transfer functions laplace transforms in principal coordinates

... problem in original way of thinking solution in transform way of thinking transform inverse transform solution in original way of thinking R Input 𝑢(𝑡) 𝑦(𝑡) System 𝐺(𝑠) 𝑈(𝑠) Input current ... 𝑖(𝑡) 𝑌(𝑠) Output Input 𝑢(𝑡) 𝑦(𝑡) Output System 𝑒 𝑖𝑛 (𝑡) C i(t), mA 12 𝑒 𝑜𝑢𝑡 (𝑡) 10 Input flowrate 𝑞 𝑖𝑛 𝑞 𝑖𝑛 (𝑡) The liquid in the bulb expands as in its temperature increases, forcing more liquid ... 𝜏𝑠𝐻(𝑠) + 𝐻(𝑠) = 𝐺𝑄 𝑖𝑛 (𝑠) 𝑄 𝑖𝑛 𝑠 = 𝐾 𝑠 algebra 𝐻 𝑠 = frequency domain (Laplace domain) 𝐺𝐾 𝑠(𝜏𝑠 + 1) Inverse Laplace transform time domain ...

Ngày tải lên: 29/10/2014, 07:00

... above It can be seen that the gain is always decreasing for increasing interference coefficients (or decreasing noise variance) It can also be seen that the gain is indeed higher than for reasonable ... σn σn by assuming5 hk ≈ h Finally, by inserting (43) and (44) into (40), the following is obtained: (38) E The adaptation rule (14) is obviously unchanged when it is written for hk instead of hk ... the tracking of FEXT channel coefficients in downstream VDSL This scheme is intended for systems with uncoordinated receivers and coordination at the transmitter, using some kind of precoding scheme...

Ngày tải lên: 22/06/2014, 23:20

... t Sin@tD + p2 p LaplaceTransformA + p t Sin@tD p 1 + p H1 + H− + pL2L p , t, pE 2.2.2 Biến đổi Laplace ngược InverseLaplaceTransform[F, s, p] biến đổi Laplace ngược hàm f(t=L [F(p)] Thí dụ: InverseLaplaceTransformA ... (t ) − sin πtH 12 (t ) + 0.H (t ) = − sin πt [H (t − 1) − H (t − 2)] = − sin πtH (t − 1) + sin πtH (t − 2) = sin π (t − 1) H (t − 1) + sin π (t − 2) H (t − 2) Dựa vào công thức biến đổi Laplace ... đổi Laplace ngược ta được: y (t ) = 2t − 2(t − 1) H (t − 1) + H (t − 1) sin(t − 1) − sin t = 2t − sin t − 2[(t − 1) + sin(t − 1)]H (t − 1) Vậy nghiệm phương trình ⎧2t − sin t y (t ) = ⎨ ⎩2 + sin(t...

Ngày tải lên: 08/04/2013, 09:50

... reasonable accuracy In a recent study, Cho et al [12] investigated the effect of a gap in the inclined rib on heat transfer in a square duct and reported that a gap in the inclined rib accelerates ... optimum width of a gap in the inclined rib to form discrete rib This study will help in determining the gap size while descritizing the inclined (non-transverse) ribs for enhancing the performance ... turbulence which will result in an increase in the heat transfer They reported that the inclined rib arrangement with a downstream gap position shows higher enhancement in heat transfer compared to that...

Ngày tải lên: 05/09/2013, 16:10

... the nesting procedure we can obtain an algorithm for computing the product in T2 which uses M multiplications of elements in T1 , A additions of elements in T1 , and S scalings of elements in T1 ... as computing a product of a matrix A(X) times a vector Y , where the entries in the matrix A(X) are linear combinations of n indeterminates x1 , , xn and y is a vector of n indeterminates y1 ... also obtained In the past several years new, more powerful, processors have been introduced Sun and HP have incorporated new vector instructions Intel has introduced its aggressive Intel’s MMX...

Ngày tải lên: 25/10/2013, 02:15

Ngày tải lên: 09/03/2014, 14:20

... the scaling theorem, of Fourier transforms The theorem tells that a contraction of the coordinates in one domain leads to a corresponding stretch of the coordinates in the other domain If a function ... signal, when the sampling interval is exactly the critical sampling interval, t = 1/(2 f max ) The sampling is called undersampling, if the sampling interval t > 1/(2 f max ) In this case, the period ... critical computing interval is the minimum computing interval which must be used in the calculation of the spectrum in such 44 Discrete Fourier transform a way that all information in the signal...

