Citations: Signal analysis - Papoulis (ResearchIndex)

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A. Papoulis. Signal Analysis. McGraw{Hill, New York, 1977.

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Self-Focusing In The Perturbed And Unperturbed Nonlinear.. - Fibich, Papanicolaou (1999) (2 citations) (Correct)

.... oscillations increase on the average as z increases: 2 cos(#s) R(s)ds, where R(z) h(z s) h(s)# is the covariance of the random force h(z) For large z the energy of the small oscillations grows linearly, 2 R(#) where 0 is the power spectral density [57] of the random forcing h, R(#) e i#s R(s)ds . Ultimately, the growth of the energy will make the linearization invalid and the full nonlinear equation (5.21) should be considered. An important issue is to estimate the probability of escape (i.e. L #) by the random ....

A. Papoulis, Signal Analysis, McGraw-Hill, New York, 1977.

Blind Adaptive Equalization of Mismatch Errors in.. - Elbornsson.. (2003) (Correct)

....We will here describe a method for exact interpolation by filtering the signal with a non causal IIR filter. If the input signal is band limited to the Nyquist frequency, and the time error parameters are known, the input signal can be perfectly reconstructed from the irregular samples [14]. In a real application the interpolation is of course approximate since we cannot use a filter of infinite length, but we can come arbitrarily close to the exact interpolation by choosing the length of the filter large enough. In [14] the interpolation is done at an arbitrary time instance. If we ....

....can be perfectly reconstructed from the irregular samples [14] In a real application the interpolation is of course approximate since we cannot use a filter of infinite length, but we can come arbitrarily close to the exact interpolation by choosing the length of the filter large enough. In [14] the interpolation is done at an arbitrary time instance. If we only need to reconstruct the signal at the nominal sampling instances t = kM l)T s ,l=0, M 1 k = 1, 0, 1, the reconstruction can be simplified. The simplified reconstruction will be described here. The time errors are ....

A. Papoulis, Signal Analysis. McGraw-Hill, 1977.

Equalization of Time Errors in Time Interleaved ADC.. - Elbornsson.. (2003) (Correct)

....[13] We will here describe a method for exact interpolation by filtering the signal with a non causal IIR filter. If the input signal is band limited to the Nyquist frequency, and the time error parameters are known, the input signal can be perfectly reconstructed from the irregular samples [14]. In a real application, the interpolation is of course approximate since we cannot use a filter of infinite length, but we can come arbitrarily close to the exact interpolation by choosing the length of the filter large enough. In [14] the interpolation is done at an arbitrary time instance ....

....can be perfectly reconstructed from the irregular samples [14] In a real application, the interpolation is of course approximate since we cannot use a filter of infinite length, but we can come arbitrarily close to the exact interpolation by choosing the length of the filter large enough. In [14] the interpolation is done at an arbitrary time instance according to the following: Solve the equation system 2 i # t i )# H i (#, t) 1 2 i # t i ) # (3) 2 i # t i ) # (M 1) j(M 1) for H i (#, t) The input signal can then be calculated at any ....

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A. Papoulis, Signal Analysis. McGraw-Hill, 1977.

Recursive Gaussian Derivative Filters - van Vliet, Young, Verbeek (1998) (6 citations) (Correct)

....a Fourier transform G(w;s) which is also a Gaussian g t e G e ; s ps w s a f a f = 2 2 2 F w (1) and where s is referred to as both the standard deviation and the scale. The Gaussian filter is the filter which minimizes the product of spatial support and frequency bandwidth [8]. It allows simultaneous localization in the time (space) and (spatial) frequency domain. 3. Discrete time recursive filter The goal is to design a discrete recursive Gaussian filter that requires a minimum number of multiplications. A discrete time (space) system is described by its z ....

A. Papoulis, Signal Analysis. McGraw--Hill, 1977.

Filter Banks for Cyclic-pre xing the Nonuniform DMT System - Vaidyanathan And Bojan (2002) (Correct)

.... the channel noise e(n) For example, when M: 6 and L = 3 we have c(0) 0 0 c(3) c(2) c(1) c(1) c(0) 0 0 c(3) c(2) c(2) c(1) c(0) 0 0 c(3) c(3) c(2) c(1) c(0) 0 0 0 c(3) c(2) c(1) c(0) 0 0 0 c(3) c(2) c(1) c(0) The fact that C is circulant implies that it can be diagonalized by the DFT matrix [5]. More precisely C = W ZAcW where W is the M x M DFT matrix with elements with W = 2 j M. Here Ac = diag C[O] C[1] C [M 1] where [k] are the DFT coefficients of the channel, i.e. M 1 L c[k] c(n)wk = nO nO Evidently C[k] are samples of the channel resposne (e jw) at the ....

