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The discrete-time Fourier transform (DTFT) X(w) = Σ=-∞x[n]e¯jwn of a sequence x[n] is displayed below for 0≤ @ < 2. X(w) + π/2 1 0.5 π 3π/2 a) Is x[n] periodic? Why or why not? If periodic, what is its period? b) Is x[n] real-valued? Why or why not? n=-00 2π 3 2 c) Use Parseval's Relation to find the total energy Σx[n]² in the sequence x[n].

The discrete-time Fourier transform (DTFT) X(w) = Σ=-∞x[n]e¯jwn of a sequence x[n] is displayed below for 0≤ @ < 2. X(w) + π/2 1 0.5 π 3π/2 a) Is x[n] periodic? Why or why not? If periodic, what is its period? b) Is x[n] real-valued? Why or why not? n=-00 2π 3 2 c) Use Parseval's Relation to find the total energy Σx[n]² in the sequence x[n].

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
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The discrete-time Fourier transform (DTFT) X(w) = Σ--∞ x[n]e-jwn of a sequence x[n] is n=100 displayed below for 0≤@ < 2πt. 1 0.5 X(w) 1 a) Is x[n] periodic? Why or why not? If periodic, what is its period? b) Is x[n] real-valued? Why or why not? Y(w) 0.5 π/2 T 00 d) Sketch |Q (w)| = |Σn=-∞ q[n]e¯jwn| if q[n] = x[n − 3]. π/2 ∞0 c) Use Parseval's Relation to find the total energy | x[n] in the sequence x[n]. n=-∞0 3π/2 T e) The discrete-time Fourier transform Y(w) = Σ--∞y[n]e¯ -jwn of another sequence y[n] is displayed below for 0 ≤ @ < 2. Using the Frequency Shift property of the DTFT, derive a relationship between x[n] and y[n]. 3π/2 5 2π 2π 3 3
Transcribed Image Text:The discrete-time Fourier transform (DTFT) X(w) = Σ--∞ x[n]e-jwn of a sequence x[n] is n=100 displayed below for 0≤@ < 2πt. 1 0.5 X(w) 1 a) Is x[n] periodic? Why or why not? If periodic, what is its period? b) Is x[n] real-valued? Why or why not? Y(w) 0.5 π/2 T 00 d) Sketch |Q (w)| = |Σn=-∞ q[n]e¯jwn| if q[n] = x[n − 3]. π/2 ∞0 c) Use Parseval's Relation to find the total energy | x[n] in the sequence x[n]. n=-∞0 3π/2 T e) The discrete-time Fourier transform Y(w) = Σ--∞y[n]e¯ -jwn of another sequence y[n] is displayed below for 0 ≤ @ < 2. Using the Frequency Shift property of the DTFT, derive a relationship between x[n] and y[n]. 3π/2 5 2π 2π 3 3
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d) Sketch |Q(w)| = |Σn=-oq[n]e-jun | if q [n] = x[n - 3]. =-a e) The discrete-time Fourier transform Y(w) = Σ - y[n]e-jun of another sequence y[n] is displayed below for 0 <<2. Using the Frequency Shift property of the DTFT, derive a relationship between x[n] and y[n]. Y(w) 1 0.5 π/2 π 3π/2 2π W
Transcribed Image Text:d) Sketch |Q(w)| = |Σn=-oq[n]e-jun | if q [n] = x[n - 3]. =-a e) The discrete-time Fourier transform Y(w) = Σ - y[n]e-jun of another sequence y[n] is displayed below for 0 <<2. Using the Frequency Shift property of the DTFT, derive a relationship between x[n] and y[n]. Y(w) 1 0.5 π/2 π 3π/2 2π W
d) Sketch |Q(w)| = |Σn=-oq[n]e-jun | if q [n] = x[n - 3]. =-a e) The discrete-time Fourier transform Y(w) = Σ - y[n]e-jun of another sequence y[n] is displayed below for 0 <<2. Using the Frequency Shift property of the DTFT, derive a relationship between x[n] and y[n]. Y(w) 1 0.5 π/2 π 3π/2 2π W
Transcribed Image Text:d) Sketch |Q(w)| = |Σn=-oq[n]e-jun | if q [n] = x[n - 3]. =-a e) The discrete-time Fourier transform Y(w) = Σ - y[n]e-jun of another sequence y[n] is displayed below for 0 <<2. Using the Frequency Shift property of the DTFT, derive a relationship between x[n] and y[n]. Y(w) 1 0.5 π/2 π 3π/2 2π W
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