# How to apply the window function when finding autocorrelation?

I want to get frequencies from amplitudes and I'm following Chap 5.1.1 from Speech Signal Processing by Praat As the in pictures, I will multiply the signal $$s(t)$$ with the Hanning window $$w(t)$$, find its normalized autocorrelation $$r_a(\tau)$$, and divide by $$r_w(\tau)$$, which is the normalized autocorrelation of $$w(t)$$. In the end, I will get the corrected autocorrelations $$r(\tau)$$.
I understand that diving $$r_w$$ should somehow rescale $$r_a$$, but the $$r_w$$ I got takes negative value, and $$r$$ gets large where $$r_w$$ is close to zero. How can I get an $$r_w$$ as in the picture?

Below are my codes to get $$r_w$$:

def serial_cov(wave:List[int], lag:int)  -> int:
"""
Returns covariance of a signal with a lagged version of itself
"""
global WINDOW_LEN
n=len(wave)
y1=wave[lag:]
y2=wave[0:WINDOW_LEN - lag]
num = float(np.cov(y1,y2,bias=True)[0,1])
return num

hann = np.hanning(WINDOW_LEN)
plt.plot(hann)
plt.title("Hann window amplitude")
plt.show()
r0_hann = float(np.cov(hann, hann, bias = True)[0,0])
hann_autocorr = []
for i in range(MAX_LAG+1):
ri_hann = serial_cov(hann,i)
hann_autocorr.append(ri_hann/r0_hann)

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