Ngày tải lên: 17/03/2014, 14:45

... processes are introduced Finally, the theories of organizational learning, including individual and organizational learning, in single and double loop and a systemic model in building learning organizations ... knowledge transfer in investment projects The development of a new concept for knowledge transfer and competence development continue in 2002 in a paper machine start-up project in Finland The ... started to be transferred to the emerging markets in line with the trend in other manufacturing branches Despite expectations, not all the business start-ups of multinational companies in China have...

Ngày tải lên: 18/03/2014, 02:20

... ‘acknowledging, recognising, inquiring, being aware, understanding, intelligence, information acquired through study and learning’ According to McInerney (2002), ‘knowledge is based in sentient beings, ... Organisations are increasingly encouraging informal learning through the media of mentorship programmes and communities-of-practice Cox (1993) quoted the work of Kram (1985) in defining a mentoring relationship, ... are collectivist in nature Sharing of ideas and insights should be a natural part of the work environment, rather than individuals feeling pressurized into behaving in a certain manner (McDermott...

Ngày tải lên: 23/03/2014, 04:21

... to routine functions, as determined in Step Adjusted operating profits, in turn, are computed by eliminating deductions for investments in intangible assets from combined reported operating profits, ... purported income-shifting is accomplished principally by under-compensating the entity contributing pre-existing intangible assets to the cost-sharing arrangement As in other areas of transfer pricing ... authorities’ perspectives, include costs incurred in conducting audits and analyzing transfer pricing issues, and in resolving conflicts over income allocations with their opposite numbers in other tax jurisdictions...

Ngày tải lên: 30/03/2014, 11:20

... associated with induced expression of insulin-like growth factor binding protein-2 in the uterus and ovary and decreased expression of insulinlike growth factor binding protein-3 in the uterus ... X-linked dominant mutation in mice that involves a genomic deletion containing spermine synthase gene The following paragraphs list the existing knowledge of disruption of genes involved in polyamine ... Correlations between polyamine analogue-induced increases in spermidine/spermine N1-acetyltransferase activity, polyamine pool depletion, and growth inhibition in human melanoma cell lines Cancer Res 51,...

Ngày tải lên: 30/03/2014, 13:20

... of two functions The convolution is obtained by sliding one of the functions (reversed) past the other and integrating the point-by-point product of the functions over the whole real line Figure ... shown in Figure 3.4, with A = and T = in this case.) 28 Fourier Transforms in Radar and Signal Processing ∞ ͐−∞ sinc (x − m ) sinc (x − n ) dx = ␦ mn Using the result in item above, if m = n the integral ... We include a short discussion on convolution, as this operation is important in this work, being the operation in the transform domain corresponding to multiplication in the original domain (and...

Ngày tải lên: 18/06/2014, 10:05

... overlapping sinc functions These are shown as dotted lines in Figure 3.9(b), with the pulse spectrum as the solid line The 48 Fourier Transforms in Radar and Signal Processing Figure 3.9 Raised cosine ... given by putting ␶ = ␶ = ␶ in this expression, is U( f ) = sinc ( f␶ ) (e ␲ ifT − e −␲ ifT ) sinc ( f␶ ) sin (␲ f T ) = 2␲ if ␲f = T sinc ( f␶ ) sinc ( f T ) which is the result given in Section ... is an interesting exercise in the use of the rules-and-pairs method, showing that the method gives a solution for the spectrum quite 39 40 Fourier Transforms in Radar and Signal Processing easily...

Ngày tải lên: 18/06/2014, 10:05

... converse of repeating a waveform to obtain a line spectrum: if a waveform is repeated at intervals T, a spectrum is obtained consisting of lines (␦ -functions in the frequency domain) at intervals F ... convolving the Ramp functions with different-width rect functions (or other rounding functions, if required) as in Figure 3.11, before combining to form the smoothed pulse Before obtaining the Fourier ... form, correctly interpolated In the following sections of this chapter, the starting point is (4.1), choosing the appropriate sampling frequency F and spectral gating function G in the different...

