la) M&I 4.30, parts a, e, and d only 30. Determine and plot the DTFT magnitude and phase spectra of the following signals: (a) x[n] = (1/3)"u[n – 1]. (b) x2[m] = (1/4)" cos(Tn/4)uln – 2). (c) xyln] = sine(2:n/8) sine(2(n– 4)/8). (d) xaln] = sin(0.1)(a(u]- [n - 10). (e) xs[n] = sine (Tn/4). .....*.

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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
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26°C
W
22-Feb-22
Transcribed Image Text:I EE210_S22_HW2.pdf - Adobe Reader File Edit View Window Help Tools Fill & Sign Comment Оpen 2 100% IT Sign In Ptoblems from O&S and M&I • Export PDF • Create PDF la) M&I 4.30, parts a, c, and d only v Edit PDF Adobe Acrobat Pro 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). Easily edit text and images in PDF documents Start Now • Combine PDF 1b) M&I 4.31, parts a, b, and d only • Send Files • Store Files 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
Expert Solution
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“Since you have asked multiple question, we will solve the first question for you. If you want any specific question to be solved then please specify the question number or post only that question.”

Discrete-time Fourier transform (DTFT) is a Fourier transformation method that works on numerical sequence.

DTFT is often used to analyze work activity samples. The term discrete-time refers to the fact that change is applied to direct data, usually sampling its interval with time units.

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