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<section id="module-wonambi.trans.frequency">
<span id="wonambi-trans-frequency-module"></span><h1>wonambi.trans.frequency module<a class="headerlink" href="#module-wonambi.trans.frequency" title="Permalink to this heading"></a></h1>
<p>Module to compute frequency representation.</p>
<dl class="py function">
<dt class="sig sig-object py" id="wonambi.trans.frequency.band_power">
<span class="sig-prename descclassname"><span class="pre">wonambi.trans.frequency.</span></span><span class="sig-name descname"><span class="pre">band_power</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">data</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">freq</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">scaling</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'power'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">n_fft</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">detrend</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">array_out</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/wonambi/trans/frequency.html#band_power"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#wonambi.trans.frequency.band_power" title="Permalink to this definition"></a></dt>
<dd><p>Compute power or energy acoss a frequency band, and its peak frequency.
Power is estimated using the mid-point rectangle rule. Input can be
ChanTime or ChanFreq.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>data</strong> (<em>instance</em><em> of </em><a class="reference internal" href="wonambi.datatype.html#wonambi.datatype.ChanTime" title="wonambi.datatype.ChanTime"><em>ChanTime</em></a><em> or </em><a class="reference internal" href="wonambi.datatype.html#wonambi.datatype.ChanFreq" title="wonambi.datatype.ChanFreq"><em>ChanFreq</em></a>) – data to be analyzed, one trial only</p></li>
<li><p><strong>freq</strong> (<em>tuple</em><em> of </em><em>float</em>) – Frequencies for band of interest. Power will be integrated across this
band, inclusively, and peak frequency determined within it. If a value
is None, the band is unbounded in that direction.</p></li>
<li><p><strong>input_type</strong> (<em>str</em>) – ‘time’ or ‘spectrum’</p></li>
<li><p><strong>scaling</strong> (<em>str</em>) – ‘power’ or ‘energy’, only used if data is ChanTime</p></li>
<li><p><strong>n_fft</strong> (<em>int</em>) – length of FFT. if shorter than input signal, signal is truncated; if
longer, signal is zero-padded to length</p></li>
<li><p><strong>array_out</strong> (<em>bool</em>) – if True, will return two arrays instead of two dict.</p></li>
</ul>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p><ul class="simple">
<li><p><em>dict of float, or ndarray</em> – keys are channels, values are power or energy</p></li>
<li><p><em>dict of float, or ndarray</em> – keys are channels, values are respective peak frequency</p></li>
</ul>
</p>
</dd>
</dl>
</dd></dl>
<dl class="py function">
<dt class="sig sig-object py" id="wonambi.trans.frequency.frequency">
<span class="sig-prename descclassname"><span class="pre">wonambi.trans.frequency.</span></span><span class="sig-name descname"><span class="pre">frequency</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">data</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">output</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'spectraldensity'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">scaling</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'power'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">sides</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'one'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">taper</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">halfbandwidth</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">3</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">NW</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">duration</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">overlap</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">0.5</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">step</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">detrend</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'linear'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">n_fft</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">log_trans</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">centend</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'mean'</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/wonambi/trans/frequency.html#frequency"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#wonambi.trans.frequency.frequency" title="Permalink to this definition"></a></dt>
<dd><p>Compute the
power spectral density (PSD, output=’spectraldensity’, scaling=’power’), or
energy spectral density (ESD, output=’spectraldensity’, scaling=’energy’) or
the complex fourier transform (output=’complex’, sides=’two’)</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>data</strong> (<em>instance</em><em> of </em><a class="reference internal" href="wonambi.datatype.html#wonambi.datatype.ChanTime" title="wonambi.datatype.ChanTime"><em>ChanTime</em></a>) – one of the datatypes</p></li>
<li><p><strong>detrend</strong> (<em>str</em>) – None (no detrending), ‘constant’ (remove mean), ‘linear’ (remove linear
trend)</p></li>
<li><p><strong>output</strong> (<em>str</em>) – ‘spectraldensity’ or ‘csd’ or ‘complex’
‘spectraldensity’ meaning the autospectrum or auto-spectral density,
a special case of ‘csd’ (cross-spectral density), where the signal is
cross-correlated with itself
if ‘csd’, both channels in data are used as input</p></li>
<li><p><strong>sides</strong> (<em>str</em>) – ‘one’ or ‘two’, where ‘two’ implies negative frequencies</p></li>
<li><p><strong>scaling</strong> (<em>str</em>) – ‘power’ (units: V ** 2 / Hz), ‘energy’ (units: V ** 2), ‘fieldtrip’,
‘chronux’</p></li>
<li><p><strong>taper</strong> (<em>str</em>) – Taper to use, commonly used tapers are ‘boxcar’, ‘hann’, ‘dpss’</p></li>
<li><p><strong>halfbandwidth</strong> (<em>int</em>) – (only if taper=’dpss’) Half bandwidth (in Hz), frequency smoothing will
be from +halfbandwidth to -halfbandwidth</p></li>
<li><p><strong>NW</strong> (<em>int</em>) – (only if taper=’dpss’) Normalized half bandwidth
(NW = halfbandwidth * dur). Number of DPSS tapers is 2 * NW - 1.
