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7/31/2019 DSP Problems_dsp1_co thuc_full, dsp1, co thuc, xu li tin hieu, bkdn, dsp
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BI TP CHNG 1
7/31/2019 DSP Problems_dsp1_co thuc_full, dsp1, co thuc, xu li tin hieu, bkdn, dsp
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Bi 1 - Tnh tn s ly mu
Cho mt tn hiu lin tc c ph t 120-160 kHz. Vph 2 pha ca tn hiu ri rc c c bng cch ly
mu tn hiu trn vi 3 tn s ly mu khc nhau sau
y :
fs = 80 kHz
fs = 100 kHz
fs = 120 kHzTn s ly mu thch hp l bao nhiu trong 3 tn s
trn? Gii thch
7/31/2019 DSP Problems_dsp1_co thuc_full, dsp1, co thuc, xu li tin hieu, bkdn, dsp
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Bi 2 - Quan h tn s
Cho tn hiu tng t:
a) Xc nh tn s ly mu nh nht trnh chng ph
b) Gi s tn hiu trn c ly mu vi tn s fS = 200
Hz, tn hiu ri rc sau ly mu l g ?c) Gi s tn hiu trn c ly mu vi tn s fS = 75 Hz,
tn hiu ri rc sau ly mu l g ?
d) Xc nh tn s (0 < f < fS) ca tn hiu sin c cc mutrn vi cc mu ca tn hi u c
ax (t) 3cos100 t
7/31/2019 DSP Problems_dsp1_co thuc_full, dsp1, co thuc, xu li tin hieu, bkdn, dsp
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7/31/2019 DSP Problems_dsp1_co thuc_full, dsp1, co thuc, xu li tin hieu, bkdn, dsp
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Bi 4 - Quan h tn s
Cho tn hiu tng t :
a) Xc nh tn s Nyquist
b) Gi s tn hiu c ly mu vi tc 5000 (mu/s),
tm tn hiu ri rc c c sau ly mu
c) Xc nh tn hiu tng t ya(t) khi phc t tn hiu
ri rc (gi s ni suy l tng)
a
x (t) 3cos2000 t+5sin6000 t+10cos12000 t
7/31/2019 DSP Problems_dsp1_co thuc_full, dsp1, co thuc, xu li tin hieu, bkdn, dsp
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Cu hiCu 1:Nu s khc nhau gia tn hiu tng t v
tn hiu s.
Cu 2:Tn hiu tng t c chuyn thnh s,
sau chuyn li thnh tng t (khng qua DSP).
Hi tn hiu tng t ra c khc tn hiu tng tvo hay khng? Gii thch.
Cu 3:Phn tch cc u khuyt im ca x l s
so vi x l tng t
7/31/2019 DSP Problems_dsp1_co thuc_full, dsp1, co thuc, xu li tin hieu, bkdn, dsp
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BI TP CHNG 2
7/31/2019 DSP Problems_dsp1_co thuc_full, dsp1, co thuc, xu li tin hieu, bkdn, dsp
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Bi 1 - Cc php ton trn tn hiuri rc
a) Cho
V th ca:
b) V th ca tn hiu: x[n] = u[ 3 - n ]
c) Cho x[n] = 2u[n+2].Tm v v z[n] = x[3-2n]
d) Cho y[n] = anu[n], a>1.Tm v v z[n] = y[-2n+2]
[ ] [ ]n
x n a u n 1a
[ ] [ 3]y n x n
7/31/2019 DSP Problems_dsp1_co thuc_full, dsp1, co thuc, xu li tin hieu, bkdn, dsp
9/51
Bi 2 - Cc php ton trn tn hiuri rc
Cho
a)V th tn hiu x[n]
b) V th tn hiu x[-n+4], x[-n-4],
c) Biu din x[n]theo tn hiu dirac v tn hiu bc nhy
elsewhere,0
3n0,1
1n3,3
n1
]n[x
7/31/2019 DSP Problems_dsp1_co thuc_full, dsp1, co thuc, xu li tin hieu, bkdn, dsp
