important properties of the z transform

... Reconstruction of Analog Signals 3.5 Problems 59 67 80 97 THE z -TRANSFORM 103 4.1 The Bilateral z -Transform 4.2 Important Properties of the z -Transform 4.3 Inversion of the z -Transform 4.4 ... then their product is well-defined The result is also a matrix with the number of rows equal to that of the first matrix and the number of columns equal to that of the second matrix Note that the ... introduced to analyze z- transforms and to compute inverse ztransforms Solutions of difference equations using the z- transform and MATLAB are provided Chapter 5, The Discrete Fourier Transform: This...

Ngày tải lên: 18/10/2015, 20:05

... affecting the synthesis of the time domain signal Here's a puzzle: If there are N samples entering the DFT, and N%2 samples exiting, where did the extra information come from? The answer: two of the ... aperiodic Together these define four possible combinations, each having its own version of the Fourier transform The names are not well organized; simply memorize them type of Fourier transform that ... example because they have a value of zero, and therefore provide no contribution The synthesis equation, Eq 8-2, is then used to convert the amplitudes of the cosine waves, (b), into the time domain...

Ngày tải lên: 13/09/2012, 09:49

... conjugate of the complex number z In[5]: ?Abs Out[5]: Abs [z] gives the absolute value of the real or complex number z In[6]: ?Arg Out[6]: Arg [z] gives the argument of z DRAFT of “Mathematics of the ... ?Re Out[2]: Re [z] gives the real part of the complex number z In[3]: ?Im Out[3]: Im [z] gives the imaginary part of the complex number z DRAFT of “Mathematics of the Discrete Fourier Transform (DFT),” ... ( the real part of z = x + jy is x”) im {z} = y ( the imaginary part of z = x + jy is y”) Note that the real numbers are the subset of the complex numbers having a zero imaginary part (y = 0) The...

Ngày tải lên: 31/03/2014, 15:21

... Why yet another transform? After all, we now have FT tools for periodic and aperiodic signals in both CT and DT! What is left? DTFT One of the most important properties of the DTFT is the convolution ... case the “inverse” is named appropriately, since we really recover x[n] exactly from {X[k]} k=0 The proof of this is essentially identical to the proof given for the self-consistency of the DTFS ... ←→ a X[k] +b Y [k] N Post for properties Most of the properties of the DTFT have analogous relationships for the DFT However, our previous definitions of signal properties and operations like...

Ngày tải lên: 08/06/2014, 20:19

... Processing The bilinear transform maps the analog domain to the discrete domain one-to-one It maps points in the s-domain with Re{s} = ( jω axis) to the unit circle in the z- plane |z| = However, the ... discretize the HermiteGaussian differential equation Since the bilinear transform maps the analog domain to the discrete domain one-to-one, we find eigenvectors which are close to the samples of the ... forward difference method maps the jω to a circle of radius 0.5 and centered at the point z = 0.5 as shown in Figure Bilinear transform maps every point in the jω-plane to the z- plane without aliasing...

Ngày tải lên: 21/06/2014, 16:20

... s(t) The peak magnitude of the Gibbs oscillation is 13% − + of the size of the jump discontinuity s(t0 ) − s(t0 ) regardless of the number of terms used in the approximation As N increases, the ... special case of the complex Fourier transform (or bilateral Laplace transform) , the DTFT is a special case of the bilateral z- transform with z = ej ω t The more general bilateral z- transform is ... (1.14b) The set of all values of u for which the integral of (1.14b) converges is called the region of convergence (ROC) Because the transform S(u) is defined only for values of u within the ROC, the...

Ngày tải lên: 27/01/2014, 03:20

... Figure The computation of the DFT as coprocessor then has three stages (a) The serial data transfer to the coprocessor (b) The computation of the DFT, until the first output value is available (c) The ... a CZT of length 64 and a Rader transform of length 61 Again, the direct comparison of Rader and CZT shows a reduced effort for CZT R + 50 Note that in the ∗×5+ block multiplier architecture, the ... Table shows the advantages of the CZT implementation The effort for the CSD, MAG, and RAG-n methods for the CZT DFT up to a length of 256 is graphically interpreted in Figure Note that the DFTs with...

