很久之前寫了一篇信號下的基本時域頻域特征(上)，后來一直催更，直到今天才更新，實在是不好意思食零，理解萬歲。

這次將所有我平時用的16個時域特征和10個頻域特征的程序都放到這里

)了寂屏，另外這次單獨列出頻域的公式供大家參考贰谣。

圖1：十個頻域特征計算圖

程序如下：大家可以對照公式看程序，如果有錯誤迁霎，歡迎指出交流

# ======================= STATISTICAL FEATURES IN TIME DOMAIN =======================
# def fft_fft(sequence_data):
#   fft_trans = np.abs(np.fft.fft(sequence_data))
#   dc = fft_trans[0]
#   freq_spectrum = fft_trans[1:int(np.floor(len(sequence_data) * 1.0 / 2)) + 1]
#   freq_sum_ = np.sum(freq_spectrum)
#   return dc, freq_spectrum, freq_sum_

def fft_mean(sequence_data):
    def fft_fft(sequence_data):
        fft_trans = np.abs(np.fft.fft(sequence_data))
        # dc = fft_trans[0]
        freq_spectrum = fft_trans[1:int(np.floor(len(sequence_data) * 1.0 / 2)) + 1]
        _freq_sum_ = np.sum(freq_spectrum)
        return freq_spectrum, _freq_sum_
    freq_spectrum, _freq_sum_ = fft_fft(sequence_data)
    return np.mean(freq_spectrum)

def fft_var(sequence_data):
    def fft_fft(sequence_data):
        fft_trans = np.abs(np.fft.fft(sequence_data))
        # dc = fft_trans[0]
        freq_spectrum = fft_trans[1:int(np.floor(len(sequence_data) * 1.0 / 2)) + 1]
        _freq_sum_ = np.sum(freq_spectrum)
        return freq_spectrum, _freq_sum_
    freq_spectrum, _freq_sum_ = fft_fft(sequence_data)
    return np.var(freq_spectrum)

# def fft_std(sequence_data):
#   def fft_fft(sequence_data):
#       fft_trans = np.abs(np.fft.fft(sequence_data))
#       # dc = fft_trans[0]
#       freq_spectrum = fft_trans[1:int(np.floor(len(sequence_data) * 1.0 / 2)) + 1]
#       _freq_sum_ = np.sum(freq_spectrum)
#       return freq_spectrum, _freq_sum_
#   freq_spectrum, _freq_sum_ = fft_fft(sequence_data)
#   return np.std(freq_spectrum)

def fft_entropy(sequence_data):
    def fft_fft(sequence_data):
        fft_trans = np.abs(np.fft.fft(sequence_data))
        # dc = fft_trans[0]
        freq_spectrum = fft_trans[1:int(np.floor(len(sequence_data) * 1.0 / 2)) + 1]
        _freq_sum_ = np.sum(freq_spectrum)
        return freq_spectrum, _freq_sum_
    freq_spectrum, _freq_sum_ = fft_fft(sequence_data)
    pr_freq = freq_spectrum * 1.0 / _freq_sum_
    entropy = -1 * np.sum([np.log2(p+1e-5) * p for p in pr_freq])
    return entropy

def fft_energy(sequence_data):
    def fft_fft(sequence_data):
        fft_trans = np.abs(np.fft.fft(sequence_data))
        # dc = fft_trans[0]
        freq_spectrum = fft_trans[1:int(np.floor(len(sequence_data) * 1.0 / 2)) + 1]
        _freq_sum_ = np.sum(freq_spectrum)
        return freq_spectrum, _freq_sum_
    freq_spectrum, _freq_sum_ = fft_fft(sequence_data)
    return np.sum(freq_spectrum ** 2) / len(freq_spectrum)

def fft_skew(sequence_data):
    def fft_fft(sequence_data):
        fft_trans = np.abs(np.fft.fft(sequence_data))
        # dc = fft_trans[0]
        freq_spectrum = fft_trans[1:int(np.floor(len(sequence_data) * 1.0 / 2)) + 1]
        _freq_sum_ = np.sum(freq_spectrum)
        return freq_spectrum, _freq_sum_
    freq_spectrum, _freq_sum_ = fft_fft(sequence_data)
    _fft_mean, _fft_std = fft_mean(sequence_data), fft_std(sequence_data)
    return np.mean([0 if _fft_std < epsn else np.power((x - _fft_mean) / _fft_std, 3)
                    for x in freq_spectrum])

