Skip to content

M
musicinformationretrieval-com
Commit 95677803 authored by Steve Tjoa's avatar Steve Tjoa
Browse files
Options

stft; chroma

parent 3cf45164
Show whitespace changes
Inline Side-by-side
Showing with 14466 additions and 19 deletions
alphabetical_index.html
View file @ 95677803
......@@ -11840,6 +11840,17 @@ div#notebook {
<td></td>
<td>Energy</td>
</tr>
<tr>
<td>Spectrogram</td>
<td><a href="stft.html">STFT and Spectrogram</a></td>
<td><a href="https://en.wikipedia.org/wiki/Spectrogram">Spectrogram</a></td>
<td></td>
<td>29, 55</td>
<td>STFT</td>
</tr>
<tr>
<td>Short-time Fourier transform</td>
</tr>
</tbody>
</table>
......
alphabetical_index.ipynb
View file @ 95677803
......@@ -29,7 +29,9 @@
"source": [
"|Term|musicinformationretrieval.com|Wikipedia|librosa|FMP|Related|\n",
"|-|-|-|-|-|-|\n",
"|Root-mean-square energy|[Energy and RMSE](energy.html)|[Root mean square](https://en.wikipedia.org/wiki/Root_mean_square)|[`librosa.feature.rmse`](https://librosa.github.io/librosa/generated/librosa.feature.rmse.html)| |Energy|\n"
"|Root-mean-square energy|[Energy and RMSE](energy.html)|[Root mean square](https://en.wikipedia.org/wiki/Root_mean_square)|[`librosa.feature.rmse`](https://librosa.github.io/librosa/generated/librosa.feature.rmse.html)| |Energy|\n",
"|Spectrogram|[STFT and Spectrogram](stft.html)|[Spectrogram](https://en.wikipedia.org/wiki/Spectrogram)||29, 55|STFT|\n",
"|Short-time Fourier transform|\n"
]
},
{
......
chroma.html 0 → 100644
View file @ 95677803
This source diff could not be displayed because it is too large. You can view the blob instead.
chroma.ipynb 0 → 100644
View file @ 95677803
This source diff could not be displayed because it is too large. You can view the blob instead.
index.html
View file @ 95677803
......@@ -11863,8 +11863,8 @@ div#notebook {
<li><a href="energy.html">Energy and RMSE</a> (<a href="energy.ipynb">ipynb</a>)</li>
<li><a href="zcr.html">Zero Crossing Rate</a> (<a href="zcr.ipynb">ipynb</a>)</li>
<li><a href="fourier_transform.html">Fourier Transform</a> (<a href="fourier_transform.ipynb">ipynb</a>)</li>
<li><a href="stft.html">Short-Time Fourier Transform and CQT</a> (<a href="stft.ipynb">ipynb</a>)</li>
<li><a href="chroma.html">Chroma</a> (<a href="chroma.ipynb">ipynb</a>)</li>
<li><a href="stft.html">Short-time Fourier Transform and Spectrogram</a> (<a href="stft.ipynb">ipynb</a>)</li>
<li><a href="chroma.html">Constant-Q Transform and Chroma</a> (<a href="chroma.ipynb">ipynb</a>)</li>
<li><a href="spectral_features.html">Spectral Features</a> (<a href="spectral_features.ipynb">ipynb</a>)</li>
<li><a href="autocorrelation.html">Autocorrelation</a> (<a href="autocorrelation.ipynb">ipynb</a>)</li>
<li><a href="pitch_transcription_exercise.html">Pitch Transcription Exercise</a> (<a href="pitch_transcription_exercise.ipynb">ipynb</a>)</li>
......
