Inverse Short Time Fourier Transformation (ISTFT)#

Versioned name: ISTFT-16

Category: Signal processing

Short description: ISTFT operation performs Inverse Short-Time Fourier Transform (complex-to-real).

Detailed description: ISTFT performs Inverse Short-Time Fourier Transform of complex-valued input tensor of shape [fft_results, frames, 2] or [batch, fft_results, frames, 2], where:

  • batch is a batch size dimension

  • frames is a number of frames calculated as ((signal_length - frame_size) / frame_step) + 1 of the original signal if not centered, or (signal_length / frame_step) + 1 otherwise.

  • fft_results is a number calculated as (frame_size / 2) + 1 of the original signal

  • 2 is the last dimension for complex value represented by floating-point values pair (real and imaginary part accordingly)

The output is a restored real-valued signal in a discrete time domain. The shape of the output is 1D [signal_length] or 2D [batch, signal_length]. If the signal_length is not provided as an input value, it is calculated according to the following rules:

  • default_signal_length = (frames - 1) * frame_step for center == true

  • default_signal_length = (frames - 1) * frame_step + frame_size for center == false

If the signal_length input is provided, the number of output values will be adjusted accordingly.

  • If signal_length > default_signal_length the output is padded with zeros at the end.

  • If signal_length < default_signal_length any additional generated samples are cut to the signal_length size.

The window_length can not be larger than frame_size, but if smaller the window values will be padded with zeros on the left and right side. The size of the left padding is calculated as (frame_size - window_length) // 2, then right padding size is filled to match the frame_size.

Attributes:

  • center

    • Description: Flag that indicates whether padding has been applied to the original signal. It affects output shape, if the signal_length input is not provided.

    • Range of values:

      • false - padding has not been applied, default signal length is calculated as (frames - 1) * frame_step + frame_size

      • true - padding has been applied, default signal length is calculated as (frames - 1) * frame_step

    • Type: boolean

    • Required: yes

  • normalized

    • Description: Flag that indicates whether the input has been normalized. It is needed to correctly restore the signal and denormalize the output. Output of the STFT is divided by sqrt(frame_size), when normalized.

    • Range of values:

      • false - input has not been normalized

      • true - input has been normalized

    • Type: boolean

    • Required: yes

Inputs

  • 1: data - Tensor of type T, the ISTFT data input (compatible with a result of STFT operation). Required.

    • The data input shape can be 3D [fft_results, frames, 2] or 4D [batch, fft_results, frames, 2].

  • 2: window - Tensor of type T and 1D shape [window_length], specifying the window values applied to restore the signal. The window_length is required to be equal or smaller than frame_size, if smaller the window will be padded with zeros on the left and right sides. Required.

  • 3: frame_size - Scalar tensor of type T_INT describing the size of a single frame of the signal to be provided as input to FFT. Required.

  • 4: frame_step - Scalar tensor of type T_INT describing the distance (number of samples) between successive frames. Required.

  • 5: signal_length - Scalar or single element 1D tensor of type T_INT describing the desired length of the output signal, if not provided it’s calculated accordingly to the rules presented in the detailed description above. Optional.

Outputs

  • 1: signal - Tensor of type T and 1D shape [signal_length] or 2D shape [batch, signal_length] with a real valued signal data. Required.

Types

  • T: any supported floating-point type.

  • T_INT: int64 or int32.

Examples:

Example 3D input, 1D output signal, center=false, default signal_length:

 <layer ... type="ISTFT" ... >
     <data center="false" ... />
     <input>
         <port id="0">
             <dim>6</dim>
             <dim>16</dim>
             <dim>2</dim>
         </port>
         <port id="1">
             <dim>7</dim>
         </port>
         <port id="2"></port> <!-- frame_size value: 11 -->
         <port id="3"></port> <!-- frame_step value: 3 -->
     </input>
     <output>
         <port id="4">
             <dim>56</dim>
         </port>
     </output>
 </layer>

Example 4D input, 2D output signal, center=false, default signal_length:

 <layer ... type="ISTFT" ... >
     <data center="false" ... />
     <input>
         <port id="0">
             <dim>4</dim>
             <dim>6</dim>
             <dim>16</dim>
             <dim>2</dim>
         </port>
         <port id="1">
             <dim>7</dim>
         </port>
         <port id="2"></port> <!-- frame_size value: 11 -->
         <port id="3"></port> <!-- frame_step value: 3 -->
     </input>
     <output>
         <port id="4">
             <dim>4</dim>
             <dim>56</dim>
         </port>
     </output>
 </layer>

Example 3D input, 1D output signal, center=true, default signal_length:

 <layer ... type="ISTFT" ... >
     <data center="true" ... />
     <input>
         <port id="0">
             <dim>6</dim>
             <dim>16</dim>
             <dim>2</dim>
         </port>
         <port id="1">
             <dim>7</dim>
         </port>
         <port id="2"></port> <!-- frame_size value: 11 -->
         <port id="3"></port> <!-- frame_step value: 3 -->
     </input>
     <output>
         <port id="4">
             <dim>45</dim>
         </port>
     </output>
 </layer>

Example 4D input, 2D output signal, center=true, default signal_length:

 <layer ... type="ISTFT" ... >
     <data center="true" ... />
     <input>
         <port id="0">
             <dim>4</dim>
             <dim>6</dim>
             <dim>16</dim>
             <dim>2</dim>
         </port>
         <port id="1">
             <dim>7</dim>
         </port>
         <port id="2"></port> <!-- frame_size value: 11 -->
         <port id="3"></port> <!-- frame_step value: 3 -->
     </input>
     <output>
         <port id="4">
             <dim>4</dim>
             <dim>45</dim>
         </port>
     </output>
 </layer>

Example 3D input, 1D output signal, center=false, signal_length input provided:

 <layer ... type="ISTFT" ... >
     <data center="false" ... />
     <input>
         <port id="0">
             <dim>6</dim>
             <dim>16</dim>
             <dim>2</dim>
         </port>
         <port id="1">
             <dim>7</dim>
         </port>
         <port id="2"></port> <!-- frame_size value: 11 -->
         <port id="3"></port> <!-- frame_step value: 3 -->
         <port id="4"></port> <!-- signal_length value: 64 -->
     </input>
     <output>
         <port id="5">
             <dim>64</dim>
         </port>
     </output>
 </layer>