""" Module: libfmp.c3.c3s1_transposition_tuning Author: Meinard Müller License: The MIT license, https://opensource.org/licenses/MIT This file is part of the FMP Notebooks (https://www.audiolabs-erlangen.de/FMP) """ import numpy as np from matplotlib import pyplot as plt from scipy.interpolate import interp1d from scipy import signal import libfmp.b def cyclic_shift(C, shift=1): """Cyclically shift a chromagram Notebook: C3/C3S1_TranspositionTuning.ipynb Args: C: Chromagram shift: Number cyclic shifts Returns: C_shift: Cyclically shifted chromagram """ C_shift = np.roll(C, shift=shift, axis=0) return C_shift def compute_freq_distribution(x, Fs, N=16384, gamma=100, local=True, filt=True, filt_len=101): """Compute an overall frequency distribution Notebook: C3/C3S1_TranspositionTuning.ipynb Args: x: Signal Fs: Sampling rate N: Window size gamma: Constant for logarithmic compression local=True: Computes STFT and averages; otherwise computes global DFT filt=True: Applies local frequency averaging and by rectification filt_len: Filter length for local frequency averaging (length given in cents) Returns: v: Vector representing an overall frequency distribution F_coef_cents: Frequency axis (given in cents) """ if local: # Compute an STFT and sum over time if N > len(x)//2: raise Exception('The signal length (%d) should be twice as long as the window length (%d)' % (len(x), N)) Y, T_coef, F_coef = libfmp.c2.stft_convention_fmp(x=x, Fs=Fs, N=N, H=N//2, mag=True, gamma=gamma) # Error "range() arg 3 must not be zero" occurs when N is too large. Why? Y = np.sum(Y, axis=1) else: # Compute a single DFT for the entire signal N = len(x) Y = np.abs(np.fft.fft(x)) / Fs Y = Y[:N//2+1] Y = np.log(1 + gamma * Y) # Y = libfmp.c3.log_compression(Y, gamma=100) F_coef = np.arange(N // 2 + 1).astype(float) * Fs / N # Convert linearly spaced frequency axis in logarithmic axis (given in cents) # The minimum frequency F_min corresponds 0 cents. f_pitch = lambda p: 440 * 2 ** ((p - 69) / 12) p_min = 24 # C1, MIDI pitch 24 F_min = f_pitch(p_min) # 32.70 Hz p_max = 108 # C8, MIDI pitch 108 F_max = f_pitch(p_max) # 4186.01 Hz F_coef_log, F_coef_cents = libfmp.c2.compute_f_coef_log(R=1, F_min=F_min, F_max=F_max) Y_int = interp1d(F_coef, Y, kind='cubic', fill_value='extrapolate')(F_coef_log) v = Y_int / np.max(Y_int) if filt: # Subtract local average and rectify filt_kernel = np.ones(filt_len) Y_smooth = signal.convolve(Y_int, filt_kernel, mode='same') / filt_len # Y_smooth = signal.medfilt(Y_int, filt_len) Y_rectified = Y_int - Y_smooth Y_rectified[Y_rectified < 0] = 0 v = Y_rectified / np.max(Y_rectified) theta_axis, sim, ind_max, theta_max, template_max = tuning_similarity(v) return v, F_coef_cents def template_comb(M, theta=0): """Compute a comb template on a pitch axis Notebook: C3/C3S1_TranspositionTuning.ipynb Args: M: Length template (given in cents) theta: Shift parameter (given in cents); -50 <= theta < 50 Returns: template: comb template shifted by theta """ template = np.zeros(M) peak_positions = (np.arange(0, M, 100) + theta) peak_positions = np.intersect1d(peak_positions, np.arange(M)).astype(int) template[peak_positions] = 1 return template def tuning_similarity(v): """Compute tuning similarity Notebook: C3/C3S1_TranspositionTuning.ipynb Args: v: Vector representing an overall frequency distribution Returns: theta_axis: Axis consisting of all tuning parameters -50 <= theta < 50 sim: Similarity values for all tuning parameters ind_max: Maximizing index theta_max: Maximizing tuning parameter template_max: Similiarty-maximizing comb template """ theta_axis = np.arange(-50, 50) # Axis (given in cents) num_theta = len(theta_axis) sim = np.zeros(num_theta) M = len(v) for i in range(num_theta): theta = theta_axis[i] template = template_comb(M=M, theta=theta) sim[i] = np.inner(template, v) sim = sim / np.max(sim) ind_max = np.argmax(sim) theta_max = theta_axis[ind_max] template_max = template_comb(M=M, theta=theta_max) return theta_axis, sim, ind_max, theta_max, template_max def plot_tuning_similarity(sim, theta_axis, theta_max, ax=None, title=None, figsize=(4, 3)): """Plots tuning similarity Notebook: C3/C3S1_TranspositionTuning.ipynb Args: sim: Similarity values theta_axis: Axis consisting of cent values [-50:49] theta_max: Maximizing tuning parameter ax: Axis (in case of ax=None, figure is generated) title: Title of figure (or subplot) figsize: Size of figure (only used when ax=None) Returns: fig, ax, line: Handles for figure, axis, and plot """ fig = None if ax is None: fig = plt.figure(figsize=figsize) ax = plt.subplot(1, 1, 1) if title is None: title = 'Estimated tuning: %d cents' % theta_max line = ax.plot(theta_axis, sim, 'k') ax.set_xlim([theta_axis[0], theta_axis[-1]]) ax.set_ylim([0, 1.1]) ax.plot([theta_max, theta_max], [0, 1.1], 'r') ax.set_xlabel('Tuning parameter (cents)') ax.set_ylabel('Similarity') ax.set_title(title) if fig is not None: plt.tight_layout() return fig, ax, line def plot_freq_vector_template(v, F_coef_cents, template_max, theta_max, ax=None, title=None, figsize=(8, 3)): """Plots frequency distribution and similarity-maximizing template Notebook: C3/C3S1_TranspositionTuning.ipynb Args: v: Vector representing an overall frequency distribution F_coef_cents: Frequency axis template_max: Similarity-maximizing template theta_max: Maximizing tuning parameter ax: Axis (in case of ax=None, figure is generated) title: Title of figure (or subplot) figsize: Size of figure (only used when ax=None) Returns: fig, ax, line: Handles for figure, axis, and plot """ fig = None if ax is None: fig = plt.figure(figsize=figsize) ax = plt.subplot(1, 1, 1) if title is None: title = r'Frequency distribution with maximizing comb template ($\theta$ = %d cents)' % theta_max line = ax.plot(F_coef_cents, v, c='k', linewidth=1) ax.set_xlim([F_coef_cents[0], F_coef_cents[-1]]) ax.set_ylim([0, 1.1]) x_ticks_freq = np.array([0, 1200, 2400, 3600, 4800, 6000, 7200, 8000]) ax.plot(F_coef_cents, template_max * 1.1, 'r:', linewidth=0.5) ax.set_xticks(x_ticks_freq) ax.set_xlabel('Frequency (cents)') plt.title(title) if fig is not None: plt.tight_layout() return fig, ax, line