共查询到20条相似文献,搜索用时 15 毫秒
1.
《IEEE transactions on information theory / Professional Technical Group on Information Theory》1978,24(2):254-256
An upper bound is derived for the mean-square error involved when a non-band-limited, wide-sense stationary random processx(t) (possessing an integrable power spectral density) is approximated by a cardinal series expansion of the formsum^{infty}_{-infty}x(n/2W) sinc2W(t-n/2W) , a sampling expansion based on the choice of some nominal bandwidthW > 0 . It is proved thatlim_{N rightarrow infty} E {|x(t) - x_{N}(t)|^{2}} leq frac{2}{pi}int_{| omega | > 2 pi W}S_{x}( omega) d omega, wherex_{N}(t) = sum_{-N}^{N}x(n/2W) sinc2W(t-n/2W) , andS_{x}(omega) is the power spectral density forx(t) . Further, the constant2/ pi is shown to be the best possible one if a bound of this type (involving the power contained in the frequency region lying outside the arbitrarily chosen band) is to hold uniformly int . Possible reductions of the multiplicative constant as a function oft are also discussed, and a formula is given for the optimal value of this constant. 相似文献
2.
《IEEE transactions on information theory / Professional Technical Group on Information Theory》1974,20(3):311-316
Upper bounds to the capacity of band-limited Gaussianm th-order autoregressive channels with feedback and average energy constraintE are derived. These are the only known hounds on one- and two-way autoregressive channels of order greater than one. They are the tightest known for the first-order case. In this case letalpha_1 be the regression coefficient,sigma^2 the innovation variance,N the number of channel iterations per source symbol, ande = E/N ; then the first-order capacityC^1 is bounded by begin{equation} C^1 leq begin{cases} frac{1}{2} ln [frac{e}{sigma^2}(1+ mid alpha_1 mid ) ^ 2 +1], & frac{e}{sigma^2} leq frac{1}{1- alpha_1^2} \ frac{1}{2} ln [frac{e}{sigma^2} + frac{2mid alpha_1 mid}{sqrt{1-alpha_1^2}} sqrt{frac{e}{simga^2}} + frac{1}{1-alpha_1^2}], & text{elsewhere}.\ end{cases} end{equation} This is equal to capacity without feedback for very low and very highe/sigma^2 and is less than twice this one-way capacity everywhere. 相似文献
3.
《IEEE transactions on information theory / Professional Technical Group on Information Theory》1964,10(1):72-74
Upper and lower bounds are established for the mean-square variation of a stationary processX(t) whose power spectrum is bounded byomega_{c} , in terms of its average powerP_{0} and the average powerP_{1} of its derivative. It is shown thatleft( frac{2}{pi} right)^{2} P_{1} tau^{2} leq E {|X(t+tau )-X(t)|^{2}} leq P_{1} tau^{2} leq omega_{c}^{2}P_{0}tau^{2} where the upper bounds are valid for anytau and the lower bound fortau < pi / omega_{c} . These estimates are applied to the mean-square variation of the envelope of a quasi-monochromatic process. 相似文献
4.
《Quantum Electronics, IEEE Journal of》1981,17(8):1324-1325
Classically, the thermal noise in electricalRC circuits andLCR series circuits is governed by the equipartition lawfrac{1}{2}overline{CV^{2}} = frac{1}{2}kT , whereV(t) is the noise voltage developed acrossC . When quantum effects are taken into account, the equipartition law no longer holds forRC circuits, although an equipartition law can be deemed for the measured mean square noise voltage under certain conditions. InLCR series circuits the equipartition lawfrac{1}{2}overline{CV^{2}} = frac{1}{2}kT , changes intofrac{1}{2}overline{CV^{2}} = frac{1}{2}bar{E}(f_{0}) for high-Q tuned circuits, wherebar{E}(f_{0}) is the average energy of a harmonic oscillator tuned at the tuning frequency of the tuned circuit. 相似文献
5.
