Estimate power spectral density using Welch’s method.
Welch’s method [R120] computes an estimate of the power spectral density by dividing the data into overlapping segments, computing a modified periodogram for each segment and averaging the periodograms.
Parameters :  x : array_like
fs : float, optional
window : str or tuple or array_like, optional
nperseg : int, optional
noverlap: int, optional :
nfft : int, optional
detrend : str or function, optional return_onesided : bool, optional
scaling : { ‘density’, ‘spectrum’ }, optional
axis : int, optional


Returns :  f : ndarray
Pxx : ndarray

See also
Notes
An appropriate amount of overlap will depend on the choice of window and on your requirements. For the default ‘hanning’ window an overlap of 50% is a reasonable trade off between accurately estimating the signal power, while not over counting any of the data. Narrower windows may require a larger overlap.
If noverlap is 0, this method is equivalent to Bartlett’s method [R121].
New in version 0.12.0.
References
[R120]  (1, 2) P. Welch, “The use of the fast Fourier transform for the estimation of power spectra: A method based on time averaging over short, modified periodograms”, IEEE Trans. Audio Electroacoust. vol. 15, pp. 7073, 1967. 
[R121]  (1, 2) M.S. Bartlett, “Periodogram Analysis and Continuous Spectra”, Biometrika, vol. 37, pp. 116, 1950. 
Examples
>>> from scipy import signal
>>> import matplotlib.pyplot as plt
Generate a test signal, a 2 Vrms sine wave at 1234 Hz, corrupted by 0.001 V**2/Hz of white noise sampled at 10 kHz.
>>> fs = 10e3
>>> N = 1e5
>>> amp = 2*np.sqrt(2)
>>> freq = 1234.0
>>> noise_power = 0.001 * fs / 2
>>> time = np.arange(N) / fs
>>> x = amp*np.sin(2*np.pi*freq*time)
>>> x += np.random.normal(scale=np.sqrt(noise_power), size=time.shape)
Compute and plot the power spectral density.
>>> f, Pxx_den = signal.welch(x, fs, 1024)
>>> plt.semilogy(f, Pxx_den)
>>> plt.xlabel('frequency [Hz]')
>>> plt.ylabel('PSD [V**2/Hz]')
>>> plt.show()
If we average the last half of the spectral density, to exclude the peak, we can recover the noise power on the signal.
>>> np.mean(Pxx_den[256:])
0.0009924865443739191
Now compute and plot the power spectrum.
>>> f, Pxx_spec = signal.welch(x, fs, 'flattop', 1024, scaling='spectrum')
>>> plt.figure()
>>> plt.semilogy(f, np.sqrt(Pxx_spec))
>>> plt.xlabel('frequency [Hz]')
>>> plt.ylabel('Linear spectrum [V RMS]')
>>> plt.show()
The peak height in the power spectrum is an estimate of the RMS amplitude.
>>> np.sqrt(Pxx_spec.max())
2.0077340678640727