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Approximation 1) Property of |N(jw)|2 associated to a function ration them N(s): to) |N(jw)|2 are a relationship of polinomi
equal in w ci² are obtained
replacing jw = s in b) replacing
2) massimamente flat Function: Function is one |N(jw)|2 that it is massimamente flat
to ridosso of the origin, remembering that |N(jw)|2 are a relationship of polinomi
equal
3) Function of Butterworth: It is proposed to us to realize one |N(jw)|2 massimamente flat therefore to = bthe i , of pass-low type therefore all the zeroes of transmission are to infinite and therefore all the b are zero like pure therefore to except that one of the maximum degree, are had:
where to the denominator there is w2n in how much |N(jw)|2 must be a relationship of
polinomi equal. The position of the poles is obtained that is
replacingjw = s w2= - s2 in |N(jw)|2 , are had to) for n uneven b) for n pari only the poles that are found in the left semiplan
are stable, they are
4) Polynomial di Butterworth: It is the polynomial that one finds denominator of the
function of Butterworth
5) Determination of the order of one function of Butterworth: The order nB of a function of Butterworth is 6) Denormalizzazione of frequency: The function of standardized Butterworth previews a
frequency of cut to 1 rad/sec for which Kp is 3dB, for having a various attenuation to the same
frequency, the pulsation is necessary to carry out the
denormalizzazione of
7) Polinomi di Chebyshev: where i polinomi Cn(w) is defined by means of one of following: to) b) c) d) they are such that the module is fair-ripple in
passing band and monotonic decreasing in dark band. The
pulsations w which an
attenuation of â?"3dB corresponds to the pulsation of 1rad/s are
given from the relation The poles are gained replacing
8) Determination of the order of one function of Chebyshev: Order nC of a
function of Chebyshev is 9) Function of inverse Chebyshev:
it introduces one characteristic fair-ripple in decreasing the dark and monotonic band in the passing band. It is obtained replacing w with 1/w in 10) Determination of the order of the function of inverse Chebyshev:
confronting this expression with that one found for the filter of Chebyshev it is had that they are equal on condition that is had
11) elliptic Filters: They are also sayings filters of fair-ripple Cauer and
introduce one characteristic is in dark band that in passing band
moreover is characterizes from one greater slope to you in
correspondence of the frequency of cut regarding the other typology
of filters. The typical shape of a elliptic filter is
12) Transformation from pass-high pass-low: If a pass-low function is defined in complex plan s = s jw by means of the
13) Transformation from pass-low to pass-band: If a pass-low function is defined in complex plan s = s jw by means of the
14) Realization of a filter pass-band of Broad-Band type: It is a filter pass-band with a greater bandwidth regarding the standardized filter, denormalizzazione in frequency is obtained then operating one on the pass-low filter and executing the transformation pass-low® pass-band. 15) Realization of a filter eliminate-band: It is necessary to apply the
16) Approximation of tight band: A filter pass-band is said to be to tight band if its
bandwidth is smaller of tenth regarding the center frequency a band
that is if |