Gaussian white noise X(t) with power spectral density of 1 passes through two band-limited filters H₁(jw) and H₂(jw) respectively, and the output is Y₁(t) and Y₂(t) respectively. (a) If H₁(jw) and H₂(jw) satisfy what condition, Y₁(t) and Y₂(t) are not dependent only at the same time (b) H₁(jw) and H₂(jw) are designed so that the correlation 1>p>0 coefficient between Y₁(t) and Y₂(t) is a given value

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Gaussian white noise X(t) with power spectral density of 1
passes through two band-limited filters H₁(jw) and H₂(jw)
respectively, and the output is Y₁(t) and Y₂(t) respectively.
(a) If H₁(jw) and H₂(jw) satisfy what condition, Y₁(t) and Y₂(t) are
not dependent only at the same time
(b) H₁(jw) and H₂(jw) are designed so that the correlation
1>p>0
coefficient between Y₁(t) and Y₂(t) is a given value
Transcribed Image Text:Gaussian white noise X(t) with power spectral density of 1 passes through two band-limited filters H₁(jw) and H₂(jw) respectively, and the output is Y₁(t) and Y₂(t) respectively. (a) If H₁(jw) and H₂(jw) satisfy what condition, Y₁(t) and Y₂(t) are not dependent only at the same time (b) H₁(jw) and H₂(jw) are designed so that the correlation 1>p>0 coefficient between Y₁(t) and Y₂(t) is a given value
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