A. Papoulis, Signal analysis, McGraw Hill, 1977.

Amplitude and Gain Error Influence on Time Error.. - Elbornsson.. (Correct)

....[k] y i [k] A = 1 g i )u( kM i)Ts t i ) 3) Next, the gain errors should be removed. This is done by dividing the subsequences by the correct gain. x i [k] z i [k] 1 g i = u( kM i)Ts t i ) 4) Finally, the time errors should be removed. This is done in the frequency domain [6]. Calculate the DFTs of the M subsequences x i [k] i=1, M: X i [n] DFT x i [k] 5) The DFT of u i [k] can then be calculated from X i [n] as U i [n] e j 2#nt i Y i [n] 6) N 2, N 2 U [n] can then be calculated from these M subsequences. U [n] e j 2#(i 1)n U i [ n ....

A. Papoulis, Signal Analysis, McGraw-Hill, 1977.

Improved Locality For Irregular Sampling Algorithms - Feichtinger, Werther (2000) (Correct)

....Whittaker and Kotel nikov provides an explicit reconstruction. Given a bandlimited function f 2 L (R) with spectrum in [ 0 ; 0 ] f can be represented as a cardinal series f(t) f( sinc 0 (t ) where sinc 0 (t) t) sin(2 0 t) for t 6= 0 and sinc 0 (0) 1, cf. 3] [10]. The series converges uniformly and in the L sense. In the case of oversampling, i.e. if sampling values ff( n)gn2Z for some 1=2 0 are known, the SINC function can be replaced by sampling functions with better decay, cf. 2] Such welllocalized sampling functions improve the local ....

A. Papoulis, \Signal analysis", McGraw-Hill, NY, 1977.

Digital Signal Processing Techniques in the Analysis of DNA/RNA.. - Bajic (Correct)

....to increase the length of x 1 up to the length of x 2 in order to make sets S 1 and S 2 equal. This provides a way of interpolation in the frequency domain and increases the computational resolution of the spectrum of x 1 to 1=N 2 [13] However, due to the Uncertainty Principle of Fourier analysis [14], physical resolution of the spectrum of x 1 is limited by its original length and remains 1=N 1 [13] This eectively means that we cannot discover any new information about the spectrum of the signal by performing the zero padding operation interpolation is done on the wrong curve [13] unless ....

A. Papoulis, Signal Analysis, McGraw-Hill, 1977.

Fast and Robust Blind-Equalization Based On Cyclic Prefix - Vaidyanathan, Vrcelj (2002) (Correct)

....0 c(3) c(2) c(1) c(0) I a block of I M symbols I I room ,o T L samples copy copy , 111llllll, If the channel is known, we can perform the equalization by inverting (5) assuming C is nonsingular. The eigenvalues of the M x M circulant are equal to the DFT coefficients of the top row [4]. Since the top row has the channel coefficients in reversed order, these eigenvalues are M 1 (n)w where W : e j2r: M and C(e j) represents the channel frequency response. Thus ] k) are obtained by sampling C(e j) uniformly at M frequencies. Note that c(n) 0 for L n M. The circulant matrix ....

....in reversed order, these eigenvalues are M 1 (n)w where W : e j2r: M and C(e j) represents the channel frequency response. Thus ] k) are obtained by sampling C(e j) uniformly at M frequencies. Note that c(n) 0 for L n M. The circulant matrix C can be diagonalized with the DFT matrix [4]. More specifically we have C = W AW where W is the M x M DFT matrix and he = cu[0] 0 0 . 0 0 Cull] 0 . 0 : 0 0 0 . CM[M 1] where M [ L : 0 c(n) W k : M point DFT of c(n) Note that M [k] is a permuted version of the eigenvalues Thus the implementation of the ....

A. Papoulis, Signal analysis, McGraw Hill, 1977.

Theory Of Fractionally Spaced Cyclic-Prefix Equalizers - Vaidyanathan, Vrcelj (2002) (Correct)

....show in absence of noise that y(ra) Cs(m) where C is a circulant matrix. For example when L: 2 and : 4, 40) 0 42) 40) 0 c: c(02) 40) 02) 42) 40) If (Z) is known, we can perform the equalization by inverting C assuming it is nonsingular. Any circulant can be diagonalized with the DFT matrix [2], that is, C: W lAc w where W is the DFT matrix and Ac: diag C[0] C[1] C[M 1] Here 2 C[k] M 1 : n 0 C(n) Wnk M point DFT of c(n) Thus the implementation of the communication system with cyclic prefix can be represented as shown in Fig. 3. The box labelled blocking is a serial to ....

.... components separated by M 2 are added to form the vector t(n) The output noise is the unblocked version of 0 5t t We ( have lk(t) qk(t)E[c] q qk M 2(t)E[ q M 2] For fixed [ and [c q M 2] we can optimize the coefficients and [c q M 2] subject to the constraint (3) such that [ lk(t)[ 2] is minimized. Define the vectors v k [E [k] E [k q M 2] T, qk = qk(n)q M 2(n) T, and c k = C[k] C[k q M 2] T. Then 2] I I vikRkvk. 3) can Vk[qkqk]V k: The constraint be writ ten as v ck: 2. Assuming Rk is nonsingular, we can show that [ltk (n)12] is minimized subject to this ....

A. Papoulis, Signal analysis, McGraw Hill, 1977.