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Bi 3 - Tn hiu ri rctun hon
Cc tn hiu sau c tun hon khng? Nu
c, tnh chu k c bn
a)
b)
4[ ] cos(1 2 )x n n
35[ ]
nj
x n e
7/31/2019 DSP Problems_dsp1_co thuc_full, dsp1, co thuc, xu li tin hieu, bkdn, dsp
11/51
Bi 4Tnh nhn qu ca h ri rc
Xt tnh nhn qu ca cc h thng ri rc sau:
a)
b)
n
k
]k[x]n[y
]4n[x3]n[x]n[y
7/31/2019 DSP Problems_dsp1_co thuc_full, dsp1, co thuc, xu li tin hieu, bkdn, dsp
12/51
Bi 5Tnh n nh ca h ri rc
Xt tnh n nh ca cc h thng ri rc sau:
a)
b)
[ ] cos( [ ])y n x n
[ ] [ ]n
k
y n x k
7/31/2019 DSP Problems_dsp1_co thuc_full, dsp1, co thuc, xu li tin hieu, bkdn, dsp
13/51
Bi 6Tnh tuyn tnh bt bin ca h
Xt tnh tuyn tnh bt bin ca cc h thng ri rcsau:
[ ] cos( [ ])y n x n
[ ] [ ]n
k
y n x k
0
[ ] [ ]n
k
y n x k
[ ] [ ] [ ]y n x n u n
7/31/2019 DSP Problems_dsp1_co thuc_full, dsp1, co thuc, xu li tin hieu, bkdn, dsp
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Bi 7Tnh p ng xung ca h LTI
Cho h LTI c quan h vo-ra sau:
y[n] 0.9y[n-1] = x[n] + 2x[n-1]+3x[n-2]
a) Tnh p ng xung bng phng php th
b) V s thc hin h trn
c) Xt tnh n nh ca h
7/31/2019 DSP Problems_dsp1_co thuc_full, dsp1, co thuc, xu li tin hieu, bkdn, dsp
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Bi 8Tnh tng chp tuyn tnh
a) Xc nh p ng ca h LTI c p ng xung sau:
h[n] = an u[n] i vi tn hiu vo l:
x[n] = u[n] u[n-10]
Gi :S dng tnh cht tuyn tnh bt bin
.
[ ] [ ]x n u n
[ ] [ 2] 1nh n a u n a
2
[2 ] [ 3]
1 1
na a
u n u n
a a
b) Chng minh rng khi cho tn hiu
i qua h thng LTI c p ng xung l:
th tn hiu ra l:
7/31/2019 DSP Problems_dsp1_co thuc_full, dsp1, co thuc, xu li tin hieu, bkdn, dsp
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Bi 9Tnh tng chp tuyn tnh
Cho h LTI c s nh hnh sau:
Xc nh h[n], cho bit:
]2n[]n[h
]n[u)1n(]n[h]n[h
2/1,4/1,2/1]n[h
4
32
1
h1[n]h2[n]
h3[n] h4[n]
7/31/2019 DSP Problems_dsp1_co thuc_full, dsp1, co thuc, xu li tin hieu, bkdn, dsp
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Bi 10Xc nh quan h vo-ra
Cho h LTI c s nh sau:
a) Xc nh phng trnh vo-ra
Z-1
Z-1
23
4
b) H trn c n nh khng?
7/31/2019 DSP Problems_dsp1_co thuc_full, dsp1, co thuc, xu li tin hieu, bkdn, dsp
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Bi 11 - Gii phng trnh sai phn
0n],n[y
]1n[x2]n[x]2n[y4]1n[y3]n[y
Tm
ca h sau:
vi x[n] = 4n u[n] v cc iu kin u bng 0
7/31/2019 DSP Problems_dsp1_co thuc_full, dsp1, co thuc, xu li tin hieu, bkdn, dsp
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BI TP CHNG 3
7/31/2019 DSP Problems_dsp1_co thuc_full, dsp1, co thuc, xu li tin hieu, bkdn, dsp
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Bi 1Tnh bin i Z thun
Tm bin i Z v min hi t ca cc tn hiu sau y:
0n0
0n2]n[h)d
0n)(
0n)(
]n[v)c
4n0
5n)(]n[y)b
4,1,6,0,0,0,0,3]n[x)a
nn
31
n21
n
31
n
2
1
7/31/2019 DSP Problems_dsp1_co thuc_full, dsp1, co thuc, xu li tin hieu, bkdn, dsp