If specified, NW takes precedence over halfbandwidth</p></li>
<li><p><strong>duration</strong> (<em>float</em><em>, </em><em>in s</em>) – If not None, it divides the signal in epochs of this length (in seconds)
and then average over the PSD / ESD (not the complex result)</p></li>
<li><p><strong>overlap</strong> (<em>float</em><em>, </em><em>between 0 and 1</em>) – The amount of overlap between epochs (0.5 = 50%, 0.95 = almost complete
overlap).</p></li>
<li><p><strong>step</strong> (<em>float</em><em>, </em><em>in s</em>) – step in seconds between epochs (alternative to overlap)</p></li>
<li><p><strong>n_fft</strong> (<em>int</em>) – Length of FFT, in samples. If less than input axis, input is cropped.
If longer than input axis, input is padded with zeros. If None, FFT
length set to axis length.</p></li>
<li><p><strong>log_trans</strong> (<em>bool</em>) – If True, spectral values will be natural log-transformed. The
transformation is applied before averaging (or taking the median).</p></li>
<li><p><strong>centend</strong> (<em>str</em>) – (only if duration is not None). Central tendency measure to use, either
mean (arithmetic) or median.</p></li>
</ul>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p><em>instance of ChanFreq</em> – If output=’complex’, there is an additional dimension (‘taper’) which
is useful for ‘dpss’ but it’s also present for all the other tapers.</p>
</dd>
<dt class="field-odd">Raises<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>TypeError</strong> – If the data does not have a ‘time’ axis. It might work in the
future on other axes, but I cannot imagine how.</p></li>
<li><p><strong>ValueError</strong> – If you use duration (to create multiple epochs) and output=’complex’,
because it does not average the complex output of multiple epochs.</p></li>
</ul>
</dd>
</dl>
<p class="rubric">Notes</p>
<p>See extensive notes at wonambi.trans.frequency._fft</p>
<p>It uses sampling frequency as specified in s_freq, it does not
recompute the sampling frequency based on the time axis.</p>
<p>Use of log or median for Welch’s method is included based on
recommendations from Izhikevich et al., bioRxiv, 2018.</p>
</dd></dl>
<dl class="py function">
<dt class="sig sig-object py" id="wonambi.trans.frequency.morlet">
<span class="sig-prename descclassname"><span class="pre">wonambi.trans.frequency.</span></span><span class="sig-name descname"><span class="pre">morlet</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">freq</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">s_freq</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">ratio</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">5</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">sigma_f</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">dur_in_sd</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">4</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">dur_in_s</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">normalization</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'wonambi'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">zero_mean</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/wonambi/trans/frequency.html#morlet"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#wonambi.trans.frequency.morlet" title="Permalink to this definition"></a></dt>
<dd><p>Create a Morlet wavelet.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>freq</strong> (<em>float</em>) – central frequency of the wavelet</p></li>
<li><p><strong>s_freq</strong> (<em>int</em>) – sampling frequency</p></li>
<li><p><strong>ratio</strong> (<em>float</em>) – ratio for a wavelet family ( = freq / sigma_f)</p></li>
<li><p><strong>sigma_f</strong> (<em>float</em>) – standard deviation of the wavelet in frequency domain</p></li>
<li><p><strong>dur_in_sd</strong> (<em>float</em>) – duration of the wavelet, given as number of the standard deviation in
the time domain, in one side.</p></li>
<li><p><strong>dur_in_s</strong> (<em>float</em>) – total duration of the wavelet, two-sided (i.e. from start to finish)</p></li>
<li><p><strong>normalization</strong> (<em>str</em>) – ‘wonambi’ (default) returns an amplitude of 1 in frequency-domain for a
sine wave of amplitude 1 in the time-domain;
‘juniper’ returns amplitude which is dependent on sampling frequency;
‘area’ normalizes the area of the Gaussian envelope to be 1;
‘peak’ normalizes the peak of the Gaussian envelope to be 1.
