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Last updated 3:21 AM on 3/3/26
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18 Terms

1
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x(t) = rect(t)

X(w) = (2sin(w/2))/w

2
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x(t) = δ(t)

X(w) = 1

3
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x(t) = e^(jw0t)

X(w) = 2πδ(w−w0)

4
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x(t) = sin(w0t)

X(w) = (π/j)(δ(w−w0)−δ(w+ w0))

5
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x(t) = cos(w0t)

X(w) = π[δ(w−w0) + δ(w+ w0)]

6
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x(t) = 1

X(w) = 2πδ(w)

7
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x(t) = sin(Wt)/(πt)

X(w) = 1, |w| < W, 0 |w| > W

8
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x(t) = u(t)

X(w) = 1/(jw) + πδ(w)

9
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x(t)e^(jw0t)

X(w-w0)

10
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x(t-t0)

X(w)e^(-jwt0)

11
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x(-t)

X(-w)

12
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x(at)

(1/|a|)X(w/a)

13
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d(x(t))/dx

jwX(w)

14
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d²(x(t))/dx

-w²X(w)

15
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x(t) * y(t)

X(w)Y(w)

16
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x(t)y(t)

1/(2π) integral -inf +inf X(y)Y(w-y)dy

17
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cos (w0t)

(1/2)(e^jwt + e^-jwt)

18
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sin (w0t)

(1/2j)(e^jwt - e^-jwt)