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MindSpore Signal+ 使用手册
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<li class="toctree-l3 current"><a class="current reference internal" href="#">FFTImag</a></li>
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<li class="toctree-l3"><a class="reference internal" href="log_grad.html">LogGrad</a></li>
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<li class="toctree-l3"><a class="reference internal" href="lstm.html">LSTM</a></li>
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<li class="toctree-l3"><a class="reference internal" href="lstmgrad.html">LstmGrad</a></li>
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<li class="toctree-l3"><a class="reference internal" href="lstmgraddata.html">LstmGradData</a></li>
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<li class="toctree-l3"><a class="reference internal" href="maxpool_grad.html">MaxPoolGrad</a></li>
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<li class="toctree-l3"><a class="reference internal" href="power_grad.html">PowerGrad</a></li>
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<li class="toctree-l3"><a class="reference internal" href="prelufusion.html">PReLUFusion</a></li>
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<li class="toctree-l3"><a class="reference internal" href="quant_dtype_cast.html">QuantDTypeCast</a></li>
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<li class="toctree-l3"><a class="reference internal" href="random_normal.html">RandomNormal</a></li>
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<li class="toctree-l3"><a class="reference internal" href="random_standard_normal.html">RandomStandardNormal</a></li>
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<li class="toctree-l3"><a class="reference internal" href="range.html">Range</a></li>
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<li class="toctree-l3"><a class="reference internal" href="rank.html">Rank</a></li>
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<li class="toctree-l3"><a class="reference internal" href="reduce.html">Reduce</a></li>
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<li class="toctree-l3"><a class="reference internal" href="reshape.html">Reshape</a></li>
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<li class="toctree-l3"><a class="reference internal" href="resize.html">Resize</a></li>
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<li class="toctree-l3"><a class="reference internal" href="resizegrad.html">Resizegrad</a></li>
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<li class="toctree-l3"><a class="reference internal" href="rsqrt.html">Rsqrt</a></li>
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<li class="toctree-l3"><a class="reference internal" href="rsqrt_grad.html">RsqrtGrad</a></li>
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<li class="toctree-l3"><a class="reference internal" href="scatter_nd.html">ScatterNd</a></li>
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<li class="toctree-l3"><a class="reference internal" href="scatter_nd_update.html">ScatterNdUpdate</a></li>
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<li class="toctree-l3"><a class="reference internal" href="select.html">Select</a></li>
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<li class="toctree-l3"><a class="reference internal" href="sgd.html">SGD</a></li>
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<li class="toctree-l3"><a class="reference internal" href="shape.html">Shape</a></li>
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<li class="toctree-l3"><a class="reference internal" href="sigmoidcrossentropywithlogits.html">SigmoidCrossEntropyWithLogits</a></li>
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<a href="../../_sources/functionlib/dsplib/fftimag.rst.txt" rel="nofollow"> 查看页面源码</a>
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<section id="fftimag">