《IEEE transactions on information theory / Professional Technical Group on Information Theory》1986,32(3):410-412
For a complex-valued deterministic signal of finite energy band-limited to the normalized frequency band|w| leq pi explicit coefficients{a_{kn}} are found such that for anyT satisfying0 < T leq 1/2 ,left| f(t)-sum^{2n}_{k=1}a_{kn}f(t - kT)right| leq E_{f}cdot beta^{n} whereE_{f} is the signal energy andbeta doteq 0.6863 . Thus the estimate off(t) in terms of2n past samples taken at a rate equal to or in excess of twice the Nyquist rate converges uniformly at a geometric rate tof(t) on(- infty , infty) . The suboptimal coefficients{a_{kn}} have the desirable property of being pure numbers independent of both the particular band-limited signal and of the selected sampling rate1/T . It is also shown that these same coefficients can be used to estimate the value ofx(t) of a wide-sense stationary random process in terms of past samples. 相似文献
6.
《IEEE transactions on information theory / Professional Technical Group on Information Theory》1967,13(1):91-94
The probability of a set of binaryn -tuples is defined to be the sum of the probabilities of the individualn -tuples when each digit is chosen independently with the same probabilityp of being a "one." It is shown that, under such a definition, the ratio between the probability of a subgroup of order2^{k} and any of its proper cosets is always greater than or equal to a functionF_{k}(p) , whereF_{k}(p) geq 1 forp leq frac{1}{2} with equality when and only whenp = frac{1}{2} . It is further shown thatF_{k}(p) is the greatest lower bound on this ratio, since a subgroup and proper coset of order2^{k} can always be found such that the ratio between their probabilities is exactlyF_{k}(p) . It is then demonstrated that for a linear code on a binary symmetric channel the "tall-zero" syndrome is more probable than any other syndrome. This result is applied to the problem of error propagation in convolutional codes. 相似文献
7.
《IEEE transactions on information theory / Professional Technical Group on Information Theory》1986,32(5):706-709
Recently Kasami {em et al.} presented a linear programming approach to the weight distribution of binary linear codes [2]. Their approach to compute upper and lower bounds on the weight distribution of binary primitive BCH codes of length2^{m} - 1 withm geq 8 and designed distance2t + 1 with4 leq t leq 5 is improved. From these results, the relative deviation of the number of codewords of weightjleq 2^{m-1} from the binomial distribution2^{-mt} left( stackrel{2^{m}-1}{j} right) is shown to be less than 1 percent for the following cases: (1)t = 4, j geq 2t + 1 andm geq 16 ; (2)t = 4, j geq 2t + 3 and10 leq m leq 15 ; (3)t=4, j geq 2t+5 and8 leq m leq 9 ; (4)t=5,j geq 2t+ 1 andm geq 20 ; (5)t=5, j geq 2t+ 3 and12 leq m leq 19 ; (6)t=5, j geq 2t+ 5 and10 leq m leq 11 ; (7)t=5, j geq 2t + 7 andm=9 ; (8)t= 5, j geq 2t+ 9 andm = 8 . 相似文献
8.
《IEEE transactions on information theory / Professional Technical Group on Information Theory》1970,16(6):745-751
In this paper, we establish the following result. Theorem:A_i , the number of codewords of weighti in the second-order binary Reed-Muller code of length2^m is given byA_i = 0 unlessi = 2^{m-1} or2^{m-1} pm 2^{m-l-j} , for somej, 0 leq j leq [m/2], A_0 = A_{2^m} = 1 , and begin{equation} begin{split} A_{2^{m-1} pm 2^{m-1-j}} = 2^{j(j+1)} &{frac{(2^m - 1) (2^{m-1} - 1 )}{4-1} } \ .&{frac{(2^{m-2} - 1)(2^{m-3} -1)}{4^2 - 1} } cdots \ .&{frac{(2^{m-2j+2} -1)(2^{m-2j+1} -1)}{4^j -1} } , \ & 1 leq j leq [m/2] \ end{split} end{equation} begin{equation} A_{2^{m-1}} = 2 { 2^{m(m+1)/2} - sum_{j=0}^{[m/2]} A_{2^{m-1} - 2^{m-1-j}} }. end{equation} 相似文献
9.
