband filter with two and four-pole Butterworth spectra with symbol-rate normalized 3-dB bandwidths of 0.1 and 0.25. >

Proceedings ArticleDOI
12 Jun 1988
TL;DR: Fading and the near/far problem in multiuser frequency-hop spread spectrum systems are investigated and the conditional probability of a symbol error when it is hit by undesired signals is derived.
Abstract: Fading and the near/far problem in multiuser frequency-hop spread spectrum systems are investigated. The received signals from different users have different power levels due to these problem. This phenomenon makes it possible for the system to use the receiver with capture ability, i.e. the receiver can detect accurately the strongest signal, with greater possibility, when more than one signal is present at the receiver. Noncoherent multilevel frequency-shift keying modulation, Reed-Solomon coding, and asynchronous slow frequency-hop transmission are assumed. The emphasis is on deriving the conditional probability of a symbol error when it is hit by undesired signals. >

Proceedings ArticleDOI
25 Jan 1988
TL;DR: In this paper, the feasibility of a Gbit/s range QPSK system with external cavity LDs was confirmed through theoretical calculation and the simulation experiment, and the key factors, modulation method, and linewidth requirement for a QRSK coherent detection system were discussed.
Abstract: Recently, there have been several efforts to build optical heterodyne detection systems in the Gbit/s range.1–3 However, it is becoming difficult to achieve high receiver sensitivity in this range, because the heterodyne receiver requires a broad IF bandwidth. An optical quadriphase shift keying (QPSK) heterodyne system can achieve the same receiver sensitivity as the biphase shift keying (BPSK) system, requiring a half-bandwidth of the BPSK system. Therefore, the QPSK system has advantages in the Gbit/s range. The key factors, modulation method, and linewidth requirement for a QPSK coherent detection system are discussed. The feasibility of a Gbit/s range QPSK system with external cavity LDs was confirmed through theoretical calculation and the simulation experiment.

Proceedings ArticleDOI
15 Jun 1988
TL;DR: A simple interleaver at the transmitter is proposed which permits the use of multiple differential detectors at the receiver which improves the performance of the differentially detected trellis-coded PSK (phase-shift keying).
Abstract: Using multiple differential detectors improves the performance of the differentially detected trellis-coded PSK (phase-shift keying). To achieve further improvements without increasing the receiver complexity considerably, the noise correlation must be reduced. For this purpose, a simple interleaver at the transmitter is proposed which permits the use of multiple differential detectors at the receiver. >

Patent
22 Jan 1988
TL;DR: In this paper, the authors proposed to improve the rate of conversion of KANA(Japanese syllabary)- KANJI(Chinese character) conversion by comparing detected interval of keying and average interval of kying, and inserting punctuation information in a KANA index when the interval is more than specified interval.
Abstract: PURPOSE:To improve the rate of conversion of KANA(Japanese syllabary)- KANJI(Chinese character) conversion by comparing detected interval of keying and average interval of keying, and inserting punctuation information in a KANA index when the interval is more than specified interval. CONSTITUTION:Interval of keying is detected, and at the same time, average interval of keying is calculated, and detected interval of keying is compared with average interval of keying calculated by an average keying interval calculating means. Punctuation information is inserted when the interval exceeds specified interval, and KANJI converting process is made by a KANJI conversion processing means 4 basing on a KANA index to which punctuation information is inserted. Thereby, for instance, stored data of FIFO 3 [saichosairai] (reexamination require expressed in KANA) is converted to a character string [sai/chosa/irai] in an index buffer, and further converted to [SAICHOSAIRAI] (reexamination require expressed in KANJI). Thus objective KANJI writing can be obtained as the first possible though it is three clauses.

