...of the form: «W-^. where P(x) and Q(x) are polynomials. The fraction P(x)/Q(x) is called proper if the degree of the numerator is less than the degree of the denominator. Let m be the degree of the numerator P(x) and n the degree of the denominator Q(x). If m > n, then...

...numerator is greater than the degree of the denominator, the graph has no horizontal asymptote. (c) Since the degree of the numerator is less than the degree of the denominator, the x-axis, y = 0, is the horizontal asymptote. (¿0 Since numerator and denominator both have degree...

...symmetrically located with respect to the real axis. When a transfer function T(s) is strictly proper, ie, the degree of the numerator is less than the degree of the denominator, the inverse Laplace transform of T(s) represents a well-defined time function known as the impulse...

...degree of a polynomial is given by the highest power of the variable. An algebraic fraction in which the degree of the numerator is less than the degree of the denominator is called a proper fraction. If the algebraic fraction is not a proper fraction it is called an improper...

...Functions of this type are called rational functions. Let us first consider rational functions where the degree of the numerator is less than the degree of the denominator. There are two facts about polynomials which we will make use of: • Any polynomial can be factorised...

...proper and stable H(s). 10.4.2 Using the Impulse Invariance Method Only if H(s) is strictly proper (the degree of the numerator is less than the degree of the denominator) will the Impulse Invariance method give you correct results. 10.4.3 The Choice of the Sampling Interval...

...expressions can be written as a polynomial in x plus a proper rational function of x, one in which the degree of the numerator is less than the degree of the denominator. Let polynomial multiples of the first n of the y 's be subtracted from the later y 's in order to make...

...degree of a polynomial is given by the highest power of the variable. An algebraic fraction in which the degree of the numerator is less than the degree of the denominator is called a proper fraction. If the algebraic fraction is not a proper fraction it is called an improper...

...initial-value theorem requires the function V^s) to be a proper rational fraction. It is in this case because the degree of the numerator is less than the degree of the denominator. I can apply the initial-value theorem: c(0+)=lim(5FcW) = lim = 15V. 15 62500* + 200x10 s (s2 + 42500...

...thus: Integration of the remainder, which is then a proper rational function (that is, one in which the degree of the numerator is less than the degree of the denominator) is based on the decomposition of the fraction into elementary fractions, the so-called partial fractions....