《IEEE transactions on information theory / Professional Technical Group on Information Theory》1976,22(3):363-366
This article presents new tighter upper bounds on the rate of Gaussian autoregressive channels with linear feedback. The separation between the upper and lower bounds is small. We havefrac{1}{2} ln left( 1 + rho left( 1+ sum_{k=1}^{m} alpha_{k} x^{- k} right)^{2} right) leq C_{L} leq frac{1}{2} ln left( 1+ rho left( 1+ sum_{k = 1}^{m} alpha_{k} / sqrt{1 + rho} right)^{2} right), mbox{all rho} , whererho = P/N_{0}W, alpha_{l}, cdots, alpha_{m} are regression coefficients,P is power,W is bandwidth,N_{0} is the one-sided innovation spectrum, andx is a root of the polynomial(X^{2} - 1)x^{2m} - rho left( x^{m} + sum^{m}_{k=1} alpha_{k} x^{m - k} right)^{2} = 0. It is conjectured that the lower bound is the feedback capacity. 相似文献
10.
《IEEE transactions on information theory / Professional Technical Group on Information Theory》1986,32(3):436-440
Using earlier methods a combinatorial upper bound is derived for|C|. cdot |D| , where(C,D) is adelta -decodable code pair for the noisy two-access binary adder channel. Asymptotically, this bound reduces toR_{1}=R_{2} leq frac{3}{2} + elog_{2} e - (frac{1}{2} + e) log_{2} (1 + 2e) = frac{1}{2} - e + H(frac{1}{2} - e) - frac{1}{2}H(2e), wheree = lfloor (delta - 1)/2 rfloor /n, n rightarrow infty andR_{1} resp.R_{2} is the rate of the codeC resp.D . 相似文献
11.
《Electron Devices, IEEE Transactions on》1977,24(10):1245-1248
A knowledge of the MOSFET operating in weak inversion is important for circuits with low leakage specifications. This paper discusses the effect of temperature on the MOSFET in weak inversion. The reciprocal slopen of the log IDS versus VGS relationship between source-drain current IDS and gate bias VGS may be given byfrac{1}{(n - 1 - gamma)^{2}} = frac{2Cmin{ox}max{2}}{qepsilon_{s}N_{B}} [frac{3}{4} frac{E_{g^{0}}{q} - (frac{3}{2}alpha + frac{k}{q})T] withalpha equiv (k/q)(38.2 - ln N_{B} + (3/2) ln T) and γ ≡C_{ss}/C_{ox} , where Cox is the oxide capacitance per unit area, Css the surface states capacitance per unit area,q the electronic charge, εs the permittivity of silicon, NB the bulk doping concentration,k the Boltzmann's constant,T the absolute temperature, andE_{g0} the extrapolated value of the energy gap of lightly doped silicon atT = 0 K. This theoretical formula was in good agreement with experimental results in a temperature range of interest. 相似文献
12.
《IEEE transactions on information theory / Professional Technical Group on Information Theory》1976,22(5):568-573
Modern communication theory and practice are heavily dependent on the representation of continuous parameter signals by linear combinations, involving a denumerable set of random variables. Among the best known and most useful is the cardinal seriesf_{n} (t) = sum^{+n}_{-n} f(k) frac{sin pi (t - k)}{ pi ( t - k )} for deterministic functions and wide-sense stationary stochastic processes bandlimited to(-pi, pi) . When, as invariably occurs in applications, samplesf(k) are available only over a finite period, the resulting finite approximation is subject to a truncation error. For functions which areL_{1} Fourier transforms supported on[-pi + delta, + pi - delta] , uniform trunction error bounds of the formO(n^{-1}) are known. We prove that analogousO(n^{-1}) bounds remain valid without the guard banddelta and for Fourier-Stieltjes transforms; we require only a bounded variation condition in the vicinity of the endpoints- pi and+ pi of the basic interval. Our methods depend on a Dirichlet kernel representation forf_{n}(t) and on properties of functions of bounded variation; this contrasts with earlier approaches involving series or complex variable theory. Other integral kernels (such as the Fejer kernel) yield certain weighted truncated cardinal series whose errors can also be bounded. A mean-square trunction error bound is obtained for bandlimited wide-sense stationary stochastic processes. This error estimate requires a guard band, and leads to a uniformO(n^{-2}) bound. The approach again employs the Dirichlet kernel and draws heavily on the arguments applied to deterministic functions. 相似文献
13.
