Bilinear Transformation Method (Mathematics in Science and Engineering)

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Essential topics from college algebra and trigonometry for students intending to enroll in calculus. Function concepts. Polynomial, rational, exponential, and logarithmic functions. Systems of equations and inequalities. Matrices and determinants. Sequences and series. Analytic geometry and conic sections. Trigonometric functions; graphs, identities, equations, inequalities; inverse trigonometric functions; solutions of triangles with applications; complex numbers; polar coordinates.

Theory of arithmetic of whole numbers, fractions, and decimals. Introduction to algebra, estimation and problem-solving strategies. Last Taught: Spring , Fall , Spring A continuation of MATH in geometry, statistics, and probability. Specific topics are announced in the Schedule of Classes each time the class is offered.

Course Rules: Open only to freshmen. Regularly offered courses may not be taken as Independent Study. Prerequisites: 2. Elementary deterministic and probabilistic discrete mathematics and applications to a wide variety of disciplines. Topics may include linear programming, Markov chains, optimization, stochastic processes. A one-semester survey with applications to business administration, economics, and non-physical sciences.

Topics include coordinate systems, equations of curves, limits, differentiation, integration, applications. Course Rules: May not be used as a prereq for Math No cr for students with cr in Math , , or Limits, derivatives, graphing.

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Antiderivatives, the definite integral, and the fundamental theorem of calculus. Additional techniques and applications pertinent to the life sciences throughout the course. Calculus of functions of one and several variables; sequences, series, differentiation, integration; introduction to differential equations; vectors and vector functions; applications. Limits, derivatives, and graphs of algebraic, trigonometric, exponential, and logarithmic functions; antiderivatives, the definite integral, and the fundamental theorem of calculus, with applications.

Continuation of Math Applications of integration, techniques of integration; infinite sequences and series; parametric equations, conic sections, and polar coordinates. Continuation of MATH Three-dimensional analytic geometry and vectors; partial derivatives; multiple integrals; vector calculus, with applications. Elementary differential equations.

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Vectors; matrices; linear transformations; quadratic forms; eigenvalues; applications. Prerequisites: grade of C or better in Math P. Vectors, vector spaces, systems of linear equations, matrices, determinants, linear transformations, diagonalization, eigenvalues, eigenvectors; selected topics from quadratic forms, difference equations, numerical methods, and applications. Course provides a strong foundation in the exploration, teaching and communication oral and written of mathematical concepts via problem-solving experiences and discussion.

Prerequisites: grade of C or better in Math P or cons instr. Topics for K-8 teachers. Basic patterns and rules that govern number systems, geometric transformations, and manipulation of algebraic expressions. Geometry as measuring tool-congruence, similarity, area, volume, and coordinates; geometry as axiomatic system-definitions, conjectures, proofs, counterexamples; rigid motions, symmetry. Course Rules: Math and MthStat are jointly offered; they count as repeats of one another. Specific topics and any additional prerequisites announced in Schedule of Classes each time course is offered.

Prerequisites: acceptance for Study Abroad Prog. Course created expressly for offering in a specified enrollment period. In exceptional circumstances, can be offered in one add'l sem. Prerequisites: none; add'l prereqs may be assigned to specific topic. Construction and analysis of discrete and continuous mathematical models in applied, natural, and social sciences. Elements of programming, simulations, case studies from scientific literature. Examination of annuities, loans, bonds, portfolio immunization, and interest rate swaps.

Primal and dual formulations of linear programming problems; simplex and related methods of solution; algorithms for transportation; optimization. Introduction to operations research. Network analysis; integer programming; game theory; nonlinear programming; dynamic programming. Number theory topics related to cryptography; discrete structures including graphs, partial orders, Latin squares and block designs; advanced counting techniques.

Elementary types and systems of differential equations, series solutions, numerical methods, Laplace transforms, selected applications. Topics selected from vector algebra; scalar and vector fields; line, surface, and volume integrals; theorems of Green, Gauss, and Stokes; vector differential calculus. Prerequisites: jr st, grade of C or better in Math P ; or grad st.

Partial differential equations of mathematical physics, boundary value problems in heat flow, vibrations, potentials, etc. Solved by Fourier series; Bessel functions and Legendre polynomials. Facility with mathematical language and method of conjecture, proof and counter example, with emphasis on proofs. Topics: logic, sets, functions and others. Topics from the development of mathematics, such as famous problems, mathematicians, calculating devices; chronological outlines.

Significant reading and writing assignments. Add'l prereqs announced in SOC each offering. Elementary modeling of financial instruments for students in mathematics, economics, business, etc. Statistical and stochastic tools leading to the Black-Scholes model. Real data parameter fitting.

Significant topics to illustrate to non-mathematicians the characteristic features of mathematical thought. Only H. Prerequisites: soph st; Honors P ; cons Honors College dir. Not open for cr toward a major in Math. Modeling techniques for analysis and decision-making in social and life sciences and industry. Deterministic and stochastic modeling. Topics may vary with instructors. From H z , the difference equation is obtained whose solution y nT approximates the actual differential solution y t. If this is your thesis or dissertation, and want to learn how to access it or for more information about readership statistics, contact us at STARS ucf.

Retrospective Theses and Dissertations. University of Central Florida. College of Engineering [LC]. Engineering Commons.

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Why impulse invariant method is not preferred in the design of IIR filters other than low pass filter? Write the steps in designing chebyshev filter. Find the order of the filter. Find the value of major and minor axis. Calculate the poles. Find the denominator function using the above poles. The numerator polynomial value depends on the value of n. Write down the steps for designing a Butterworth Low pass filter. From the given specifications find the order of the filter N.