def fft_kurt(sequence_data):
    def fft_fft(sequence_data):
        fft_trans = np.abs(np.fft.fft(sequence_data))
        # dc = fft_trans[0]
        freq_spectrum = fft_trans[1:int(np.floor(len(sequence_data) * 1.0 / 2)) + 1]
        _freq_sum_ = np.sum(freq_spectrum)
        return freq_spectrum, _freq_sum_
    freq_spectrum, _freq_sum_ = fft_fft(sequence_data)
    _fft_mean, _fft_std = fft_mean(sequence_data), fft_std(sequence_data)
    return np.mean([0 if _fft_std < epsn else np.power((x - _fft_mean) / _fft_std, 4)
                    for x in freq_spectrum])

def fft_shape_mean(sequence_data):
    def fft_fft(sequence_data):
        fft_trans = np.abs(np.fft.fft(sequence_data))
        # dc = fft_trans[0]
        freq_spectrum = fft_trans[1:int(np.floor(len(sequence_data) * 1.0 / 2)) + 1]
        _freq_sum_ = np.sum(freq_spectrum)
        return freq_spectrum, _freq_sum_
    freq_spectrum, _freq_sum_ = fft_fft(sequence_data)
    shape_sum = np.sum([x * freq_spectrum[x]
                        for x in range(len(freq_spectrum))])
    return 0 if _freq_sum_ < epsn else shape_sum * 1.0 / _freq_sum_

def fft_shape_std(sequence_data):
    def fft_fft(sequence_data):
        fft_trans = np.abs(np.fft.fft(sequence_data))
        # dc = fft_trans[0]
        freq_spectrum = fft_trans[1:int(np.floor(len(sequence_data) * 1.0 / 2)) + 1]
        _freq_sum_ = np.sum(freq_spectrum)
        return freq_spectrum, _freq_sum_
    freq_spectrum, _freq_sum_ = fft_fft(sequence_data)
    shape_mean = fft_shape_mean(sequence_data)
    var = np.sum([0 if _freq_sum_ < epsn else np.power((x - shape_mean), 2) * freq_spectrum[x]
                  for x in range(len(freq_spectrum))]) / _freq_sum_
    return np.sqrt(var)

def fft_shape_skew(sequence_data):
    def fft_fft(sequence_data):
        fft_trans = np.abs(np.fft.fft(sequence_data))
        # dc = fft_trans[0]
        freq_spectrum = fft_trans[1:int(np.floor(len(sequence_data) * 1.0 / 2)) + 1]
        _freq_sum_ = np.sum(freq_spectrum)
        return freq_spectrum, _freq_sum_
    freq_spectrum, _freq_sum_ = fft_fft(sequence_data)
    shape_mean = fft_shape_mean(sequence_data)
    return np.sum([np.power((x - shape_mean), 3) * freq_spectrum[x]
                   for x in range(len(freq_spectrum))]) / _freq_sum_

def fft_shape_kurt(sequence_data):
    def fft_fft(sequence_data):
        fft_trans = np.abs(np.fft.fft(sequence_data))
        # dc = fft_trans[0]
        freq_spectrum = fft_trans[1:int(np.floor(len(sequence_data) * 1.0 / 2)) + 1]
        _freq_sum_ = np.sum(freq_spectrum)
        return freq_spectrum, _freq_sum_
    freq_spectrum, _freq_sum_ = fft_fft(sequence_data)
    shape_mean = fft_shape_mean(sequence_data)
    return np.sum([np.power((x - shape_mean), 4) * freq_spectrum[x] - 3
                   for x in range(len(freq_spectrum))]) / _freq_sum_
# =================================== END =====================================

關(guān)于所有的特征的程序吱抚，大家從文章開頭的鏈接里找，Thanks?(?ω?)?