index.ipynb
View file @ 95677803
......@@ -75,8 +75,8 @@
"1. [Energy and RMSE](energy.html) ([ipynb](energy.ipynb))\n",
"1. [Zero Crossing Rate](zcr.html) ([ipynb](zcr.ipynb))\n",
"1. [Fourier Transform](fourier_transform.html) ([ipynb](fourier_transform.ipynb))\n",
"1. [Short-Time Fourier Transform and CQT](stft.html) ([ipynb](stft.ipynb))\n",
"1. [Chroma](chroma.html) ([ipynb](chroma.ipynb))\n",
"1. [Short-time Fourier Transform and Spectrogram](stft.html) ([ipynb](stft.ipynb))\n",
"1. [Constant-Q Transform and Chroma](chroma.html) ([ipynb](chroma.ipynb))\n",
"1. [Spectral Features](spectral_features.html) ([ipynb](spectral_features.ipynb))\n",
"1. [Autocorrelation](autocorrelation.html) ([ipynb](autocorrelation.ipynb))\n",
"1. [Pitch Transcription Exercise](pitch_transcription_exercise.html) ([ipynb](pitch_transcription_exercise.ipynb))"
......
stft.html
View file @ 95677803
......@@ -11773,7 +11773,7 @@ div#notebook {
<div class="cell border-box-sizing code_cell rendered">
<div class="input">
<div class="prompt input_prompt">In&nbsp;[1]:</div>
<div class="prompt input_prompt">In&nbsp;[4]:</div>
<div class="inner_cell">
<div class="input_area">
<div class=" highlight hl-ipython2"><pre><span></span><span class="o">%</span><span class="k">matplotlib</span> inline
......@@ -11809,14 +11809,41 @@ div#notebook {
</div>
<div class="inner_cell">
<div class="text_cell_render border-box-sizing rendered_html">
<p>Let's listen to a file:</p>
<p>Musical signals are highly non-stationary, i.e., their statistics change over time. It would be rather meaningless to compute a single Fourier transform over an entire 10-minute song.</p>
</div>
</div>
</div>
<div class="cell border-box-sizing text_cell rendered"><div class="prompt input_prompt">
</div>
<div class="inner_cell">
<div class="text_cell_render border-box-sizing rendered_html">
<p>The <strong>short-time Fourier transform (STFT)</strong> (<a href="https://en.wikipedia.org/wiki/Short-time_Fourier_transform">Wikipedia</a>; FMP, p. 53) is obtained by computing the Fourier transform for successive frames in a signal.</p>
$$ X(m, \omega) = \sum_n x(n) w(n-m) e^{-j \omega n} $$
</div>
</div>
</div>
<div class="cell border-box-sizing text_cell rendered"><div class="prompt input_prompt">
</div>
<div class="inner_cell">
<div class="text_cell_render border-box-sizing rendered_html">
<p>As we increase $m$, we slide the window function $w$ to the right. For the resulting frame, $x(n) w(n-m)$, we compute the Fourier transform. Therefore, the STFT $X$ is a function of both time, $m$, and frequency, $\omega$.</p>
</div>
</div>
</div>
<div class="cell border-box-sizing text_cell rendered"><div class="prompt input_prompt">
</div>
<div class="inner_cell">
<div class="text_cell_render border-box-sizing rendered_html">
<p>Let's load a file:</p>
</div>
</div>
</div>
<div class="cell border-box-sizing code_cell rendered">
<div class="input">
<div class="prompt input_prompt">In&nbsp;[2]:</div>
<div class="prompt input_prompt">In&nbsp;[20]:</div>
<div class="inner_cell">
<div class="input_area">
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">x</span><span class="p">,</span> <span class="n">sr</span> <span class="o">=</span> <span class="n">librosa</span><span class="o">.</span><span class="n">load</span><span class="p">(</span><span class="s1">&#39;audio/simple_piano.wav&#39;</span><span class="p">)</span>
......@@ -11833,7 +11860,7 @@ div#notebook {
<div class="output_area">
<div class="prompt output_prompt">Out[2]:</div>
<div class="prompt output_prompt">Out[20]:</div>
......@@ -11851,6 +11878,156 @@ div#notebook {
</div>
</div>
</div>
<div class="cell border-box-sizing text_cell rendered"><div class="prompt input_prompt">
</div>
<div class="inner_cell">
<div class="text_cell_render border-box-sizing rendered_html">
<p><a href="https://librosa.github.io/librosa/generated/librosa.core.stft.html#librosa.core.stft"><code>librosa.stft</code></a> computes a STFT. We provide it a frame size, i.e. the size of the FFT, and a hop length, i.e. the frame increment:</p>
</div>
</div>
</div>
<div class="cell border-box-sizing code_cell rendered">
<div class="input">
<div class="prompt input_prompt">In&nbsp;[21]:</div>
<div class="inner_cell">
<div class="input_area">
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">hop_length</span> <span class="o">=</span> <span class="mi">512</span>
