{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", "\"FMP\"\n", "\"AudioLabs\"\n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", "\"C2\"\n", "

STFT: Frequency Interpolation

\n", "
\n", "\n", "
\n", "\n", "

\n", "In the FMP notebook on Frequency Grid Density, we showed how to increase the density by suitably padding the windowed sections in the STFT computation. As an alternative, we discuss in this notebook interpolation techniques along the frequency direction to adjust the frequency resolution.\n", "

" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Interpolation\n", "\n", "Given a sequence of data points, the goal of **interpolation** is to compute intermediate data points that refine the sequence in some meaningful way. To be more concrete, let us consider a function $f\\colon\\mathbb{R}\\to\\mathbb{R}$ that maps a parameter $t\\in\\mathbb{R}$ to a value $f(t)\\in\\mathbb{R}$. Suppose that we have values $f(t_n)$ only for a discrete set of parameters $t_n\\in\\mathbb{R}$ for $n\\in\\mathbb{Z}$, where we assuming $t_{n} > t_{n-1}$. Then, the goal of interpolation is to estimate values $f^\\ast(t)$ from the known values $f(t_n)$ such that \n", "\n", "$$\n", "f^\\ast(t) \\approx f(t)\n", "$$\n", "\n", "for any $t\\in\\mathbb{R}$. In practice, the function $f$ is not known. However, one often assumes certain properties of $f$ such as continuity, smoothness, differentiability, and so on. \n", "\n", "The simplest interpolation method is known as **piecewise constant interpolation** (or **nearest-neighbor interpolation**). Given a parameter $t\\in\\mathbb{R}$, one simply takes the nearest parameter $t_n$ and defines \n", "\n", "$$f^\\ast(t)=f(t_n).$$\n", "\n", "In the following example, we compute a nearest-neighbor interpolation using the Python class [`scipy.inperploate.interp1d`](https://docs.scipy.org/doc/scipy/reference/generated/scipy.interpolate.interp1d.html). " ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "execution": { "iopub.execute_input": "2024-02-15T08:58:52.452211Z", "iopub.status.busy": "2024-02-15T08:58:52.451929Z", "iopub.status.idle": "2024-02-15T08:58:54.559301Z", "shell.execute_reply": "2024-02-15T08:58:54.558763Z" } }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from scipy.interpolate import interp1d\n", "import librosa\n", "%matplotlib inline\n", "\n", "# Simulates the original function\n", "t = np.arange(-0.5, 10.5, 0.01)\n", "f = np.sin(2 * t)\n", "\n", "# Known funcion values\n", "t_n = np.arange(0, 11)\n", "f_n = np.sin(2 * t_n)\n", "\n", "# Interpolation\n", "f_interpol_nearest = interp1d(t_n, f_n, kind='nearest', fill_value='extrapolate')(t)\n", "\n", "plt.figure(figsize=(8, 2)) \n", "plt.plot(t, f, color=(0.8, 0.8, 0.8))\n", "plt.plot(t, f_interpol_nearest, 'r-')\n", "plt.plot(t_n, f_n, 'ko')\n", "plt.ylim([-1.5,1.5])\n", "plt.title('Piecewise constant interpolation')\n", "plt.tight_layout()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Nearest-neighbor interpolation typically yields a discontinuous function. To obtain a continuous interpolation function, a simple alternative is **linear interpolation**. Given some parameter $t$ that lies between $t_{n-1}$ and $t_n$, one defines\n", "\n", "$$\n", "f^\\ast(t)=f(t_{n-1}) + (f(t_{n})-f(t_{n-1}))\\cdot\\frac{t-t_{n-1}}{t_{n} - t_{n-1}}. \n", "$$\n", "\n", "Continuing our example above, we obtain the following result:" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "execution": { "iopub.execute_input": "2024-02-15T08:58:54.591097Z", "iopub.status.busy": "2024-02-15T08:58:54.590793Z", "iopub.status.idle": "2024-02-15T08:58:54.681298Z", "shell.execute_reply": "2024-02-15T08:58:54.680768Z" } }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "f_interpol_linear = interp1d(t_n, f_n, kind='linear', fill_value='extrapolate')(t)\n", "\n", "plt.figure(figsize=(8, 2)) \n", "plt.plot(t, f, color=(0.8, 0.8, 0.8))\n", "plt.plot(t, f_interpol_linear, 'r-')\n", "plt.plot(t_n, f_n, 'ko')\n", "plt.ylim([-1.5,1.5])\n", "plt.title('Linear interpolation')\n", "plt.tight_layout()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The Python class [`scipy.inperploate.interp1d`](https://docs.scipy.org/doc/scipy/reference/generated/scipy.interpolate.interp1d.html) offer several kinds of interpolation methods including nearest-neighbor, linear, and spline interpolations of various orders. As another example, we show the result for **cubic interpolation** (spline of third order) and refer to the [Python documentation](https://docs.scipy.org/doc/scipy/reference/generated/scipy.interpolate.interp1d.html) for further details." ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "execution": { "iopub.execute_input": "2024-02-15T08:58:54.684118Z", "iopub.status.busy": "2024-02-15T08:58:54.683928Z", "iopub.status.idle": "2024-02-15T08:58:54.771410Z", "shell.execute_reply": "2024-02-15T08:58:54.770866Z" } }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "f_interpol_cubic = interp1d(t_n, f_n, kind='cubic', fill_value='extrapolate')(t)\n", "\n", "plt.figure(figsize=(8, 2)) \n", "plt.plot(t, f, color=(0.8, 0.8, 0.8))\n", "plt.plot(t, f_interpol_cubic, 'r-')\n", "plt.plot(t_n, f_n, 'ko')\n", "plt.ylim([-1.5,1.5])\n", "plt.title('Cubic interpolation')\n", "plt.tight_layout()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Frequency Interpolation\n", "\n", "To increase the density of the linear **frequency grid** introduced by the DFT, one may use a [larger DFT based on zero-padding](../C2/C2_STFT-FreqGridDensity.html). We now introduce an alternative by applying interpolation techniques in the frequency domain. Following Section 2.1.3 of [Müller, FMP, Springer 2015], let $x\\in \\mathbb{R}^N$ be a discrete signal of length $N\\in\\mathbb{N}$, $F_\\mathrm{s}$ the sampling rate, $X = \\mathrm{DFT}_N \\cdot x$ the DFT, and $Y=|X|$ the magnitude DFT. Then the index $k$ of $Y(k)$ corresponds to the physical frequency\n", "\n", "\\begin{equation}\n", " F_\\mathrm{coef}(k) := \\frac{k\\cdot F_\\mathrm{s}}{N}\n", "\\end{equation}\n", "\n", "given in Hertz. In other words, the resulting frequency grid has a resolution of $F_\\mathrm{s}/N$. Introducing a factor $\\rho\\in\\mathbb{N}$, we refine the frequency grid considering the resolution $F_\\mathrm{s}/(\\rho\\cdot N)$. Based on this refined frequency grid, we compute magnitude frequency coefficients using interpolation techniques. This strategy is implemented in the following code example." ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "execution": { "iopub.execute_input": "2024-02-15T08:58:54.774057Z", "iopub.status.busy": "2024-02-15T08:58:54.773858Z", "iopub.status.idle": "2024-02-15T08:58:55.472671Z", "shell.execute_reply": "2024-02-15T08:58:55.472149Z" } }, "outputs": [ { "data": { "image/png": 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\n", 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\n", 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\n", 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\n", 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "Fs = 32\n", "duration = 2\n", "omega1 = 5\n", "omega2 = 15\n", "N = int(duration * Fs)\n", "t = np.arange(N) / Fs\n", "t1 = t[:N//2]\n", "t2 = t[N//2:]\n", "\n", "x1 = 1.0 * np.sin(2 * np.pi * omega1 * t1)\n", "x2 = 0.7 * np.sin(2 * np.pi * omega2 * t2)\n", "x = np.concatenate((x1, x2))\n", "\n", "plt.figure(figsize=(6, 2))\n", "plt.plot(t, x, c='k')\n", "plt.title('Orginal signal ($N$=%d)' % N)\n", "plt.xlabel('Time (seconds)')\n", "plt.xlim([t[0], t[-1]]) \n", "plt.tight_layout()\n", "\n", "Y = np.abs(np.fft.fft(x)) / Fs\n", "Y = Y[:N//2+1]\n", "F_coef = np.arange(N//2+1)*Fs/N\n", "plt.figure(figsize=(6, 2))\n", "plt.plot(F_coef,Y, c='k')\n", "plt.title('Magnitude DFT ($N$=%d)' % N)\n", "plt.xlabel('Frequency (Hz)')\n", "plt.xlim([F_coef[0], F_coef[-1]]) \n", "plt.tight_layout()\n", "\n", "def interpolate_plot_DFT(N, Fs, F_coef, rho, int_method):\n", " F_coef_interpol = np.arange(F_coef[0], F_coef[-1], Fs/(rho*N))\n", " Y_interpol = interp1d(F_coef, Y, kind=int_method)(F_coef_interpol)\n", " plt.figure(figsize=(6, 2))\n", " plt.plot(F_coef_interpol, Y_interpol, c='k')\n", " plt.title(r'Magnitude DFT (interpolation: %s, $\\rho$=%d)'%(int_method,rho))\n", " plt.xlabel('Frequency (Hz)')\n", " plt.xlim([F_coef[0], F_coef[-1]])\n", " plt.tight_layout()\n", "\n", "rho = 4\n", "interpolate_plot_DFT(N=N, Fs=Fs, F_coef=F_coef, rho=rho, int_method='nearest')\n", "interpolate_plot_DFT(N=N, Fs=Fs, F_coef=F_coef, rho=rho, int_method='linear')\n", "interpolate_plot_DFT(N=N, Fs=Fs, F_coef=F_coef, rho=rho, int_method='cubic')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Frequency Interpolation for STFT\n", "\n", "To refine the frequency grid of an STFT, one can apply the interpolation strategy along the frequency direction. In the next example, we use the note C4 played by a violin (with vibrato)." ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "execution": { "iopub.execute_input": "2024-02-15T08:58:55.475398Z", "iopub.status.busy": "2024-02-15T08:58:55.475198Z", "iopub.status.idle": "2024-02-15T08:58:55.597712Z", "shell.execute_reply": "2024-02-15T08:58:55.597202Z" } }, "outputs": [ { "data": { "text/html": [ "\n", " \n", " " ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "import os\n", "import IPython.display as ipd\n", "\n", "# Load wav\n", "fn_wav = os.path.join('..', 'data', 'C2', 'FMP_C2_F05c_C4_violin.wav')\n", "\n", "Fs = 11025\n", "x, Fs = librosa.load(fn_wav, sr=Fs)\n", "ipd.display(ipd.Audio(x, rate=Fs))\n", "\n", "t_wav = np.arange(0, x.shape[0]) * 1 / Fs\n", "plt.figure(figsize=(6, 1))\n", "plt.plot(t_wav, x, c='gray')\n", "plt.xlim([t_wav[0], t_wav[-1]])\n", "plt.xlabel('Time (seconds)');" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "execution": { "iopub.execute_input": "2024-02-15T08:58:55.600671Z", "iopub.status.busy": "2024-02-15T08:58:55.600447Z", "iopub.status.idle": "2024-02-15T08:58:56.132257Z", "shell.execute_reply": "2024-02-15T08:58:56.131758Z" } }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "def stft_convention_fmp(x, Fs, N, H, pad_mode='constant', center=True, mag=False, gamma=0):\n", " \"\"\"Compute the discrete short-time Fourier transform (STFT)\n", "\n", " Notebook: C2/C2_STFT-FreqGridInterpol.ipynb\n", "\n", " Args:\n", " x (np.ndarray): Signal to be transformed\n", " Fs (scalar): Sampling rate\n", " N (int): Window size\n", " H (int): Hopsize\n", " pad_mode (str): Padding strategy is used in librosa (Default value = 'constant')\n", " center (bool): Centric view as used in librosa (Default value = True)\n", " mag (bool): Computes magnitude STFT if mag==True (Default value = False)\n", " gamma (float): Constant for logarithmic compression (only applied when mag==True) (Default value = 0)\n", "\n", " Returns:\n", " X (np.ndarray): Discrete (magnitude) short-time Fourier transform\n", " \"\"\"\n", " X = librosa.stft(x, n_fft=N, hop_length=H, win_length=N,\n", " window='hann', pad_mode=pad_mode, center=center)\n", " if mag:\n", " X = np.abs(X)**2\n", " if gamma > 0:\n", " X = np.log(1 + gamma * X)\n", " F_coef = librosa.fft_frequencies(sr=Fs, n_fft=N)\n", " T_coef = librosa.frames_to_time(np.arange(X.shape[1]), sr=Fs, hop_length=H)\n", " # T_coef = np.arange(X.shape[1]) * H/Fs\n", " # F_coef = np.arange(N//2+1) * Fs/N\n", " return X, T_coef, F_coef\n", "\n", "def compute_f_coef_linear(N, Fs, rho=1):\n", " \"\"\"Refines the frequency vector by factor of rho\n", "\n", " Notebook: C2/C2_STFT-FreqGridInterpol.ipynb\n", "\n", " Args:\n", " N (int): Window size\n", " Fs (scalar): Sampling rate\n", " rho (int): Factor for refinement (Default value = 1)\n", "\n", " Returns:\n", " F_coef_new (np.ndarray): Refined frequency vector\n", " \"\"\"\n", " L = rho * N\n", " F_coef_new = np.arange(0, L//2+1) * Fs / L\n", " return F_coef_new\n", "\n", "def interpolate_freq_stft(Y, F_coef, F_coef_new):\n", " \"\"\"Interpolation of STFT along frequency axis\n", "\n", " Notebook: C2/C2_STFT-FreqGridInterpol.ipynb\n", "\n", " Args:\n", " Y (np.ndarray): Magnitude STFT\n", " F_coef (np.ndarray): Vector of frequency values\n", " F_coef_new (np.ndarray): Vector of new frequency values\n", "\n", " Returns:\n", " Y_interpol (np.ndarray): Interploated magnitude STFT\n", " \"\"\"\n", " compute_Y_interpol = interp1d(F_coef, Y, kind='cubic', axis=0)\n", " Y_interpol = compute_Y_interpol(F_coef_new)\n", " return Y_interpol\n", "\n", "def plot_compute_spectrogram_physical(x, Fs, N, H, xlim, ylim, rho=1, color='gray_r'):\n", " Y, T_coef, F_coef = stft_convention_fmp(x, Fs, N, H, mag=True, gamma=100)\n", " F_coef_new = compute_f_coef_linear(N, Fs, rho=rho)\n", " Y_interpol = interpolate_freq_stft(Y, F_coef, F_coef_new) \n", " extent=[T_coef[0], T_coef[-1], F_coef[0], F_coef[-1]]\n", " plt.imshow(Y_interpol, cmap=color, aspect='auto', origin='lower', extent=extent)\n", " plt.xlabel('Time (seconds)')\n", " plt.ylabel('Frequency (Hz)')\n", " plt.title(r'$\\rho$=%d' % rho)\n", " plt.ylim(ylim)\n", " plt.xlim(xlim)\n", " plt.colorbar()\n", "\n", "xlim_sec = [2, 3]\n", "ylim_hz = [2000, 3000]\n", "\n", "N = 256\n", "H = 64\n", "plt.figure(figsize=(10, 4))\n", " \n", "plt.subplot(1, 3, 1)\n", "plot_compute_spectrogram_physical(x, Fs, N, H, xlim=xlim_sec, ylim=ylim_hz, rho=1)\n", "\n", "plt.subplot(1, 3, 2)\n", "plot_compute_spectrogram_physical(x, Fs, N, H, xlim=xlim_sec, ylim=ylim_hz, rho=2)\n", "\n", "plt.subplot(1, 3, 3)\n", "plot_compute_spectrogram_physical(x, Fs, N, H, xlim=xlim_sec, ylim=ylim_hz, rho=4)\n", "\n", "plt.tight_layout()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Log-Frequency STFT via Interpolation\n", "\n", "This interpolation techniques