Highlander-SP
Member level 3
Whats the response by unit step input for the following High Pass Filter:
H(ω) = [ 1 – G2W(ω) ] . exp(-jωto)
x(t) = h(t)
X(ω) = F[x(t)] = πδ(ω) + 1/(j ω)
Y(ω) = X(ω).H(ω)
Y(ω) = [ πδ(ω) - πδ(ω). G2W(ω) + 1/(j ω) – G2W(ω)/(j ω)] . exp(-jωto )
y(t) = ?
where:
h(t) = step function (Heaviside)
π = pi
δ(ω) = delta Dirac in frequence domain
G2W(ω) = Gate function with 2W of band width
j = complex number = sqrt(-1)
to = constant time
Somebody can show step by step desenvolte the inverse Fourier transform?
thanks
H(ω) = [ 1 – G2W(ω) ] . exp(-jωto)
x(t) = h(t)
X(ω) = F[x(t)] = πδ(ω) + 1/(j ω)
Y(ω) = X(ω).H(ω)
Y(ω) = [ πδ(ω) - πδ(ω). G2W(ω) + 1/(j ω) – G2W(ω)/(j ω)] . exp(-jωto )
y(t) = ?
where:
h(t) = step function (Heaviside)
π = pi
δ(ω) = delta Dirac in frequence domain
G2W(ω) = Gate function with 2W of band width
j = complex number = sqrt(-1)
to = constant time
Somebody can show step by step desenvolte the inverse Fourier transform?
thanks