Patent
27 Jan 1988
TL;DR: In this paper, a magnetic recording apparatus comprising an audio signal processing circuit (32a, 32b, 33a, 33b, 34a, 34b, 35), a modulating circuit (36) for subjecting the digital audio signal to a modulation selected from a multi-phase differential phase shift keying modulation (DPSK) or an offset-multi-phase DPSK modulation (ODPSK), an adding circuit (39) for adding a high-frequency bias signal to the modulated digital audio signals, and audio signal recording unit (41a
Abstract: A magnetic recording apparatus comprising an audio signal processing circuit (32a, 32b, 33a, 33b, 34a, 34b, 35) for converting an input analog audio signal into a digital audio signal; a modulating circuit (36) for subjecting the digital audio signal to a modulation selected from a multi-phase differential phase shift keying modulation (DPSK) or an offset-multi-phase differential shift keying modulation (ODPSK) to produce a modulated digital audio signal; an adding circuit (39) for adding a high-frequency bias signal to the modulated digital audio signal; an audio signal recording unit (41a, 41b) for recording the modulated digital audio signal with the high-frequency bias signal added thereto on a track formed in a deep layer portion of a magnetic layer of a magnetic tape (43); and a video signal recording circuit (26, 27, 28a, 28b) for recording an input video signal on a video track formed in a surface layer portion of the magnetic layer of the magnetic tape.

Patent
03 Jun 1988
TL;DR: In this article, an average keying speed detection device is used to detect the speed of keys which are operated by an operator and output the detected result to a message level switching device.
Abstract: PURPOSE:To improve operability by obtaining proficiency degree based on a keying speed and the variance of the keying speed and executing the display of a message corresponding to the proficiency degree. CONSTITUTION:A keyboard 4 which is the input means of a word processor, etc., input desired sentences, etc., by operating its keys. The keyboard 4 is connected to an average keying speed detection device 5, which detects the speed of keys which are operated by an operator (time between a keying and a keying) so as to output the detected result to a message level switching device 7. Moreover, a keying speed variation detection device 6 is connected to the keyboard 4 and obtains how the time between respective keyings alters so as to output to the switching device 7 in the same way. And the proficiency degree is obtained from two kinds of values and data in plural stored messages is selected corresponding to the proficiency degree from a message table 8 connected to the message level switching device 7. And the data is displayed on a display 10 through a display controller 9.

01 May 1988
TL;DR: The modem architecture as well as some of the signal processing techniques employed in the modem to combat the LMS channel impairments are described, and the modem performance over the fading channel is presented.
Abstract: This paper describes the real-time digital implementation of an 8-differentiated phase-shift keying (DPSK) trellis-coded modulation (TCM) modem for operation on an L-band, 5 kHz wide, land mobile satellite (LMS) channel. The modem architecture as well as some of the signal processing techniques employed in the modem to combat the LMS channel impairments are described, and the modem performance over the fading channel is presented.

Patent
04 Mar 1988
TL;DR: In this paper, a 4-phase differential phase shift keying (DPSK) modulator, a 300 baud FSK modulator and a dual tone multi-frequency (DTMF) generator are implemented using a digital DAC.
Abstract: A circuit includes the following features: a 1200 baud 4-phase differential phase shift keying (DPSK) modulator, a 300 baud frequency shift keying (FSK) modulator, a dual tone multi-frequency (DTMF) generator, and 2100/2225 Hz answer tone generators … The DPSK modulator utilizes time-domain filtering techniques using a sequence of signals D0-D3 It includes a spectrum controller S1-S3, M7-M12 that shapes the in-band frequency spectrum and attenuates the adjacent channel frequency components to eliminate the conventional requirement of band-pass filters after the modulator The FSK modulator also utilizes a spectrum controller which, during each data transition, sends out six intermediate frequencies to smooth the frequency changeover DTMF generation is accomplished by multiplexing two sine-wave counters into a DPSK sinewave look-up ROM By varying the duty cycle of the multiplexing control signal, the DTMF generator provides a digital pre-emphasis function that boosts the amplitude of the high-band frequencies as referenced to the low-band frequencies The circuit is implemented digitally Figs 1a - 1h, a digital DAC being provided for converting the modulated signal (parallel) to a serial bit stream … The modulated signal in analog form is available after a low cost low pass filter … …