Fourier transform of t*rect(t)

1. What is the Fourier transform of a rect function?
2. What will be the Fourier transform of dX T DT?
3. What is the Fourier transform of gate pulse?
4. What is the Fourier transform of cos t?

What is the Fourier transform of a rect function?

Therefore, the Fourier transform of the rectangular function is. F[∏(tτ)]=τ⋅sinc(ωτ2) Or, it can also be represented as, ∏(tτ)FT↔τ⋅sinc(ωτ2)

What will be the Fourier transform of dX T DT?

The Fourier transform of a function x(t) is X(ω). What will be the Fourier transform of \fracdX(t)dt? = jω X(ω) = j2πfX(f).

What is the Fourier transform of gate pulse?

Fourier transform of x(t) is X(ω) expressed as below. X ( ω ) = ∫ − ∞ ∞ ⁡ d t. G i v e n x ( t ) = 1 f o r t ϵ ( − 0.5 T , 0.5 T ) 0 o t h e r w i s e. X ( ω ) = ∫ ∞ − ∞ x ( t ) e − j ω t d t = ∫ 0.5 T − 0.5 T e − j ω t .

What is the Fourier transform of cos t?

Therefore, the Fourier transform of cosine wave function is, F[cosω0t]=π[δ(ω−ω0)+δ(ω+ω0)]