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Bi 2Tnh bin i Z thun
Tm bin i Z v min hi t ca cc tn hiu sau y davo cc tnh cht v bng bin i Z:
])10n[u]n[u(]n[h)d
]1n[un]n[v)c
]n[u2)1(]n[y)b
]n[u)n1(]n[x)a
n
21
1n
3
1
2
1
nn
7/31/2019 DSP Problems_dsp1_co thuc_full, dsp1, co thuc, xu li tin hieu, bkdn, dsp
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Bi 3Tnh bin i Z ngc
a) Tm bin i Z ngc sau bng phng php
khai trin thnh chui ly tha:
1|z|zz21
z21)z(X
21
1
b) Tm cc bin i Z ngc sau bng phng php khai
trin ring phn:
2|z|)z5.01)(z2z21(
zz61
4
1)z(X)c
2|z|z2z31
z31)z(X)b
2|z|
)z1)(z21(
1)z(X)a
121
21
21
1
211
7/31/2019 DSP Problems_dsp1_co thuc_full, dsp1, co thuc, xu li tin hieu, bkdn, dsp
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Bi 4Tnh bin i Z ngc
Tm cc tn hiu x[n] nhn qu nu X(z) nh sau :
21
21
2
2
1
76
2
211
z4z41
zz21)z(X)d
z1
z21
)z(X)c
z1zz)z(X)b
zz1
1)z(X)a
7/31/2019 DSP Problems_dsp1_co thuc_full, dsp1, co thuc, xu li tin hieu, bkdn, dsp
24/51
Bi 5im cc v im khng
a) Tm X(z) bit X(0) = 1v cc im cc khng nh sau:
b) Tm x[n] nhn qu t X(z) trn
x
x
x
-1/2 -1/4 1/2
2/1r
7/31/2019 DSP Problems_dsp1_co thuc_full, dsp1, co thuc, xu li tin hieu, bkdn, dsp
25/51
Bi 6ng dng ZT tnh tng chp
Tnh tng chp ca cc cp tn hiu sau y:
]1n[u2]n[h,]n[nu]n[x)d
]n[u).ncos(]n[h,]n[u)(]n[x)c
]n[u)(]n[]n[h,]n[u]n[x)b
]n[u])(1[]n[h,]1n[u]n[x)a
n
n
21
n
21
n
21n
41
7/31/2019 DSP Problems_dsp1_co thuc_full, dsp1, co thuc, xu li tin hieu, bkdn, dsp
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Bi 7Tnh cht o hm
a) Tm bin i Z ca tn hiu nx[n] v n2x[n] theo X(z)
b) ng dng kt qu cu (a) tnh cc bin i Z sau:
]1n[una]n[x)c]n[nusinna]n[x)b
]1n[u))(nn(]n[x)a
n
0
n
1n
312
21
7/31/2019 DSP Problems_dsp1_co thuc_full, dsp1, co thuc, xu li tin hieu, bkdn, dsp
27/51
Bi 8Phn tch h thng
a) H thng nhn qu sau c n nh khng?
)z2.01)(z5.01)(z1(zz2z21)z(H 111
321
b) Tnh p ng xung v p ng bc ca h trn
7/31/2019 DSP Problems_dsp1_co thuc_full, dsp1, co thuc, xu li tin hieu, bkdn, dsp
28/51
Bi 9Phn tch h thng
Cho h thng sau:
2
25
21
5
3
2
211
zz1
zz)z(H
a) Tnh p ng xung ca h trn
b) Tnh p ng bc trng thi 0 v p ng bc viiu kin u l y(-1) = 1 v y(-2) = 2
c) V s thc hin h trn
7/31/2019 DSP Problems_dsp1_co thuc_full, dsp1, co thuc, xu li tin hieu, bkdn, dsp
29/51
Bi 10Tng hp h thng
Ta mun thit k mt h thng tha mn iu kin sau:
Khi cho x[n] = (0.5)nu[n] -0.25(0.5)n-1u[n-1]
i vo h thng th u ra thu c y[n] = (1/3)nu[n]
a) Tm h[n] ca h trn
b) Tm H(z) ca h trn
c) Xc nh phng trnh sai phn m t quan h vo-ra
d) Xy dng s thc hin h trn
e) H trn c n nh khng? V sao?
7/31/2019 DSP Problems_dsp1_co thuc_full, dsp1, co thuc, xu li tin hieu, bkdn, dsp
30/51
Bi 11Tng hp h thng
p ng bc ca mt h LTI l:
s[n] = (1/3)n-2 .u[n+2]
a) Tm H(z) ca h trn
b) Tm h(n) ca h trn
c) Biu din cc im cc khng trn mt phng z
d) H trn c n nh khng? C nhn qu khng?