Achievable rates for multiple descriptions 总被引:12,自引:0,他引:12
《IEEE transactions on information theory / Professional Technical Group on Information Theory》1982,28(6):851-857
14.
《IEEE transactions on information theory / Professional Technical Group on Information Theory》1971,17(4):368-371
The following model for the white Gaussian channel with or without feedback is considered: begin{equation} Y(t) = int_o ^{t} phi (s, Y_o ^{s} ,m) ds + W(t) end{equation} wherem denotes the message,Y(t) denotes the channel output at timet ,Y_o ^ {t} denotes the sample pathY(theta), 0 leq theta leq t. W(t) is the Brownian motion representing noise, andphi(s, y_o ^ {s} ,m) is the channel input (modulator output). It is shown that, under some general assumptions, the amount of mutual informationI(Y_o ^{T} ,m) between the messagem and the output pathY_o ^ {T} is directly related to the mean-square causal filtering error of estimatingphi (t, Y_o ^{t} ,m) from the received dataY_o ^{T} , 0 leq t leq T . It follows, as a corollary to the result forI(Y_o ^ {T} ,m) , that feedback can not increase the capacity of the nonband-limited additive white Gaussian noise channel. 相似文献
15.
Writing on dirty paper (Corresp.) 总被引:1,自引:0,他引:1
《IEEE transactions on information theory / Professional Technical Group on Information Theory》1983,29(3):439-441
A channel with outputY = X + S + Z is examined, The stateS sim N(0, QI) and the noiseZ sim N(0, NI) are multivariate Gaussian random variables (I is the identity matrix.). The inputX in R^{n} satisfies the power constraint(l/n) sum_{i=1}^{n}X_{i}^{2} leq P . IfS is unknown to both transmitter and receiver then the capacity isfrac{1}{2} ln (1 + P/( N + Q)) nats per channel use. However, if the stateS is known to the encoder, the capacity is shown to beC^{ast} =frac{1}{2} ln (1 + P/N) , independent ofQ . This is also the capacity of a standard Gaussian channel with signal-to-noise power ratioP/N . Therefore, the stateS does not affect the capacity of the channel, even thoughS is unknown to the receiver. It is shown that the optimal transmitter adapts its signal to the stateS rather than attempting to cancel it. 相似文献
16.
《IEEE transactions on information theory / Professional Technical Group on Information Theory》1970,16(3):353-355
An interleaved fading channel whose state is known to the receiver is analyzed. The reliability functionE(R) is obtained for ratesR in the rangeR_c leq R leq C . The capacity is shown to beC = E_A { frac{1}{2} ln (1 + A^2 n)} whereA is a factor describing the fading mechanism andu is the signal-to-noise ratio per dimension. 相似文献
17.
《IEEE transactions on information theory / Professional Technical Group on Information Theory》1977,23(1):52-59
A new upper houndR_{u}(D) and lower houndR_{ell}(D) are developed for the rate-distortion function of a binary symmetric Markov source with respect to the frequency of error criterion. Both hounds are explicit in the sense that they do not depend on a blocklength parameter. In the intervalD_{c} < D < 1/2 = D_{max} , whereD_{c} is Gray's critical value of distortion,R_{u}(D) is convex downward and possesses the correct value and the correct slope at both endpoints. The new lower boundR_{ell}(D) diverges from the Shannon lower bound at the same value of distortion as does the second-order Wyner-Ziv lower bound. However, it remains strictly positive for allD leq 1/2 and therefore eventually rises above all the Wyner-Ziv lower bounds asD approaches1/2 . Some generalizations suggested by the analytical and geometrical techniques employed to deriveR_{u}(D) andR_{ell}(D) are discussed. 相似文献
18.