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<h1>FFTImag<a class="headerlink" href="#fftimag" title="此标题的永久链接"></a></h1>
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<p>对输入复数序列虚数部分执行一维快速傅里叶变换（FFT）或逆变换（IFFT）。
|
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内部基于分治 FFT 算法，
|
||
并使用预计算旋转因子（twiddle factor）以提升性能。
|
||
傅里叶变换，可以对参数进行调整，以实现FFT/IFFT/RFFT/IRFFT。</p>
|
||
<p>数学定义如下：</p>
|
||
<div class="math notranslate nohighlight">
|
||
\[X(k) = \sum_{n=0}^{N-1} x(n)\,e^{-j 2\pi kn / N} \quad (\text{Forward FFT})\]</div>
|
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<div class="math notranslate nohighlight">
|
||
\[x(n) = \sum_{k=0}^{N-1} X(k)\,e^{j 2\pi kn / N} \quad (\text{Inverse FFT})\]</div>
|
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<p>其中 <span class="math notranslate nohighlight">\(N\)</span> 为 FFT 点数。</p>
|
||
<dl class="simple">
|
||
<dt>输入：</dt><dd><ul class="simple">
|
||
<li><p><strong>input</strong> - 输入复数数据地址。</p></li>
|
||
<li><p><strong>fft_size</strong> - FFT 点数。</p></li>
|
||
<li><dl class="simple">
|
||
<dt><strong>dir</strong> - 变换方向：</dt><dd><ul>
|
||
<li><p><code class="docutils literal notranslate"><span class="pre">FFT_FORWARD</span></code>：正向 FFT</p></li>
|
||
<li><p><code class="docutils literal notranslate"><span class="pre">FFT_INVERSE</span></code>：反向 FFT</p></li>
|
||
</ul>
|
||
</dd>
|
||
</dl>
|
||
</li>
|
||
<li><p><strong>scratch_ptr</strong> - 临时缓冲区地址，用于存放旋转因子及中间计算结果。</p></li>
|
||
<li><p><strong>twiddle</strong> - 旋转因子地址（仅共享存储版本使用）。</p></li>
|
||
<li><p><strong>fft_size1</strong> - 第一阶段 FFT 点数（仅共享存储版本使用）。</p></li>
|
||
<li><p><strong>fft_size2</strong> - 第二阶段 FFT 点数（仅共享存储版本使用）。</p></li>
|
||
<li><p><strong>core_mask</strong> - 核掩码（仅共享存储版本需要）。</p></li>
|
||
</ul>
|
||
</dd>
|
||
<dt>输出：</dt><dd><ul class="simple">
|
||
<li><p><strong>output</strong> - 输出复数序列地址。</p></li>
|
||
</ul>
|
||
</dd>
|
||
</dl>
|
||
<p>内部核心计算公式如下：
|
||
对于FFT，它计算以下表达式：</p>
|
||
<div class="math notranslate nohighlight">
|
||
\[X[\omega_1, \dots, \omega_d] =
|
||
\sum_{n_1=0}^{N_1-1} \dots \sum_{n_d=0}^{N_d-1} x[n_1, \dots, n_d]
|
||
e^{-j\ 2 \pi \sum_{i=0}^d \frac{\omega_i n_i}{N_i}},\]</div>
|
||
<p>其中， <span class="math notranslate nohighlight">\(d\)</span> = <cite>signal_ndim</cite> 是信号的维度，<span class="math notranslate nohighlight">\(N_i\)</span> 则是信号第 <span class="math notranslate nohighlight">\(i\)</span> 个维度的大小。</p>
|
||
<p>对于IFFT，它计算以下表达式：</p>
|
||
<div class="math notranslate nohighlight">
|
||
\[X[\omega_1, \dots, \omega_d] =
|
||
\frac{1}{\prod_{i=1}^d N_i} \sum_{n_1=0}^{N_1-1} \dots \sum_{n_d=0}^{N_d-1} x[n_1, \dots, n_d]
|
||
e^{\ j\ 2 \pi \sum_{i=0}^d \frac{\omega_i n_i}{N_i}},\]</div>
|
||
<p>其中， <span class="math notranslate nohighlight">\(d\)</span> = <cite>signal_ndim</cite> 是信号的维度，<span class="math notranslate nohighlight">\(N_i\)</span> 则是信号第 <span class="math notranslate nohighlight">\(i\)</span> 维的大小。</p>
|
||
<div class="admonition note">
|
||
<p class="admonition-title">备注</p>
|
||
<ul class="simple">
|
||
<li><p>FFT/IFFT要求complex64或complex128类型的输入，返回complex64或complex128类型的输出。</p></li>
|
||
<li><p>RFFT要求bool, uint8, int8, int16, int32, int64, float32或float64类型的输入，
|
||
返回complex64或complex128类型的输出。</p></li>
|
||
<li><p>IRFFT要求complex64或complex128类型的输入，返回float32或float64类型的输出。</p></li>
|
||
<li><p>共享存储版本/私有存储版本支持函数及调用见RFFT。</p></li>
|
||
</ul>
|
||
</div>
|
||
<dl class="simple">
|
||
<dt>参数：</dt><dd><ul class="simple">
|
||
<li><p><strong>signal_ndim</strong> (int) - 表示每个信号中的维数，控制着傅里叶变换的维数，其值只能为1、2或3。</p></li>
|
||
<li><p><strong>inverse</strong> (bool) - 表示该操作是否为逆变换，用以选择FFT 和 RFFT 或 IFFT 和 IRFFT。</p>
|
||
<ul>
|
||
<li><p>如果为 <code class="docutils literal notranslate"><span class="pre">True</span></code> ，则为IFFT 和 IRFFT。</p></li>
|
||
<li><p>如果为 <code class="docutils literal notranslate"><span class="pre">False</span></code> ，FFT 和 RFFT。</p></li>
|
||
</ul>
|
||
</li>
|
||
<li><p><strong>real</strong> (bool) - 表示该操作是否为实变换，与 <cite>inverse</cite> 共同决定具体的变换模式：</p>
|
||
<ul>
|
||