Note that the frequency-domain values for ‘area’ and ‘peak’ will
depend on the carrier frequency of the wavelet (they depend on sigma_f).</p></li>
<li><p><strong>zero_mean</strong> (<em>bool</em>) – make sure that the wavelet has zero mean (only relevant if ratio < 5)</p></li>
</ul>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p><em>ndarray</em> – vector containing the complex Morlet wavelets</p>
</dd>
</dl>
<p class="rubric">Notes</p>
<p>‘ratio’ and ‘sigma_f’ are mutually exclusive. If you use ‘sigma_f’, the
standard deviation stays the same for all the frequency. It’s more common
to specify a constant ratio for the wavelet family, so that the frequency
resolution changes with the frequency of interest.</p>
<p>‘dur_in_sd’ and ‘dur_in_s’ are mutually exclusive. ‘dur_in_s’ specifies the
total duration (from start to finish) of the window. ‘dur_in_sd’ calculates
the total duration as the length in standard deviations in the time domain:
dur_in_s = dur_in_sd * 2 * sigma_t, with sigma_t = 1 / (2 * pi * sigma_f)</p>
</dd></dl>
<dl class="py function">
<dt class="sig sig-object py" id="wonambi.trans.frequency.timefrequency">
<span class="sig-prename descclassname"><span class="pre">wonambi.trans.frequency.</span></span><span class="sig-name descname"><span class="pre">timefrequency</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">data</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">method</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'morlet'</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">**</span></span><span class="n"><span class="pre">options</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/wonambi/trans/frequency.html#timefrequency"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#wonambi.trans.frequency.timefrequency" title="Permalink to this definition"></a></dt>
<dd><p>Compute the power spectrum over time.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>data</strong> (<em>instance</em><em> of </em><a class="reference internal" href="wonambi.datatype.html#wonambi.datatype.ChanTime" title="wonambi.datatype.ChanTime"><em>ChanTime</em></a>) – data to analyze</p></li>
<li><p><strong>method</strong> (<em>str</em>) – the method to compute the time-frequency representation, such as
‘morlet’ (wavelet using complex morlet window),
‘spectrogram’ (corresponds to ‘spectraldensity’ in frequency()),
‘stft’ (short-time fourier transform, corresponds to ‘complex’ in
frequency())</p></li>
<li><p><strong>options</strong> (<em>dict</em>) – options depend on the method used, see below.</p></li>
</ul>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p><em>instance of ChanTimeFreq</em> – data in time-frequency representation. The exact output depends on
the method. Using ‘morlet’, you get a complex output at each frequency
where the wavelet was computed.</p>
</dd>
</dl>
<p class="rubric">Examples</p>
<p>The data in ChanTimeFreq are complex and they should stay that way. You
can also get the magnitude or power the easy way using Math.</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">from</span> <span class="nn">wonambi.trans</span> <span class="kn">import</span> <span class="n">math</span><span class="p">,</span> <span class="n">timefreq</span>
<span class="gp">>>> </span><span class="n">tf</span> <span class="o">=</span> <span class="n">timefreq</span><span class="p">(</span><span class="n">data</span><span class="p">,</span> <span class="n">foi</span><span class="o">=</span><span class="p">(</span><span class="mi">8</span><span class="p">,</span> <span class="mi">10</span><span class="p">))</span>
<span class="gp">>>> </span><span class="n">tf_abs</span> <span class="o">=</span> <span class="n">math</span><span class="p">(</span><span class="n">tf</span><span class="p">,</span> <span class="n">operator_name</span><span class="o">=</span><span class="s1">'abs'</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">tf_abs</span><span class="o">.</span><span class="n">data</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">]</span>
<span class="go">1737.4662329214384)</span>
</pre></div>
</div>
<p class="rubric">Notes</p>
<p>It uses sampling frequency as specified in s_freq, it does not
recompute the sampling frequency based on the time axis.</p>
<dl class="simple">
<dt>For method ‘morlet’, the following options should be specified:</dt><dd><dl class="simple">
<dt>foi<span class="classifier">ndarray or list or tuple</span></dt><dd><p>vector with frequency of interest</p>
</dd>
<dt>ratio<span class="classifier">float</span></dt><dd><p>ratio for a wavelet family ( = freq / sigma_f)</p>
</dd>
<dt>sigma_f<span class="classifier">float</span></dt><dd><p>standard deviation of the wavelet in frequency domain</p>
</dd>
<dt>dur_in_sd<span class="classifier">float</span></dt><dd><p>duration of the wavelet, given as number of the standard deviation
in the time domain, in one side.</p>
</dd>
<dt>dur_in_s<span class="classifier">float</span></dt><dd><p>total duration of the wavelet, two-sided (i.e. from start to
finish)</p>
</dd>
<dt>normalization<span class="classifier">str</span></dt><dd><p>‘area’ means that energy is normalized to 1, ‘peak’ means that the
peak of the wavelet is set at 1, ‘max’ is a normalization used by
nitime where the max value of the output of the convolution remains
the same even if you change the sigma_f.</p>
</dd>
<dt>zero_mean<span class="classifier">bool</span></dt><dd><p>make sure that the wavelet has zero mean (only relevant if ratio
< 5)</p>
</dd>
</dl>
</dd>
<dt>For method ‘spectrogram’ or ‘stft’, the following options should be specified:</dt><dd><dl class="simple">
<dt>duraton<span class="classifier">int</span></dt><dd><p>duration of the window to compute the power spectrum, in s</p>
</dd>
<dt>overlap<span class="classifier">int</span></dt><dd><p>amount of overlap (0 -> no overlap, 1 -> full overlap)</p>
</dd>
</dl>
</dd>
</dl>
</dd></dl>
</section>
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