Ngày tải lên: 22/06/2014, 23:20

... using the FFT algorithm) First, move the N point signal into the real part of the complex DFT's time domain, and then set all of the samples in the imaginary part to zero Calculation of the complex ... of their names, all of the values in these arrays are just ordinary numbers (If you are familiar with complex numbers: the j's are not included in the array values; they are a part of the mathematics ... precision) The second test of proper operation is that the signals have the correct symmetry When the imaginary part of the time domain signal is composed of all zeros (the normal case), the frequency...

Ngày tải lên: 13/09/2012, 09:50

... Family of Fourier Transforms Just as the DFT has a real and complex version, so the other members of the Fourier transform family This produces the zoo of equations shown in Table 31-1 Rather than ... in the calculation of the imaginary part of the frequency spectrum (an option used to make the real transforms more consistent with the complex transforms) Lastly, the synthesis equations for the ... placed in the real part of the time domain, while the other is place in the imaginary part After the FFT calculation, the spectra of the two signals are separated by an even/odd decomposition The Family...

Ngày tải lên: 13/09/2012, 10:20

... (from the perspective of the POTS dial peer 1), the POTS dial peer establishes the source (via the originating telephone number or voice port) of the call The VoIP dial peer establishes the destination ... comparing the called number (the full E.164 telephone number) in the call information with the number configured as the destination pattern for the POTS peer The router then strips out the left-justified ... destination-pattern of “1310555” and a prefix of “9,” the router will strip out “1310555” from the E.164 telephone number, leaving the extension number of “2222.” It will then append the prefix, “9,” to the front...

Ngày tải lên: 22/10/2013, 09:15

... directly to the subtending system that connects on the edge of the network The subtending system aggregates the traffic from the subtended systems, switches all the traffic (its own and that of the subtended ... Quality of Service (QoS) and overbooking ratios Benefits of Subtending Minimize the Expense of Central Office DSL Deployment As DSL networks are built out to Central Office co-locations, the access ... chain systems, and are just a few of the many configurations available through subtending The subtending systems in each configuration aggregate the transmissions of the subtended systems and provide...

Ngày tải lên: 21/12/2013, 06:20

Ngày tải lên: 24/12/2013, 12:16

Ngày tải lên: 07/03/2014, 13:20

Ngày tải lên: 09/03/2014, 15:20

... on the evidence I left in the theater At the time I dreaded the consequences of being late for class over the consequences of what would happen to me if the school figured out who trashed the theater… ... I asked either of them I found history on the third floor of the same building and realized that except for French, the same people were in all of my classes so far This had to be the entire ... understand the social order of things The rest of the girls are just followers, with no minds of their own.” “Wonderful,” I mumbled under my breath “Just steer clear and they won’t bother you… most of...

Ngày tải lên: 16/03/2014, 18:20

... All the people of Egypt love singing Their voices are soft and sweet The boatmen on the Nile sing as they row The fruit-sellers sing as they cry their wares in the streets Many of the boys in the ... the mouth of the well there is a wheel 12 A rope runs over this wheel At one end of the rope there is a large leather bag The other end of the rope is fastened to the necks of a pair of bullocks ... the dogs of the villages play together You can see two boys in the picture One of them is standing by his mother The other boy is riding on a buffalo 10 In the middle of the village there is...

Ngày tải lên: 22/03/2014, 16:22

... arm The bones of the forearm The bones of the wrist 10 The bones of the fingers 11 The bones of the thigh 12 The bones of the lower leg 13 The bones of the ankle 14 The bones of the toes 15 The ... of the wrist 5, 6, 7, 8, the lower row of the bones of the wrist 9, 10, the lower ends of the bones of the fore-arm 11, 12, 13, 14, 15, the upper ends of the bones of the palm of the hand The ... ears?—"On the sides of my head." Which is the rim of the ear?— "The edge of the ear." Which is the flap of the ear?— "The lower part of the ear." Where is the drum of the ear?—"Inside of the ear."...

Ngày tải lên: 22/03/2014, 22:20

Ngày tải lên: 23/03/2014, 11:20

... link layer modeling The IEC 61158 series specifies a number of different fieldbus types in each of the parts of the series (Parts to 6) As a result of the editorial harmonization work done by ... operation IEC 61158-5 defines the services provided e) to the various user(s) of the fieldbus Application Layer at the boundary between the user(s) and the Application Layer of the fieldbus Reference ... provided by the fieldbus Data Link Layer in terms of a) the primitive actions and events of the service, b) the parameters associated with each primitive action and event, and the form which they take,...

Ngày tải lên: 04/04/2014, 12:18