7/31/2019 DSP Problems_dsp1_co thuc_full, dsp1, co thuc, xu li tin hieu, bkdn, dsp
31/51
Bi 12Gii phng trnh sai phn
Tm y[n]vi n>=0trong cc trng hp sau:
1]2[y;0]1[y;]n[u]n[x
;]n[x]2n[y]n[y)d
;1]1[y;]n[u]n[x
;]n[x]1n[y]n[y)c
0]2[y;1]1[y;0]2n[y5.0]1n[y5.1]n[y)b
1]2[y]1[y
;0]2n[y]1n[y]n[y)a
41
n
31
21
41
21
7/31/2019 DSP Problems_dsp1_co thuc_full, dsp1, co thuc, xu li tin hieu, bkdn, dsp
32/51
BI TP CHNG 4
7/31/2019 DSP Problems_dsp1_co thuc_full, dsp1, co thuc, xu li tin hieu, bkdn, dsp
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Bi 1Bin i Fourier thun
Tm bin i DTFT ca cc tn hiu sau y:
]6n[u]n[u]n[w)e
]n[u)nsin(a]n[h)d]n[u2]n[v)c
4|n|04|n|n)(2]n[y)b
2,1,0,1,2]n[x)a
0
n
n
2
1
7/31/2019 DSP Problems_dsp1_co thuc_full, dsp1, co thuc, xu li tin hieu, bkdn, dsp
34/51
Bi 2Bin i Fourier thun
Tm bin i DTFT ca cc tn hiu sau y:
1,0,0,1,0,0,1,0,0,1,0,0,1]n[x)c1,0,1,0,1,0,1,0,1]n[x)b
1,1,1,1,1]n[x)a
3
2
1
Tm mi quan h gia cc DTFT trn.
7/31/2019 DSP Problems_dsp1_co thuc_full, dsp1, co thuc, xu li tin hieu, bkdn, dsp
35/51
Bi 3Tnh bin i Fourier ngc
Tnh tn hiu x[n], cho bit bin i DTFT nh hnh v sau:
2
1
7/31/2019 DSP Problems_dsp1_co thuc_full, dsp1, co thuc, xu li tin hieu, bkdn, dsp
36/51
Bi 4Cng thc DTFT thun & ngc
Cho tn hiu sau y:
1,2,3,2,1]n[x
Tnh cc i lng sau m khng cn tnh DTFT:
)(X)d(d)(X)c()(X)b()0(X)a(
7/31/2019 DSP Problems_dsp1_co thuc_full, dsp1, co thuc, xu li tin hieu, bkdn, dsp
37/51
Bi 5Tnh cht ca DTFT
Cho tn hiu x[n] c DTFT sau y:
jae1
1)(X
Tnh DTFT ca cc tn hiu sau y:
]2n[xe)d()n3.0cos(]n[x)c(]1n[x]n[x)b(]n2[x)a(
2/nj
7/31/2019 DSP Problems_dsp1_co thuc_full, dsp1, co thuc, xu li tin hieu, bkdn, dsp
38/51
Bi 6Ph bin v ph phaTm v v ph bin v ph pha ca cc tn hiu sau y:
]3n[]2n[3]1n[3]n[81
]n[x)g
]2n[]n[2
1]n[x)f
]2n[]n[2
1]n[x)e
]1n[]1n[2
1]n[h)d
]1n[]1n[21]n[x)c
]1n[]n[2
1]n[x)b
]1n[]n[21]n[x)a
7/31/2019 DSP Problems_dsp1_co thuc_full, dsp1, co thuc, xu li tin hieu, bkdn, dsp
39/51
Bi 7p ng trng thi bn & png nht thi
Xc nh p ng trng thi bn v p ng nht thi
ca h sau:
]2n[x]n[x21
]n[y
i vi tn hiu vo l:
n60n
2cos35]n[x 0
7/31/2019 DSP Problems_dsp1_co thuc_full, dsp1, co thuc, xu li tin hieu, bkdn, dsp
40/51
Bi 8p ng i vi tn hiu vodng hm m phc v sin/cos
]10n[x]n[x]n[y
Cho b lc FIR:
n2
n5
2cos510]n[x)2(
n10
n3
sin3n10
cos]n[x)1(
a) Tnh v v p ng bin v p ng pha
a) Tnh p ng ca h thng i vi cc tn hiu vo sau:
7/31/2019 DSP Problems_dsp1_co thuc_full, dsp1, co thuc, xu li tin hieu, bkdn, dsp
41/51
Bi 9B lc
Xc nh cc h s ca b lc FIR sau:
]2n[xb]1n[xb]n[xb]n[y210
sao cho tha mn cc iu kin sau:
1. H(0) = 1
