Skip part 54. The signal x[r] = (1. –2,3, –4,0.4. –3,2. –1). has Fourier transform X(e»"). Find the following quantities without explicitly computing X(e"): (d) X(e" ), (e) L", \X(e)Fd£2. 2b) O&S 2.36 parts a and b only. 2.36. An LTI diserete-time system has froquency response given by (a) Use one of the above forms of the frequency response to obtain an equation for the impulse response Ale] of the system. (b) From the frequency response, determine the difference equation that is satistied by the input x[n] and the output yln] of the system. rch O Ai 26°C
Skip part 54. The signal x[r] = (1. –2,3, –4,0.4. –3,2. –1). has Fourier transform X(e»"). Find the following quantities without explicitly computing X(e"): (d) X(e" ), (e) L", \X(e)Fd£2. 2b) O&S 2.36 parts a and b only. 2.36. An LTI diserete-time system has froquency response given by (a) Use one of the above forms of the frequency response to obtain an equation for the impulse response Ale] of the system. (b) From the frequency response, determine the difference equation that is satistied by the input x[n] and the output yln] of the system. rch O Ai 26°C
Introductory Circuit Analysis (13th Edition)
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I ned answers for 2 a) and 2 b)
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30. Determine and plot the DTFT magnitude and phase spectra of the following signals:
(a) x1[n] = (1/3)" u[n – 1],
(b) x2[n] = (1/4)" cos(1n/4)u[n – 2],
(c) x3[n] = sinc(27 n/8) * sinc{2r (n – 4)/8},
(d) ха[n] 3 sin(0.1лп)(и(n] — и(п — 10),
(e) x5[n] = sinc² (Tn/4).
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31. Determine the sequence x[n] corresponding to each of the following Fourier trans-
forms:
(a) X(ej®) = 8(@) – 8(@ – 1 /2) – 8(@+r/2),
(b) X(ej®) = 1, 0 < lwl < 0.27 and X(ej@) = 0, 0.27 < |@[ < 1
(c) X(ei«) = 2|w|/T, 0 < |@| < 1/2 and X(ej®) = 0, 7 /2 < |@l < r
(d) With Aw > 0 and we > Aw/2, X(el@) is given by
Aw
|0,
< lwl < @c + Aw
Wc
2
X(ej@)
1.
otherwise
2a) M&I 4.54, skip part b
54. The signal x[n] = {1, –2,3, –-4,0,4, –3, 2, – 1}, has Fourier transform X(ejo). Find
the following quantities without explicitly computing X(ej@):
(a) X(e®), (b) ZX(ej®), (c) ƒ*, X(ei®)d2,
(d) X(ej™), (e) /¨, |X(ej@)]²ds2.
2b) O&S 2.36 parts a and b only.
2.36. An LTI discrete-time system has frequency response given by
+ je-jw)
1 – 0.8e-jw
(1 – je-j@(1
-j2w
1+e-j2w
1
H(ej®) =
1 – 0.8e-j@
1– 0.8e-jw
1 – 0.8e-j@'
(a) Use one of the above forms of the frequency response to obtain an equation for the
impulse response h[n] of the system.
(b) From the frequency response, determine the difference equation that is satisfied by
the input x[n] and the output y[n] of the system.
8:03 PM
Type here to search
26°C
W
22-Feb-22](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa9dbd869-ff64-4775-b981-88c991fe888a%2Fda52e469-69d0-4a2e-8f20-dadcbce8dafd%2F273uu3e_processed.png&w=3840&q=75)
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30. Determine and plot the DTFT magnitude and phase spectra of the following signals:
(a) x1[n] = (1/3)" u[n – 1],
(b) x2[n] = (1/4)" cos(1n/4)u[n – 2],
(c) x3[n] = sinc(27 n/8) * sinc{2r (n – 4)/8},
(d) ха[n] 3 sin(0.1лп)(и(n] — и(п — 10),
(e) x5[n] = sinc² (Tn/4).
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1b) M&I 4.31, parts a, b, and d only
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31. Determine the sequence x[n] corresponding to each of the following Fourier trans-
forms:
(a) X(ej®) = 8(@) – 8(@ – 1 /2) – 8(@+r/2),
(b) X(ej®) = 1, 0 < lwl < 0.27 and X(ej@) = 0, 0.27 < |@[ < 1
(c) X(ei«) = 2|w|/T, 0 < |@| < 1/2 and X(ej®) = 0, 7 /2 < |@l < r
(d) With Aw > 0 and we > Aw/2, X(el@) is given by
Aw
|0,
< lwl < @c + Aw
Wc
2
X(ej@)
1.
otherwise
2a) M&I 4.54, skip part b
54. The signal x[n] = {1, –2,3, –-4,0,4, –3, 2, – 1}, has Fourier transform X(ejo). Find
the following quantities without explicitly computing X(ej@):
(a) X(e®), (b) ZX(ej®), (c) ƒ*, X(ei®)d2,
(d) X(ej™), (e) /¨, |X(ej@)]²ds2.
2b) O&S 2.36 parts a and b only.
2.36. An LTI discrete-time system has frequency response given by
+ je-jw)
1 – 0.8e-jw
(1 – je-j@(1
-j2w
1+e-j2w
1
H(ej®) =
1 – 0.8e-j@
1– 0.8e-jw
1 – 0.8e-j@'
(a) Use one of the above forms of the frequency response to obtain an equation for the
impulse response h[n] of the system.
(b) From the frequency response, determine the difference equation that is satisfied by
the input x[n] and the output y[n] of the system.
8:03 PM
Type here to search
26°C
W
22-Feb-22
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