if normalize:
    a = (a - mean(a)) / (std(a) * len(a))
    v = (v - mean(v)) /  std(v)

def cross_correlation(a1, a2):
        lags = range(-len(a1)+1, len(a2))
        cs = []
        for lag in lags:
            idx_lower_a1 = max(lag, 0)
            idx_lower_a2 = max(-lag, 0)
            idx_upper_a1 = min(len(a1), len(a1)+lag)
            idx_upper_a2 = min(len(a2), len(a2)-lag)
            b1 = a1[idx_lower_a1:idx_upper_a1]
            b2 = a2[idx_lower_a2:idx_upper_a2]
            c = np.correlate(b1, b2)[0]
            c = c / np.sqrt((b1**2).sum() * (b2**2).sum())
            cs.append(c)
        return cs