This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Assignment #12 w Solutions  pd
ECSE—2410 Signals & Systems — Fall 2006 Fri 10/24/06 1(5). Consider the signal x(t)$3 cos(:rt)+—2cos(3ar)+ces(8m). Find the Nyquist sampling frequency, ms,
which guarantees that x(t) can be recovered from its samples. ii—gﬁeri
75% we > 258???) ﬁle??? i Marge melee. afar?” £12549: 8??“ I j 2(10). Find the largest sampling frequency, 605, so that the signal x(t)mcos(10z), when sampled and
appropriately ﬁltered, i.e.,with cutoff frequency, (06 2 32603. has an alias frequency of ca=5 rad/sec. Assignment #12 .... Solutions  p.2
ECSE2410 Signals & Systems  Fall 2006 Fri 10/24/06 4(10). Find the equation of the frequency response function H(co) whose straightniine Bode magnitude plot
is shown below. EvaIuate all constants. Assume the system is minimum phase, i.e., ail terms in H( co)
have positive signs" [H(a;) in dB +20dB/decade ~40dB/decade
A w Assignment #12 ~— Solutions » 13.3 ECSE~2410 Signals & Systems  Fall 2006 Fri 10/24/06 5(10). Use the Bode magnitude approximation to ﬁnd the approximate magnitude of 100[1+j—w] EM $6663} Y" ........ _ H(jm):“mm""ﬂ‘ﬂa:“ atmmle/I(l. m Gm)”. gm mil}. E“ (1+jw)£1+’;—0] wig it? E M
witﬁﬁ? 6(10). Find an expression for H(a)) so that the straightline Bode magnitude diagram shown crosses the
9 dB —axis at a} = 100 . Calculate all terms in your expression. Assume H ((0) is minimum phase.
H(m)[ in dB 20 a’Bﬁ'decacle 40 dBr'decade ‘ 20 dﬂidecade 10K 40 ddeecade Assignment #12  Soiutions « p.4
ECSE2410 Signals & Systems — Fail 2006 Fri i0/24/06 7(30). Indicate on all your sketches: DC gain (1H (0) in dB), break (corner) frequencies, and Slopes. 10 (a) Sketch the straight~line Bode Magnitude plot and sketch the Phase plot for H(w) m 5 _ .
+103 2.
Metzwg; ,2 zewwédg é ir’ifasii ég i (b) Find the gain crossover frequency, can, , of the straight line magnitude plot in (a), i.e., when H((oc)=1.
'2.
(Wm ‘3 e 2‘ mas3
* {We g. ”at. gwaeisi
e Assignment #12 — Solutions n 13.5
ECSE24IO Signals & Systems  Fall 2006 Fri 10/24/06 7(30). Indicate on all your sketches: DC gain (1H(O)J in dB), break (corner) frequencies, and slopes.
(0) Sketch the straightline Bode Magnitude plot and sketch the Phase plot for jaJSO
H :——————————.
(w) (1+jw5)(10+jw) (d) Find the phase crossover frequency, 606, of the phase piot in (c), 1.8., when LH(a)C) = 0. "L WM; wigs Z igaW' 5‘?
iﬁéﬁﬁgéfﬁ
' §
.. ﬁgmemgzwss an, %m% $me
9 Assignment #12 ~— Solutions  9.6
BCSE~2410 Signals & Systems — Fail 2006 Fri 10/24/06 7(30). indicate on ali your sketches: DC gain (!H(O)! in (18), break (comer) frequencies, and slopes.
10(1+;'a)) . ja)
a) 3+— [ 19] (6) Sketch the straight~iine Bode Magnitude and sketch the Phase plot for HUG) m (f) Find the gain crossover frequency, we , of the straight—line magnitude plot in (e), i.e., when Vitae) =E . Assignment #12 —— Solutions ~ [3.7
ECSE2410 Signals & Systems  Fall 2006 Fri 10/24/06 8(10). For the conﬁguration design a compensator G(a)) — Le. ﬁnd the frequency response, 6(a)) — so that the overall cascade
system H(w)mG( (0)8“;(03) satisﬁes both the following speciﬁcations: (:1) 1516:3121 for all frequencies M1000. (b) The straight line Bode magnitude plot ofH(a)) has a slope of —40 dB/decade for all
frequencies (@1000. Sketch the straight line Bode magnitude plots G( (0), H(w), and H1(co) all on the same plot. Label all
critical values. ...
View
Full Document
 Spring '07
 WOZNY

Click to edit the document details