Find the transfer function h s for the value of N 3. Find the cut off frequency gc 4. Distinguish between Butterworth and Chebyshev filter. No Butterworth filters Chebyshev filters 1 The magnitude response H jw The magnitude response of the Chebyshev of the butter-worth filter filter fluctuates or show ripples in the pass decreases with increase in band and stop band depending on the type frequency from 0 to infinity of the filter.

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What are the main advantages and disadvantages of bilinear transformation? What are the different types of structures for realization of IIR systems? The different types of structures for realization of IIR system are. What are the disadvantages of direct form realization? Define condition for stability.

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The left half plane of S plane should map into the inside of the unit circle in the z plane. Thus a stable analog filter will be converted to a stable digital filter. FIR filters can be realized recursively IIR filters can be realized 2 and non-recursively recursively Greater flexibility to control the shape Less flexibility, usually limited to 3 of their magnitude response kind of filters Errors due to round-off noise are less The round-off noise in IIR filters 4 severe in FIR filters, mainly because are more feedback is not used What is the expression for the order and poles of chebyshev filter?

What is the expression for order and poles of Butterworth filter? What is the necessary and sufficient condition for linear phase characteristics in FIR filter? What are the properties of FIR filter? It does not depend on previous output. What are the desirable characteristics of the windows? This abrupt truncation of impulse response introduces oscillations in the pass band and stop band. FIR filters can be realized recursively IIR filters can be realized 2 and non-recursively recursively Greater flexibility to control the shape Less flexibility, usually limited to 3 of their magnitude response kind of filters Errors due to round-off noise are less The round-off noise in IIR filters 4 severe in FIR filters, mainly because are more feedback is not used 7.

What is linear phase characteristic of an FIR filter? What are the characteristics of FIR filters designed using windows. Give hamming window function. What is the reason that FIR filter is always stable? This means FIR filter poles are always inside the unit circle. Hence FIR filters are always stable. Write the equation of blackman window function. Compare the rectangular window and Hanning window. Compare the rectangular window and hamming window. Give rectangular window function. Give hanning window function. What are the disadvantages of FIR filter?

List the well known design technique for linear phase FIR filter design. Under what conditions a finite duration sequence h n will yield constant group delay in its frequency response characteristics and not the phase delay? Write the steps involved in FIR filter design. Choose the desired frequency response H d w. Take the inverse Fourier transform and obtain hd n 3.

Take Z transform of h n to get H Z. What are the conditions on the FIR sequence h n are to be imposed N order that this filter can be called a liner phase filter? Define filter coefficients. Filter Coefficients are the set of constants, also called tap weights, used to multiply against delayed sample values. For an FIR filter, the filter coefficients are, by definition, the impulse response of the filter.

Define impulse response. An impulse is a single unity-valued sample followed and preceded by zero-valued samples. What is the principle of designing FIR filter using frequency sampling method? In frequency sampling method, a set of sample is determined from the desired frequency response and are identified as discrete Fourier transform coefficients. N-1 uniformly spaced around the unit circle. Define tap of FIR filter. The number of FIR taps, typically N, tells us a couple things about the filter. Most importantly it tells us the amount of memory needed, the number of calculations required, and the amount of "filtering" that it can do.

Basically, the more taps in a filter results in better stop band attenuation, less rippling less variations in the pass band , and steeper roll off a shorter transition between the pass band and the stop band. What are the conditions to be satisfied for constant phase delay in linear phase FIR filters? What are the possible types of impulse response for linear phase FIR filters? Write the characteristic features of rectangular window. List the features of FIR filter designed using rectangular window.

Why the limit cycle problem does not exist when FIR digital filter is realized in direct form or cascade form? In case of FIR filter there are no limit cycle oscillations, if the filter is realized in direct form or cascade form since these structures have no feedback. Compare Hamming window with Kaiser Window. Compare the fixed point and floating point arithmetic. No Fixed point arithmetic. Floating point arithmetic. Define dead band [Dec ] or What is meant by "dead band" of the filter?

The amplitudes of the output during a limit cycle are confined to a range of values called the dead band of the filter. What is finite word length effect? Input quantization error 2.

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Coefficient quantization error 3. Product quantization error 4. Why rounding is preferred to truncation in realizing digital filter? Let bu -b bits truncated. What are the quantization methods? What is input quantization error? The filter coefficients are computed to infinite precision in theory. But in digital computation the filter coefficients are represented in binary and are stored in registers. If a b bit register is used the filter coefficients must be rounded or truncated to b bits, which produces an error. What is product quantization error?


The product quantization errors arise at the output of the multiplier. Multiplication of a b bit data with a b bit coefficient results a product having 2b bits. Since a b bit register is used the multiplier output will be rounded or truncated to b bits which produce the error. What is zero limit cycle oscillation? For an IIR filter, implemented with infinite precision arithmetic the output should approach zero in the steady state if the input is zero. Such oscillations in recursive systems are called zero input limit cycle oscillations. What is overflow error?

What are the methods to eliminate the overflow? What are the methods used to prevent overflow? In case of adding two fixed-point arithmetic numbers the sum exceeds the word size available to store the sum which cause overflow error. This overflow caused make the filter output to oscillate between maximum amplitude limits. Such limit cycles have been referred to as over flow oscillations There are two methods used to prevent overflow 1.

Saturation arithmetic 2. Scaling What are the different types of arithmetic in digital systems? There are three types of arithmetic used in digital system 1.