《IEEE transactions on information theory / Professional Technical Group on Information Theory》1979,25(4):448-452
A model of an additive non-Gaussian noise channel with generalized average input energy constraint is considered. The asymptotic channel capacityC_{zeta}(S) , for large signal-to-noise ratioS , is found under certain conditions on the entropyH_{ tilde{ zeta}}( zeta) of the measure induced in function space by the noise processzeta , relative to the measure induced bytilde{zeta} , where is a Gaussian process with the same covariance as that ofzeta . IfH_{ tilde{zeta}}( zeta) < infty and the channel input signal is of dimensionM< infty , thenC_{ zeta}(S)= frac{1}{2}M ln(1 + S/M) + Q_{zeta}( M ) + {o}(1) , where0 leq Q_{ zeta}( M ) leq H_{ tilde{ zeta}}( zeta) . If the channel input signal is of infinite dimension andH_{ tilde{ zeta}}( zeta) rightarrow 0 forS rightarrow infty , thenC_{ zeta}(S) = frac{1}{2}S+{o}(1) . 相似文献
19.
A first-order Markov process is used to model the sequence of quantization noise samples in delta modulation. An autocorrelation parameterC in the Markov model controls the shape of the noise spectrum, and asC decreases from 1 to 0 and then to -1, the spectrum changes from a low-pass to a flat, and then to a high-pass characteristic. One can also use the Markov model to predict the so-called out-of-band noise rejection that is obtained when delta modulation is performed with an oversampled input, and the resulting quantization noise is lowpass filtered to the input band. The noise rejectionG is a function ofC as well as an oversampling factorF and an interesting asymptotic result is thatG=frac{1-C}{1+C} dot F ifF gg frac{1+C}{1-C} dot frac{pi}{2} . Delta modulation literature has noted the importance of the specialG values,F and2F . These correspond to autocorrelation values of 0 and -1/3. 相似文献
20.
《IEEE transactions on information theory / Professional Technical Group on Information Theory》1975,21(4):453-458
For a nondecreasing distortion characteristicphi(cdot) and a given signalx(cdot) , the "cross correlation" function defined byR_{phi} (tau) triangleq int_{-infty}^{infty} phi[x(t)]x(t - tau) dt is shown to satisfy the inequalityR_{phi}(tau) leq R_{phi}(0) , for alltau , generalizing an earlier result of Richardson that requiredphi(cdot) to be continuous and strictly increasing. The methods of the paper also show that, under weak conditions, begin{equation} R_{phi,psi}(tau) triangleq int_{-infty}^{infty} phi[x(t)]psi[x(t - tau)] dt leq R_{phi,psi}(0) end{equation} whenpsi is strictly increasing andphi is nondecreasing. In the case of hounded signals (e.g., periodic functions), the appropriate cross correlation function is begin{equation} mathcal{R}_{phi,psi}(tau} triangleq lim_{T rightarrow infty} (2T)^{-l} int_{-T}^T phi[x(t)]psi[x(t - tau)] dt. end{equation} For this case it is shown thatmathcal{R}_{phi,psi} (tau) leq mathcal{R}_{phi,psi}(0) for any nondecreasing (or nonincreasing) distortion functionsphi andpsi . The result is then applied to generalize an inequality on correlation functions for periodic signals due to Prosser. Noise signals are treated and inequalities of a similar nature are obtained for ensemble-average cross correlation functions under suitable hypotheses on the statistical properties of the noise. Inequalities of this type are the basis of a well-known method of estimating the unknown time delay of an observed signal. The extension to nondecreasing discontinuous distortion functions allows the use of hard limiting or quantization to facilitate the cross correlation calculation. 相似文献