Question

Table 6.4 More Fourier transform pairs ?(t) ? 1 sgn(t) ? 1/j?f rect(t) ? sinc(f) tri(t) ? sinc²(f) ???(t) ? f??_f?(f), f? = 1/T? cos(2?f?t) ? (1/2)[?(f - f?) + ?(f + f?)] 1 ? ?(f) u(t) ? (1/2)?(f) + 1/j2?f sinc(t) ? rect(f) sinc²(t) ? tri(f) T????(t) ? ?_f?(f), T? = 1/f? sin(2?f?t) ? (j/2)[?(f + f?) - ?(f - f?)]

          Table 6.4 More Fourier transform pairs

?(t) ? 1
sgn(t) ? 1/j?f
rect(t) ? sinc(f)
tri(t) ? sinc²(f)
???(t) ? f??_f?(f), f? = 1/T?
cos(2?f?t) ? (1/2)[?(f - f?) + ?(f + f?)]

1 ? ?(f)
u(t) ? (1/2)?(f) + 1/j2?f
sinc(t) ? rect(f)
sinc²(t) ? tri(f)
T????(t) ? ?_f?(f), T? = 1/f?
sin(2?f?t) ? (j/2)[?(f + f?) - ?(f - f?)]

Table 6.4 More Fourier transform pairs

?(t) ? 1
sgn(t) ? 1/j?f
rect(t) ? sinc(f)
tri(t) ? sinc²(f)
???(t) ? f??f?(f), f? = 1/T?
cos(2?f?t) ? (1/2)[?(f - f?) + ?(f + f?)]

1 ? ?(f)
u(t) ? (1/2)?(f) + 1/j2?f
sinc(t) ? rect(f)
sinc²(t) ? tri(f)
T????(t) ? ?f?(f), T? = 1/f?
sin(2?f?t) ? (j/2)[?(f + f?) - ?(f - f?)]

Added by Isabel M.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Sri K

03/28/2023

Step 1

From the given information, we have: Show more…

Show all steps

Thanks for your feedback!

Table 6.4 More Fourier transform pairs δ(t) ↔ 1 sgn(t) ↔ 1/jπf rect(t) ↔ sinc(f) tri(t) ↔ sinc²(f) δₜ₀(t) ↔ f₀δ_f₀(f), f₀ = 1/T₀ cos(2πf₀t) ↔ (1/2)[δ(f - f₀) + δ(f + f₀)] 1 ↔ δ(f) u(t) ↔ (1/2)δ(f) + 1/j2πf sinc(t) ↔ rect(f) sinc²(t) ↔ tri(f) T₀δₜ₀(t) ↔ δ_f₀(f), T₀ = 1/f₀ sin(2πf₀t) ↔ (j/2)[δ(f + f₀) - δ(f - f₀)]