can be also used for a non-linear deformation of the frequency grid. For example, one may convert the linearly spaced spaced frequency axis (measured in Hertz) into a logarithmically spaced frequency axis (measured in pitches or cents). This results in a [**log-frequency spectrogram**](../C3/C3S1_SpecLogFreq-Chromagram.html), a concept introduced in Section 3.1.1 of [Müller, FMP, Springer 2015]. Without explaining the details, the following code shows how one may implement a logarithmic conversion of the frequency axis. The frequency values are then obtained via interpolation as introduced above. \n", "\n", "The main step is to define a logarithmically spaced frequency grid. In the following we use the notion of **cents**, which is a logarithmic unit of measure used for musical intervals (see Section 1.3.2 of [Müller, FMP, Springer 2015]. Given a reference frequency $\\omega_0$, the distance between an arbitrary frequency $\\omega$ and $\\omega_0$ is then specified as \n", "\n", "$$\n", " \\log_2\\left(\\frac{\\omega}{\\omega_0}\\right)\\cdot 1200\n", "$$\n", "\n", "given in cents. In the following function, we compute a logarithmically spaced frequency axis starting with a minimal frequency value (the parameter `F_min` is used as reference frequency $\\omega_0$, thus corresponding to $0$ cents). Furthermore, the function has a parameter `R` which specifies the logarithmic resolution in cents. In other words, two subsequent frequency bins on the logarithmic frequency axis are `R` cents apart. The maximum frequency to be considered is specified by another parameter `F_max`. In the following example, we use the frequencies `F_min = 100` (corresponding to $0$ cents) and `F_max = 3200` (corresponding to $6000$ cents). Furthermore, the resolution is set to `R=20` (corresponding to $60$ frequency bins per octave)." ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "execution": { "iopub.execute_input": "2024-02-15T08:58:56.135370Z", "iopub.status.busy": "2024-02-15T08:58:56.135190Z", "iopub.status.idle": "2024-02-15T08:58:56.143122Z", "shell.execute_reply": "2024-02-15T08:58:56.142567Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "#bins=513, F_coef[0] = 0.00, F_coef[1] = 10.77, F_coef[-1] =5512.50\n", "#bins=300, F_coef_log[0] =100.00, F_coef_log[1] =101.16, F_coef_log[-1] =3163.24\n", "#bins=300, F_coef_cents[0]= 0.00, F_coef_cents[1]= 20.00, F_coef_cents[-1]=5980.00\n" ] } ], "source": [ "def compute_f_coef_log(R, F_min, F_max):\n", " \"\"\"Adapts the frequency vector in a logarithmic fashion\n", "\n", " Notebook: C2/C2_STFT-FreqGridInterpol.ipynb\n", "\n", " Args:\n", " R (scalar): Resolution (cents)\n", " F_min (float): Minimum frequency\n", " F_max (float): Maximum frequency (not included)\n", "\n", " Returns:\n", " F_coef_log (np.ndarray): Refined frequency vector with values given in Hz)\n", " F_coef_cents (np.ndarray): Refined frequency vector with values given in cents.