Faudy
Newbie level 3
spectral density
I will consider the example of a smooth periodogram estimation, where the data is multiplied by a window:
x2(t) = x1(t) h(t)
the fourier transform of this signal is the convolution of the fourier transforms of x1(t) and h(t)
X2(f) = X1(f) * H(f)
the Power Spectral Density of x2(t) is then
Sx2(f) = |X1(f) * H(f)|^2
Given a particular window (like hanning, hamming...),
can we express Sx2(f) as a function of Sx1(f)?
I will consider the example of a smooth periodogram estimation, where the data is multiplied by a window:
x2(t) = x1(t) h(t)
the fourier transform of this signal is the convolution of the fourier transforms of x1(t) and h(t)
X2(f) = X1(f) * H(f)
the Power Spectral Density of x2(t) is then
Sx2(f) = |X1(f) * H(f)|^2
Given a particular window (like hanning, hamming...),
can we express Sx2(f) as a function of Sx1(f)?
