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Let x(t) and y(t) (with Fourier transform X(ω) and Y(ω) be related as shown in figure below
Then Y(ω) in terms of X(ω) is
Then Y(ω) in terms of X(ω) is
- a)
- b)
- c)
- d)
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
Let x(t) and y(t) (with Fourier transform X(ω) and Y(ω) be...
From the given pictures of x(t) and y(t)
We get,
y(t) = - x(2t + 2)
y(t) is time scaled and time shifted version of x(t)
Step 1:
If x(t) ↔ X(ω)
Then, x(t + 2) ↔ ej.2.ω X(ω)
Step 2:
Using time shifting property
x(2t + 2) ↔ ½ ejω X(ω/2)
Step 3:
Using time scaling property:
We get,
y(t) = - x(2t + 2)
y(t) is time scaled and time shifted version of x(t)
Step 1:
If x(t) ↔ X(ω)
Then, x(t + 2) ↔ ej.2.ω X(ω)
Step 2:
Using time shifting property
x(2t + 2) ↔ ½ ejω X(ω/2)
Step 3:
Using time scaling property:
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Community Answer
Let x(t) and y(t) (with Fourier transform X(ω) and Y(ω) be...
From the given pictures of x(t) and y(t)
We get,
y(t) = - x(2t + 2)
y(t) is time scaled and time shifted version of x(t)
Step 1:
If x(t) ↔ X(ω)
Then, x(t + 2) ↔ ej.2.ω X(ω)
Step 2:
Using time shifting property
x(2t + 2) ↔ ½ ejω X(ω/2)
Step 3:
Using time scaling property:
We get,
y(t) = - x(2t + 2)
y(t) is time scaled and time shifted version of x(t)
Step 1:
If x(t) ↔ X(ω)
Then, x(t + 2) ↔ ej.2.ω X(ω)
Step 2:
Using time shifting property
x(2t + 2) ↔ ½ ejω X(ω/2)
Step 3:
Using time scaling property:
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Let x(t) and y(t) (with Fourier transform X(ω) and Y(ω) be related as shown in figure belowThen Y(ω) in terms of X(ω) isa)b)c)d)Correct answer is option 'C'. Can you explain this answer?
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