<span class="n">n_fft</span> <span class="o">=</span> <span class="mi">2048</span>
<span class="n">X</span> <span class="o">=</span> <span class="n">librosa</span><span class="o">.</span><span class="n">stft</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">n_fft</span><span class="o">=</span><span class="n">n_fft</span><span class="p">,</span> <span class="n">hop_length</span><span class="o">=</span><span class="n">hop_length</span><span class="p">)</span>
</pre></div>
</div>
</div>
</div>
</div>
<div class="cell border-box-sizing text_cell rendered"><div class="prompt input_prompt">
</div>
<div class="inner_cell">
<div class="text_cell_render border-box-sizing rendered_html">
<p>To convert the hop length and frame size to units of seconds:</p>
</div>
</div>
</div>
<div class="cell border-box-sizing code_cell rendered">
<div class="input">
<div class="prompt input_prompt">In&nbsp;[22]:</div>
<div class="inner_cell">
<div class="input_area">
<div class=" highlight hl-ipython2"><pre><span></span><span class="nb">float</span><span class="p">(</span><span class="n">hop_length</span><span class="p">)</span><span class="o">/</span><span class="n">sr</span> <span class="c1"># units of seconds</span>
</pre></div>
</div>
</div>
</div>
<div class="output_wrapper">
<div class="output">
<div class="output_area">
<div class="prompt output_prompt">Out[22]:</div>
<div class="output_text output_subarea output_execute_result">
<pre>0.023219954648526078</pre>
</div>
</div>
</div>
</div>
</div>
<div class="cell border-box-sizing code_cell rendered">
<div class="input">
<div class="prompt input_prompt">In&nbsp;[23]:</div>
<div class="inner_cell">
<div class="input_area">
<div class=" highlight hl-ipython2"><pre><span></span><span class="nb">float</span><span class="p">(</span><span class="n">n_fft</span><span class="p">)</span><span class="o">/</span><span class="n">sr</span> <span class="c1"># units of seconds</span>
</pre></div>
</div>
</div>
</div>
<div class="output_wrapper">
<div class="output">
<div class="output_area">
<div class="prompt output_prompt">Out[23]:</div>
<div class="output_text output_subarea output_execute_result">
<pre>0.09287981859410431</pre>
</div>
</div>
</div>
</div>
</div>
<div class="cell border-box-sizing text_cell rendered"><div class="prompt input_prompt">
</div>
<div class="inner_cell">
<div class="text_cell_render border-box-sizing rendered_html">
<p>For real-valued signals, the Fourier transform is symmetric about the midpoint. Therefore, <code>librosa.stft</code> only retains one half of the output:</p>
</div>
</div>
</div>
<div class="cell border-box-sizing code_cell rendered">
<div class="input">
<div class="prompt input_prompt">In&nbsp;[24]:</div>
<div class="inner_cell">
<div class="input_area">
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">X</span><span class="o">.</span><span class="n">shape</span>
</pre></div>
</div>
</div>
</div>
<div class="output_wrapper">
<div class="output">
<div class="output_area">
<div class="prompt output_prompt">Out[24]:</div>
<div class="output_text output_subarea output_execute_result">
<pre>(1025, 166)</pre>
</div>
</div>
</div>
</div>
</div>
<div class="cell border-box-sizing text_cell rendered"><div class="prompt input_prompt">
</div>
<div class="inner_cell">
<div class="text_cell_render border-box-sizing rendered_html">
<p>This STFT has 1025 frequency bins and 166 frames in time.</p>
</div>
</div>
</div>
<div class="cell border-box-sizing text_cell rendered"><div class="prompt input_prompt">
</div>
......@@ -11864,17 +12041,214 @@ div#notebook {
</div>
<div class="inner_cell">
<div class="text_cell_render border-box-sizing rendered_html">
<p>Musical signals are highly non-stationary, i.e., their statistics change over time. It would be rather meaningless to compute a single spectrum over an entire 10-minute song.</p>
<p>Instead, we compute a spectrum for small frames of the audio signal. The resulting sequence of spectra is called a <a href="https://en.wikipedia.org/wiki/Spectrogram"><em>spectrogram</em></a>.</p>
<p>In music processing, we often only care about the spectral magnitude and not the phase content.</p>
