Consider the two signals c₁(t) = 4 cos(50000πt) and c₂(t) = 4 sin(50000πt). The real and the imaginary parts of the spectrum of two signals, m₁(t) and m²(t), are shown in the following figure. M₁(f) M₂(f) Re Im -5000 M₁(f) -5000 10 5000 f-> 0 5000 f-> -5000 M₂(f) -5000 To 5000 f 5000 1) Draw the real and the imaginary parts of the spectrum of z(t) = m₁(t)c₁(t) + m₂(t)c₂(t). 2) Draw the real and the imaginary parts of the spectrum of w(t) = m₁(t)c₁(t) — m₂ (t)c₂(t). 3) If z(t) is multiplied by c₂(t), then integrated (or equivalently, passed through a LPF), what will be the output signal? 4) If w(t) is multiplied by c₂ (t), then integrated (or equivalently, passed through a LPF), what will be the output signal?
Consider the two signals c₁(t) = 4 cos(50000πt) and c₂(t) = 4 sin(50000πt). The real and the imaginary parts of the spectrum of two signals, m₁(t) and m²(t), are shown in the following figure. M₁(f) M₂(f) Re Im -5000 M₁(f) -5000 10 5000 f-> 0 5000 f-> -5000 M₂(f) -5000 To 5000 f 5000 1) Draw the real and the imaginary parts of the spectrum of z(t) = m₁(t)c₁(t) + m₂(t)c₂(t). 2) Draw the real and the imaginary parts of the spectrum of w(t) = m₁(t)c₁(t) — m₂ (t)c₂(t). 3) If z(t) is multiplied by c₂(t), then integrated (or equivalently, passed through a LPF), what will be the output signal? 4) If w(t) is multiplied by c₂ (t), then integrated (or equivalently, passed through a LPF), what will be the output signal?
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As per bartleby's guidelines you are required apparently to answer 3 parts only so I want you to answer 2,3,4 only.
Transcribed Image Text:Consider the two signals c₁ (t) = 4 cos (50000πt) and c₂ (t) = 4 sin(50000πt). The real and the imaginary
parts of the spectrum of two signals, m₁(t) and m₂ (t), are shown in the following figure.
M₂(f)
M₁D
Re
Im
-5000
M₁(f)
-5000
10
0
5000 f->
5000 f->
-5000
M₂(f)
-5000
5000 f->
5000
f→
1) Draw the real and the imaginary parts of the spectrum of z(t) = m₁(t)c₁(t) + m₂(t)c₂(t).
2) Draw the real and the imaginary parts of the spectrum of w(t) = m₁(t)c₁(t) — m₂(t)c₂(t).
3) If z(t) is multiplied by c₂(t), then integrated (or equivalently, passed through a LPF), what will be
the output signal?
4) If w(t) is multiplied by c₂(t), then integrated (or equivalently, passed through a LPF), what will
be the output signal?
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Step 1: what is given and what is required:
VIEWStep 2: Part (i)-Finding real and imaginary parts of the spectrums of z(t):
VIEWStep 3: Part (ii)-Finding real and imaginary parts of the spectrums of w(t):
VIEWStep 4: Part (iii)- If z(t) is multiplied by c2(t) and then the product is passed by LPF:
VIEWStep 5: Part (iv)- If w(t) is multiplied by c2(t) and then the product is passed by LPF:
VIEWSolution
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