<li><p><cite>inverse</cite> 为 <code class="docutils literal notranslate"><span class="pre">False</span></code> ， <cite>real</cite> 为 <code class="docutils literal notranslate"><span class="pre">False</span></code> ：对应FFT模式。</p></li>
|
||
<li><p><cite>inverse</cite> 为 <code class="docutils literal notranslate"><span class="pre">True</span></code> ， <cite>real</cite> 为 <code class="docutils literal notranslate"><span class="pre">False</span></code> ：对应IFFT模式。</p></li>
|
||
<li><p><cite>inverse</cite> 为 <code class="docutils literal notranslate"><span class="pre">False</span></code> ， <cite>real</cite> 为 <code class="docutils literal notranslate"><span class="pre">True</span></code> ：对应RFFT模式。</p></li>
|
||
<li><p><cite>inverse</cite> 为 <code class="docutils literal notranslate"><span class="pre">True</span></code> ， <cite>real</cite> 为 <code class="docutils literal notranslate"><span class="pre">True</span></code> ：对应IRFFT模式。</p></li>
|
||
</ul>
|
||
</li>
|
||
<li><p><strong>norm</strong> (str，可选) - 表示该操作的规范化方式，可选值：[ <code class="docutils literal notranslate"><span class="pre">"backward"</span></code> , <code class="docutils literal notranslate"><span class="pre">"forward"</span></code> , <code class="docutils literal notranslate"><span class="pre">"ortho"</span></code> ]。默认值： <code class="docutils literal notranslate"><span class="pre">"backward"</span></code> 。</p>
|
||
<ul>
|
||
<li><p>“backward”，正向变换不缩放，逆变换按 <span class="math notranslate nohighlight">\(1/n\)</span> 缩放，其中 <cite>n</cite> 表示输入 <cite>x</cite> 的元素数量。。</p></li>
|
||
<li><p>“ortho”，正向变换与逆变换均按 <span class="math notranslate nohighlight">\(1/\sqrt n\)</span> 缩放。</p></li>
|
||
<li><p>“forward”，正向变换按 <span class="math notranslate nohighlight">\(1/n\)</span> 缩放，逆变换不缩放。</p></li>
|
||
</ul>
|
||
</li>
|
||
<li><p><strong>onesided</strong> (bool，可选) - 控制输入是否减半以避免冗余。默认值： <code class="docutils literal notranslate"><span class="pre">True</span></code> 。</p></li>
|
||
<li><p><strong>signal_sizes</strong> (tuple，可选) - 原始信号的大小（RFFT变换之前的信号，不包含batch这一维），只有在IRFFT模式下和设置 <cite>onesided</cite> 为True时需要该参数，需要满足
|
||
以下条件。默认值： <code class="docutils literal notranslate"><span class="pre">()</span></code> 。</p>
|
||
<ul>
|
||
<li><p><cite>signal_sizes</cite> 的长度等于IRFFT的 <cite>signal_ndim</cite> ： <span class="math notranslate nohighlight">\(len(signal\_sizes)=signal\_ndim\)</span> 。</p></li>
|
||
<li><p><cite>signal_sizes</cite> 的最后一个维度除以2等于IRFFT输入的最后一个维度： <span class="math notranslate nohighlight">\(signal\_size[-1]/2+1=x.shape[-1]\)</span> 。</p></li>
|
||
<li><p>除了最后一个维度外， <cite>signal_sizes</cite> 的维度与输入shape完全相同： <span class="math notranslate nohighlight">\(signal\_sizes[:-1]=x.shape[:-1]\)</span> 。</p></li>
|
||
</ul>
|
||
</li>
|
||
</ul>
|
||
</dd>
|
||
<dt>异常：</dt><dd><ul class="simple">
|
||
<li><p><strong>TypeError</strong> - 如果FFT/IFFT/IRFF的输入类型不是以下类型之一：complex64、complex128。</p></li>
|
||
<li><p><strong>TypeError</strong> - 如果输入的类型不是Tensor。</p></li>
|
||
<li><p><strong>ValueError</strong> - 如果输入 <cite>x</cite> 的维度小于 <cite>signal_ndim</cite> 。</p></li>
|
||
<li><p><strong>ValueError</strong> - 如果 <cite>signal_ndim</cite> 大于3或小于1。</p></li>
|
||
<li><p><strong>ValueError</strong> - 如果 <cite>norm</cite> 取值不是”backward”、”forward”或”ortho”。</p></li>
|
||
</ul>
|
||
</dd>
|
||
<dt>支持平台：</dt><dd><p><code class="docutils literal notranslate"><span class="pre">FT78NE</span></code>
|
||
<code class="docutils literal notranslate"><span class="pre">MT7004</span></code></p>
|
||
</dd>
|
||
<dt>类型支持：</dt><dd><ul class="simple">
|
||
<li><p>FT78NE：<code class="docutils literal notranslate"><span class="pre">cplx64</span></code>、<code class="docutils literal notranslate"><span class="pre">cplx128</span></code></p></li>
|
||
<li><p>MT7004：<code class="docutils literal notranslate"><span class="pre">cplx64</span></code></p></li>
|
||
</ul>
|
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</dd>
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</dl>
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