<p>The <strong>spectrogram</strong> (<a href="https://en.wikipedia.org/wiki/Spectrogram">Wikipedia</a>; FMP, p. 29, 55) shows the the intensity of frequencies over time. A spectrogram is simply the squared magnitude of the STFT:</p>
$$ S(m, \omega) = \left| X(m, \omega) \right|^2 $$
</div>
</div>
</div>
<div class="cell border-box-sizing text_cell rendered"><div class="prompt input_prompt">
</div>
<div class="inner_cell">
<div class="text_cell_render border-box-sizing rendered_html">
<p>The human perception of sound intensity is logarithmic in nature. Therefore, we are often interested in the log amplitude:</p>
</div>
</div>
</div>
<div class="cell border-box-sizing code_cell rendered">
<div class="input">
<div class="prompt input_prompt">In&nbsp;[25]:</div>
<div class="inner_cell">
<div class="input_area">
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">S</span> <span class="o">=</span> <span class="nb">abs</span><span class="p">(</span><span class="n">X</span><span class="p">)</span><span class="o">**</span><span class="mi">2</span>
</pre></div>
</div>
</div>
</div>
</div>
<div class="cell border-box-sizing text_cell rendered"><div class="prompt input_prompt">
</div>
<div class="inner_cell">
<div class="text_cell_render border-box-sizing rendered_html">
<p>To display any type of spectrogram in librosa, use <a href="http://bmcfee.github.io/librosa/generated/librosa.display.specshow.html"><code>librosa.display.specshow</code></a>.</p>
</div>
</div>
</div>
<div class="cell border-box-sizing code_cell rendered">
<div class="input">
<div class="prompt input_prompt">In&nbsp;[26]:</div>
<div class="inner_cell">
<div class="input_area">
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">librosa</span><span class="o">.</span><span class="n">display</span><span class="o">.</span><span class="n">specshow</span><span class="p">(</span><span class="n">S</span><span class="p">,</span> <span class="n">sr</span><span class="o">=</span><span class="n">sr</span><span class="p">,</span> <span class="n">x_axis</span><span class="o">=</span><span class="s1">&#39;time&#39;</span><span class="p">,</span> <span class="n">y_axis</span><span class="o">=</span><span class="s1">&#39;linear&#39;</span><span class="p">)</span>
</pre></div>
</div>
</div>
</div>
<div class="output_wrapper">
<div class="output">
<div class="output_area">
<div class="prompt output_prompt">Out[26]:</div>
<div class="output_text output_subarea output_execute_result">
<pre>&lt;matplotlib.axes._subplots.AxesSubplot at 0x10e0f3810&gt;</pre>
</div>
</div>
<div class="output_area">
<div class="prompt"></div>
<div class="output_png output_subarea ">
<img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAxQAAAE8CAYAAABZ4/fjAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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"
>
</div>
</div>
</div>
</div>
</div>
<div class="cell border-box-sizing text_cell rendered"><div class="prompt input_prompt">
</div>
<div class="inner_cell">
<div class="text_cell_render border-box-sizing rendered_html">
<h3 id="librosa.feature.melspectrogram"><code>librosa.feature.melspectrogram</code><a class="anchor-link" href="#librosa.feature.melspectrogram">&#194;&#182;</a></h3>
<h2 id="Mel-spectrogram">Mel-spectrogram<a class="anchor-link" href="#Mel-spectrogram">&#194;&#182;</a></h2>
</div>
</div>
</div>
......
stft.ipynb
View file @ 95677803
......@@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"execution_count": 4,
"metadata": {
"collapsed": true,
"slideshow": {
......@@ -40,6 +40,29 @@
"# Short-Time Fourier Transform"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Musical signals are highly non-stationary, i.e., their statistics change over time. It would be rather meaningless to compute a single Fourier transform over an entire 10-minute song."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The **short-time Fourier transform (STFT)** ([Wikipedia](https://en.wikipedia.org/wiki/Short-time_Fourier_transform); FMP, p. 53) is obtained by computing the Fourier transform for successive frames in a signal. \n",
"\n",
"$$ X(m, \\omega) = \\sum_n x(n) w(n-m) e^{-j \\omega n} $$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"As we increase $m$, we slide the window function $w$ to the right. For the resulting frame, $x(n) w(n-m)$, we compute the Fourier transform. Therefore, the STFT $X$ is a function of both time, $m$, and frequency, $\\omega$."