2. B lc ny ngn hon ton thnh phn tn s 3/20
7/31/2019 DSP Problems_dsp1_co thuc_full, dsp1, co thuc, xu li tin hieu, bkdn, dsp
42/51
Bi 10B lcp ng tn s ca mt b lc thng di l tng nh sau:
||8
30
8
3||
8
1
8||0
)(H
a) Tnh p ng xung
b) Chng minh rng c th biu din p ng xung ny
di dng tch ca v p ng xung ca
mt b lc thng thp
)4/ncos(
7/31/2019 DSP Problems_dsp1_co thuc_full, dsp1, co thuc, xu li tin hieu, bkdn, dsp
43/51
BI TP CHNG 5
7/31/2019 DSP Problems_dsp1_co thuc_full, dsp1, co thuc, xu li tin hieu, bkdn, dsp
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Bi 1 - Tnh DTFT ca tn hiu tun hon
0[ ] [ ] 2 [ 2]x n n n
0 ( )X ( )X
Cho tn hiu x[n] tun hon vi chu k l N = 3
v mt chu k l:
Tm
Kim tra kt qu bng cch tnh DTFT ngc khi phc
li x[n]
v
7/31/2019 DSP Problems_dsp1_co thuc_full, dsp1, co thuc, xu li tin hieu, bkdn, dsp
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7/31/2019 DSP Problems_dsp1_co thuc_full, dsp1, co thuc, xu li tin hieu, bkdn, dsp
46/51
Bi 3 - Tnh DFT ca tn hiu di hu hn
Cho 5 mu u tin ca DFT 8 mu ca mt tn hiu thc l:
Xc nh 3 mu cn li
0,0518.0j125.0,0,3018.0j125.0,25.0
7/31/2019 DSP Problems_dsp1_co thuc_full, dsp1, co thuc, xu li tin hieu, bkdn, dsp
47/51
Bi 4 - Tnh DFT ca tn hiu di hu hn
Tnh DFT N mu ca cc tn hiu sau:
1Nn0oddn0
evenn1]n[x)c(
]}Nn[u]n[u{a]n[x)b(
]n[]n[x)a(n
7/31/2019 DSP Problems_dsp1_co thuc_full, dsp1, co thuc, xu li tin hieu, bkdn, dsp
48/51
Bi 5 - Tnh cht tng chp vng
Cho cc tn hiu sau v cc DFT 5 mu ca chng:
]n[]n[s)c(
]1n[]n[x)b(
]4n[4]3n[3]2n[2]1n[]n[x)a(
2
1
a) Tm y[n] sao cho Y[k] = X1[k].X2[k]
b) Dy x3[n] c tn ti khng, nu S[k] = X1[k].X3[k]
7/31/2019 DSP Problems_dsp1_co thuc_full, dsp1, co thuc, xu li tin hieu, bkdn, dsp
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Bi 6 - Tnh cht dch vng
7n4,0
3n0,1]n[x
Cho DFT 8 mu ca tn hiu x[n] sau, l X[k]:
Tnh DFT ca cc tn hiu sau theo X[k]:
7n6,0
5n2,1
1n0,0
]n[x)b(
7n5,1
4n1,0
0n,1
]n[x)a(
2
1
Bi Th FFT 2 h
7/31/2019 DSP Problems_dsp1_co thuc_full, dsp1, co thuc, xu li tin hieu, bkdn, dsp
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Bi 7 - Thut ton FFT c s 2 phnthi gian
n,0
3n0,2/1]n[x
Tnh DFT 8 mu ca tn hiu x[n] sau:
s dng thut ton FFT c s 2 phn thi gian.
Yu cu v lu v ghi y cc gi tr ca tt c cc nt
trong lu
Bi 8 Th t t FFT 2 h
7/31/2019 DSP Problems_dsp1_co thuc_full, dsp1, co thuc, xu li tin hieu, bkdn, dsp
51/51
Bi 8 - Thut ton FFT c s 2 phnthi gian
V lu thut ton FFT phn thi gian tnh ti ch vi
N = 16trong hai trng hp:
1/ Cc gi tr vo sp xp theo th t t nhin
2/ Cc gi tr vo sp xp theo trt t o bit