content: import numpy as np
  import matplotlib.mlab as mlab
  import matplotlib.pyplot as plt
  from scipy.ndimage.filters import maximum_filter
  from scipy.ndimage.morphology import (generate_binary_structure,
                                        iterate_structure, binary_erosion)
  import hashlib
  from operator import itemgetter
  
  IDX_FREQ_I = 0
  IDX_TIME_J = 1
  
  ######################################################################
  # Sampling rate, related to the Nyquist conditions, which affects
  # the range frequencies we can detect. 
  DEFAULT_FS = 44100 
  
  ######################################################################
  # Size of the FFT window, affects frequency granularity
  DEFAULT_WINDOW_SIZE = 4096
  
  ######################################################################
  # Ratio by which each sequential window overlaps the last and the
  # next window. Higher overlap will allow a higher granularity of offset
  # matching, but potentially more fingerprints.
  DEFAULT_OVERLAP_RATIO = 0.5  
  
  ######################################################################
  # Degree to which a fingerprint can be paired with its neighbors --
  # higher will cause more fingerprints, but potentially better accuracy. 
  DEFAULT_FAN_VALUE = 15 
  
  ######################################################################
  # Minimum amplitude in spectrogram in order to be considered a peak. 
  # This can be raised to reduce number of fingerprints, but can negatively
  # affect accuracy.
  DEFAULT_AMP_MIN = 10
  
  ######################################################################
  # Number of cells around an amplitude peak in the spectrogram in order
  # for Dejavu to consider it a spectral peak. Higher values mean less
  # fingerprints and faster matching, but can potentially affect accuracy. 
  PEAK_NEIGHBORHOOD_SIZE = 20
  
  ######################################################################
  # Thresholds on how close or far fingerprints can be in time in order 
  # to be paired as a fingerprint. If your max is too low, higher values of
  # DEFAULT_FAN_VALUE may not perform as expected. 
  MIN_HASH_TIME_DELTA = 0
  MAX_HASH_TIME_DELTA = 200
  
  ######################################################################
  # If True, will sort peaks temporally for fingerprinting;
  # not sorting will cut down number of fingerprints, but potentially
  # affect performance.
  PEAK_SORT = True
  
  ######################################################################
  # Number of bits to throw away from the front of the SHA1 hash in the 
  # fingerprint calculation. The more you throw away, the less storage, but
  # potentially higher collisions and misclassifications when identifying songs.
  FINGERPRINT_REDUCTION = 20
  
  def fingerprint(channel_samples, Fs=DEFAULT_FS,
                  wsize=DEFAULT_WINDOW_SIZE,
                  wratio=DEFAULT_OVERLAP_RATIO,
                  fan_value=DEFAULT_FAN_VALUE,
                  amp_min=DEFAULT_AMP_MIN):
      """
      FFT the channel, log transform output, find local maxima, then return
      locally sensitive hashes.
      """
      # FFT the signal and extract frequency components
      arr2D = mlab.specgram(
          channel_samples,
          NFFT=wsize,
          Fs=Fs,
          window=mlab.window_hanning,
          noverlap=int(wsize * wratio))[0]
  
      # apply log transform since specgram() returns linear array
      arr2D = 10 * np.log10(arr2D)
      arr2D[arr2D == -np.inf] = 0  # replace infs with zeros
  
      # find local maxima
      local_maxima = get_2D_peaks(arr2D, plot=False, amp_min=amp_min)
  
      # return hashes
      return generate_hashes(local_maxima, fan_value=fan_value)
  
  
  def get_2D_peaks(arr2D, plot=False, amp_min=DEFAULT_AMP_MIN):
      # http://docs.scipy.org/doc/scipy/reference/generated/scipy.ndimage.morphology.iterate_structure.html#scipy.ndimage.morphology.iterate_structure
      struct = generate_binary_structure(2, 1)
      neighborhood = iterate_structure(struct, PEAK_NEIGHBORHOOD_SIZE)
  
      # find local maxima using our fliter shape
      local_max = maximum_filter(arr2D, footprint=neighborhood) == arr2D
      background = (arr2D == 0)
      eroded_background = binary_erosion(background, structure=neighborhood,
                                         border_value=1)
  
      # Boolean mask of arr2D with True at peaks
      detected_peaks = local_max - eroded_background
  
      # extract peaks
      amps = arr2D[detected_peaks]
      j, i = np.where(detected_peaks)
  
      # filter peaks
      amps = amps.flatten()
      peaks = zip(i, j, amps)
      peaks_filtered = [x for x in peaks if x[2] > amp_min]  # freq, time, amp
  
      # get indices for frequency and time
      frequency_idx = [x[1] for x in peaks_filtered]
      time_idx = [x[0] for x in peaks_filtered]
  
      if plot:
          # scatter of the peaks
          fig, ax = plt.subplots()
          ax.imshow(arr2D)
          ax.scatter(time_idx, frequency_idx)
          ax.set_xlabel('Time')
          ax.set_ylabel('Frequency')
          ax.set_title("Spectrogram")
          plt.gca().invert_yaxis()
          plt.show()
  
      return zip(frequency_idx, time_idx)
  
  
  def generate_hashes(peaks, fan_value=DEFAULT_FAN_VALUE):
      """
      Hash list structure:
         sha1_hash[0:20]    time_offset
      [(e05b341a9b77a51fd26, 32), ... ]
      """
      fingerprinted = set()  # to avoid rehashing same pairs
      
      if PEAK_SORT:
          peaks.sort(key=itemgetter(1))
  
      for i in range(len(peaks)):
          for j in range(1, fan_value):
              if (i + j) < len(peaks) and not (i, i + j) in fingerprinted:
                  freq1 = peaks[i][IDX_FREQ_I]
                  freq2 = peaks[i + j][IDX_FREQ_I]
  
                  t1 = peaks[i][IDX_TIME_J]
                  t2 = peaks[i + j][IDX_TIME_J]
  
                  t_delta = t2 - t1
  
                  if t_delta >= MIN_HASH_TIME_DELTA and t_delta <= MAX_HASH_TIME_DELTA:
                      h = hashlib.sha1(
                          "%s|%s|%s" % (str(freq1), str(freq2), str(t_delta)))
                      yield (h.hexdigest()[0:FINGERPRINT_REDUCTION], t1)
  
                  # ensure we don't repeat hashing
                  fingerprinted.add((i, i + j))
  