]
},
{
"cell_type": "markdown",
"metadata": {
......@@ -48,12 +71,12 @@
}
},
"source": [
"Let's listen to a file:"
"Let's load a file:"
]
},
{
"cell_type": "code",
"execution_count": 2,
"execution_count": 20,
"metadata": {
"slideshow": {
"slide_type": "subslide"
......@@ -74,7 +97,7 @@
"<IPython.lib.display.Audio object>"
]
},
"execution_count": 2,
"execution_count": 20,
"metadata": {},
"output_type": "execute_result"
}
......@@ -84,6 +107,105 @@
"ipd.Audio(x, rate=sr)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"[`librosa.stft`](https://librosa.github.io/librosa/generated/librosa.core.stft.html#librosa.core.stft) computes a STFT. We provide it a frame size, i.e. the size of the FFT, and a hop length, i.e. the frame increment:"
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {},
"outputs": [],
"source": [
"hop_length = 512\n",
"n_fft = 2048\n",
"X = librosa.stft(x, n_fft=n_fft, hop_length=hop_length)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"To convert the hop length and frame size to units of seconds:"
]
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"0.023219954648526078"
]
},
"execution_count": 22,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"float(hop_length)/sr # units of seconds"
]
},
{
"cell_type": "code",
"execution_count": 23,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"0.09287981859410431"
]
},
"execution_count": 23,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"float(n_fft)/sr # units of seconds"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"For real-valued signals, the Fourier transform is symmetric about the midpoint. Therefore, `librosa.stft` only retains one half of the output:"
]
},
{
"cell_type": "code",
"execution_count": 24,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(1025, 166)"
]
},
"execution_count": 24,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"X.shape"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This STFT has 1025 frequency bins and 166 frames in time."
]
},
{
"cell_type": "markdown",
"metadata": {
......@@ -103,20 +225,88 @@
}
},
"source": [
"Musical signals are highly non-stationary, i.e., their statistics change over time. It would be rather meaningless to compute a single spectrum over an entire 10-minute song.\n",
"In music processing, we often only care about the spectral magnitude and not the phase content.\n",
"\n",
"The **spectrogram** ([Wikipedia](https://en.wikipedia.org/wiki/Spectrogram); FMP, p. 29, 55) shows the the intensity of frequencies over time. A spectrogram is simply the squared magnitude of the STFT:\n",
"\n",
"Instead, we compute a spectrum for small frames of the audio signal. The resulting sequence of spectra is called a [*spectrogram*](https://en.wikipedia.org/wiki/Spectrogram)."
"$$ S(m, \\omega) = \\left| X(m, \\omega) \\right|^2 $$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The human perception of sound intensity is logarithmic in nature. Therefore, we are often interested in the log amplitude:"
]
},
{
"cell_type": "code",
"execution_count": 25,
"metadata": {
"collapsed": true,
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [],
"source": [
"### `librosa.feature.melspectrogram`"
"S = abs(X)**2"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "notes"
}
},
"source": [
"To display any type of spectrogram in librosa, use [`librosa.display.specshow`](http://bmcfee.github.io/librosa/generated/librosa.display.specshow.html)."
]
},
{
"cell_type": "code",
"execution_count": 26,
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.axes._subplots.AxesSubplot at 0x10e0f3810>"
]
},
"execution_count": 26,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAxQAAAE8CAYAAABZ4/fjAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nZgIFAADQTKAAAACaCRQAAECz/wcS9nYb202fEAAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x10e094810>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"librosa.display.specshow(S, sr=sr, x_axis='time', y_axis='linear')"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"## Mel-spectrogram"
]
},
{
......@@ -152,6 +342,7 @@
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": true,
"slideshow": {
"slide_type": "subslide"
}
......
Markdown is supported
0% or
You are about to add 0 people to the discussion. Proceed with caution.
Finish editing this message first!
Please register or to comment