This function, `frame_synthesis`, is likely part of an audio processing...

This function, frame_synthesis, is likely part of an audio processing or denoising system. Here's a step-by-step explanation of what it does:

1. Input and Setup:

   • DenoiseState *st: This is a pointer to a state structure (DenoiseState) that likely holds necessary state information for the denoising process.
   • float *out: This is a pointer to an output buffer where the synthesized audio frame is written.
   • const kiss_fft_cpx *y: This is input frequency-domain data (e.g., from an FFT result), represented as complex numbers (likely using the KISS FFT library).
   • A local buffer x is allocated, large enough to hold WINDOW_SIZE samples.

2. Inverse Transform:

   • inverse_transform(x, y): Converts the frequency-domain input y (likely a spectral representation) back into the time-domain signal, storing the result in x.

3. Windowing:

   • apply_window(x): Applies a window function (e.g., Hamming, Hann, or similar) to the time-domain signal stored in x. This likely smooths the edges of overlapping frames.

4. Overlap-Add for Synthesis:

   • The reconstructed time-domain signal in x is combined with the previous frame's remaining samples stored in st->synthesis_mem.
   • For the first FRAME_SIZE samples, the function adds values from x and st->synthesis_mem and stores the result in out.

5. Update Memory:

   • RNN_COPY(st->synthesis_mem, &x[FRAME_SIZE], FRAME_SIZE): Updates the synthesis_mem in the denoising state with the second half of x (the last FRAME_SIZE samples). This prepares it for the next frame to implement overlap-add synthesis.

Purpose of the Code:

This function reconstructs a time-domain audio frame from frequency-domain data through inverse transformation and combines it with the past frame using overlap-add. It's typically used in speech codecs or audio processing pipelines, such as a denoising system, where the audio signal is processed in chunks (frames). The purpose is to produce a seamless, reconstructed signal by taking care of frame boundaries using windowing and overlap-add techniques.