The signal ¤[n] is real-valued and its spectrum is nonzero only over the [-1/8, 7/8] interval. Due to the bandwidth constraint we need to "fit" the signal over the bands indicated in green in the following figure Frequency Frequency support of s[n] support of x[n] Frequency support of s[n] + -3m/4 -1/2 -1/8 0 1/8 1/2 Зя/4 To this aim, we need to design a processing block H in order to convert a[n] into a sequence s[n] satisfying the following requirements: • The support of the DTFT of s[n] must be limited to [-37/4, – 7/2] U [7/2, 37/4] • The sequence s[n] must be real-valued (x[n] is real-valued) Which of the following input/output relationships for H meet both requirements? (check all correct answers) : O s[n] = IDTFT{X(ej(w-5#/8))} s[n] = ej*n. æ[n] s[n] = sin(2n) · a(n] %3D O s[n] = cos(n) · æ[n]

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The signal 2[n] is real-valued and its spectrum is nonzero only over the [-7/8, 7/8] interval. Due to the bandwidth
constraint we need to "fit" the signal over the bands indicated in green in the following figure
Frequency
Frequency support of s[n]
support of x[n]
Frequency support of s[n]
-37/4
-T/2
-1/8 0 7/8
1/2
Зя /4
To this aim, we need to design a processing block H in order to convert a[n] into a sequence s[n] satisfying the following
requirements:
• The support of the DTFT of s[n] must be limited to [-37/4, – 7/2] U [T/2, 37/4]
• The sequence s[n] must be real-valued (x[n] is real-valued)
Which of the following input/output relationships for H meet both requirements? (check all correct answers) :
s[n] = IDTFT{X(ej(w-5n/8))}
O s[n] = ejFn. æ[n]
O s (n] = sin(2n) · æ[n]
O s (n] = cos( n) · æ[n]
Transcribed Image Text:The signal 2[n] is real-valued and its spectrum is nonzero only over the [-7/8, 7/8] interval. Due to the bandwidth constraint we need to "fit" the signal over the bands indicated in green in the following figure Frequency Frequency support of s[n] support of x[n] Frequency support of s[n] -37/4 -T/2 -1/8 0 7/8 1/2 Зя /4 To this aim, we need to design a processing block H in order to convert a[n] into a sequence s[n] satisfying the following requirements: • The support of the DTFT of s[n] must be limited to [-37/4, – 7/2] U [T/2, 37/4] • The sequence s[n] must be real-valued (x[n] is real-valued) Which of the following input/output relationships for H meet both requirements? (check all correct answers) : s[n] = IDTFT{X(ej(w-5n/8))} O s[n] = ejFn. æ[n] O s (n] = sin(2n) · æ[n] O s (n] = cos( n) · æ[n]
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