Aug 3, 2009 #1 F Faudy Newbie level 3 Joined Aug 3, 2009 Messages 3 Helped 0 Reputation 0 Reaction score 0 Trophy points 1,281 Activity points 1,301 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)?
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)?