Ngày tải lên: 18/06/2014, 10:05

... Hilbert sampling and quadrature sampling, discussed 82 Fourier Transforms in Radar and Signal Processing above, in particular from the point of view of finding the minimum sampling rate needed ... quarter cycle delay, and sampling in only a single channel rather than in two—at the cost of requiring a higher sampling rate, though, at the minimum, this single sampling device [or analogue-to-digital ... can obtain V by first shifting U by −f , then gating it with rect ( f /W ) (Figure 4.15) In order to obtain the repetitive element in the spectrum, to give the ␦ -functions in the time domain corresponding...

Ngày tải lên: 18/06/2014, 10:05

... Trapezoidal spectral gating (5.17) w r ( ␳ ) = sin X sin Y /XY [Y = ( q − 1) X /q ] Gate with trapezoidal rounding (5.21) w r ( ␳ ) = sinc x sinc (1 − ␣ ) y sinc ␣ y = sin X sin Y sin Y XY 1Y [Y = ␣ ... g [(r − ␳ )T ′ ]/ qF ͫ = sinc x sinc y + Putting sinc ( y ± 1) = we have ͬ 1 sinc ( y − 1) + sinc ( y + 1) 2 sin ␲ ( y ± 1) −sin ␲ y = ␲ ( y ± 1) ␲ ( y ± 1) (5.24) Interpolation for Delayed Waveform ... oversampling and trapezoidal spectral gate 101 102 Fourier Transforms in Radar and Signal Processing Figure 5.11 Trapezoidal rounding w r (␶ ) = ␾ [(r − ␳ ) T ′ ] = sinc x sinc (1 − ␣ ) y sinc ␣...

Ngày tải lên: 18/06/2014, 10:05

... the underlying principles The first main application was to find the FIR filter weights that would provide interpolation for any band-limited signal In principle, this filter will be infinitely ... substituting in (6.15), we obtain (−␲ i )r (2x )r rect (x ) ⇔ sinc(r ) ( y ) If we introduce the notation (6.16) 132 Fourier Transforms in Radar and Signal Processing sncr ( y ) = dr ␲ r dy r sinc ... processing need not be in real time, of course, with the input and output pulses arriving and departing at the actual intervals specified The input data could be stored after sampling in real time, of...

Ngày tải lên: 18/06/2014, 10:05

... only integer delay compensation (in units of the sampling interval) [In Figure 6.8(a), this curve is identical to the dashed curve, as all the delays are within ±0.5 sampling intervals, so no integer ... be integral, in sampling periods, in which case the matching will be exact, in principle, and the response will be completely flat At the other extreme, the delays required might all be half-integral, ... be included in the integral and hence also with S.] The Fourier transform of the power spectrum in (6.42) is [as in (5.45)] ␳ a (t ) = sinc [(1 − a ) Ft /2] sinc [(1 + a ) Ft /2] (6.43) To find...

Ngày tải lên: 18/06/2014, 10:05

... degrees, angle space Array Beamforming 167 In plotting this curve, (7.4) was not used, as that would require summing a large number of sinc functions in principle an infinite number We can describe ... [sinc (v − 1) + sinc (v + 1)] + a [sinc (v − 2) + sinc (v + 2)] (7.16) + a n [sinc (v − n ) + sinc (v + n )] The n coefficients are determined by setting the gain to particular values at n points ... repetition interval in the u domain Then it is natural to choose I to be the interval [−U /2, U /2], which is equivalent to including the factor rect (u /U ) in the integrands in (7.34) In this...

Ngày tải lên: 18/06/2014, 10:05

... work, in Chapters and 6, is directed at showing the benefits of oversampling (only by a relatively small factor in some cases) in reducing the amount of computation needed in the signal processing ... Impulse responses, 51 exponential, 52 rect, 52 smoothing, 53 Interpolating function, 95 as product of sinc functions, 99 in uniform sampling, 77 Interpolation for delayed waveform time series, 89–123 ... blind signal separation 191 Index ␦ -function, 6, 15–17, 67, 150 defined, 15 envelope, 180 illustrated, 16 position of, 16 properties, 15 scaled, 16–17 in time-domain, 16 shading, 67 tapering,...

Ngày tải lên: 18/06/2014, 10:05