\n", " Note: F_min serves as reference (0 cents)\n", " \"\"\"\n", " n_bins = np.ceil(1200 * np.log2(F_max / F_min) / R).astype(int)\n", " F_coef_log = 2 ** (np.arange(0, n_bins) * R / 1200) * F_min\n", " F_coef_cents = 1200 * np.log2(F_coef_log / F_min)\n", " return F_coef_log, F_coef_cents\n", "\n", "N = 1024\n", "H = 256\n", "Y, T_coef, F_coef = stft_convention_fmp(x, Fs, N, H, mag=True, gamma=100)\n", "\n", "F_min = 100\n", "F_max = 3200\n", "R = 20\n", "F_coef_log, F_coef_cents = compute_f_coef_log(R, F_min, F_max)\n", "\n", "print('#bins=%3d, F_coef[0] =%6.2f, F_coef[1] =%6.2f, F_coef[-1] =%6.2f'%(len(F_coef),F_coef[0], F_coef[1], F_coef[-1]))\n", "print('#bins=%3d, F_coef_log[0] =%6.2f, F_coef_log[1] =%6.2f, F_coef_log[-1] =%6.2f'%(len(F_coef_log),F_coef_log[0], F_coef_log[1], F_coef_log[-1]))\n", "print('#bins=%3d, F_coef_cents[0]=%6.2f, F_coef_cents[1]=%6.2f, F_coef_cents[-1]=%6.2f'%(len(F_coef_cents),F_coef_cents[0], F_coef_cents[1], F_coef_cents[-1]))" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "execution": { "iopub.execute_input": "2024-02-15T08:58:56.145560Z", "iopub.status.busy": "2024-02-15T08:58:56.145379Z", "iopub.status.idle": "2024-02-15T08:58:56.553263Z", "shell.execute_reply": "2024-02-15T08:58:56.552759Z" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "Y_interpol = interpolate_freq_stft(Y, F_coef, F_coef_log)\n", "color = 'gray_r' \n", "\n", "plt.figure(figsize=(10, 4))\n", "plt.subplot(1, 3, 1)\n", "extent=[T_coef[0], T_coef[-1], F_coef[0], F_coef[-1]]\n", "plt.imshow(Y, cmap=color, aspect='auto', origin='lower', extent=extent)\n", "y_ticks_freq = np.array([100, 400, 800, 1200, 1600, 2000, 2400, 2800, 3200])\n", "plt.yticks(y_ticks_freq)\n", "plt.xlabel('Time (seconds)')\n", "plt.ylabel('Frequency (Hz)')\n", "plt.title('Linear frequency axis')\n", "plt.ylim([F_min, F_max])\n", "plt.colorbar()\n", "\n", "plt.subplot(1, 3, 2)\n", "extent=[T_coef[0], T_coef[-1], F_coef_cents[0], F_coef_cents[-1]]\n", "plt.imshow(Y_interpol, cmap=color, aspect='auto', origin='lower', extent=extent)\n", "y_tick_freq_cents = 1200 * np.log2(y_ticks_freq / F_min)\n", "plt.yticks(y_tick_freq_cents, y_ticks_freq)\n", "plt.xlabel('Time (seconds)')\n", "plt.ylabel('Frequency (Hz)')\n", "plt.title('Log-frequency axis')\n", "plt.title('Log-frequency axis with R=%d' % R)\n", "plt.colorbar()\n", "\n", "plt.subplot(1, 3, 3)\n", "extent=[T_coef[0], T_coef[-1], F_coef_cents[0], F_coef_cents[-1]]\n", "plt.imshow(Y_interpol, cmap=color, aspect='auto', origin='lower', extent=extent)\n", "y_ticks_cents = np.array([0, 1200, 2400, 3600, 4800, 6000])\n", "plt.yticks(y_ticks_cents)\n", "plt.xlabel('Time (seconds)')\n", "plt.ylabel('Frequency (cents)')\n", "plt.title('Log-frequency axis')\n", "plt.title('Log-frequency axis with R=%d' % R)\n", "plt.colorbar()\n", "plt.tight_layout()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Further Notes\n", "\n", "* The function `stft_convention_fmp` implements the STFT variant as used for most parts in the FMP notebooks, see also the FMP notebook on STFT conventions and implementations.\n", "* The transformation of the STFT frequency axis is a crucial step in many music processing applications. For example, in the FMP notebook on log-frequency spectrograms and chromagrams, the frequency axis is partitioned logarithmically to yield a musically motivated pitch axis. \n", "* Similarly, in the FMP notebook on salience representations, the frequency axis is converted in a logarithmic fashion." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", "Acknowledgment: This notebook was created by Meinard Müller and Sebastian Rosenzweig.\n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "\n", "
\"C0\"\"C1\"\"C2\"\"C3\"\"C4\"\"C5\"\"C6\"\"C7\"\"C8\"
" ] } ], "metadata": { "anaconda-cloud": {}, "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.16" } }, "nbformat": 4, "nbformat_minor": 1 }