Does windowing affect Parseval's theorem? I have computed Fourier transform from ecg data.It does obey Parseval's theorem,
relation 

$$\sum_{n=0}^{N-1} \Big| x[n] \Big|^2  = \frac{1}{N}  \sum_{k=0}^{N-1} \Big| X[k] \Big|^2$$ 

is fulfiled. But after I use window function (Blackman,Hann,Hanning) energy is not conserved anymore.Is this normal? If not,how can I normalize my windowed fft?

I calculate fft this way:

    N = signal.shape[0]
    frq = np.fft.fftfreq(N,freq)
    frq = frq[range(N/2)]
    window = window_func(N)
    fft_y = np.fft.fft(signal*window)/np.sqrt(N)
    fft_y = Y[range(N/2)]
    plt.plot(frq, abs(fft_y))


And thats how it look when I plot. I'm a little worried about how almost all windows drastically reduce amplitude,again is this normal?


Thank you in advance for all help.
Parseval's theorem will hold, but take into account that your signal in the time domain will no longer be $x[n]$. Namely, if you have that

$$\sum_{n=0}^{N-1} \Big| x[n] \Big|^2  = \frac{1}{N}  \sum_{k=0}^{N-1} \Big| X[k] \Big|^2$$

then, if you window the signal $x[n]$ with a window $w[n]$, your signal will now be $\hat{x}[n]=x[n]w[n]$, and the theorem will now return the following equality:

$$\sum_{n=0}^{N-1} \Big| \hat{x}[n] \Big|^2  = \frac{1}{N}  \sum_{k=0}^{N-1} \Big| \hat{X}[k] \Big|^2$$

where $\hat{X}[k]$ is the DFT of $\hat{x}[n]$ (and obviously differs from $X[k]$).