Speech Time-Frequency Representations
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Time-Frequency Representations for Speech Signals
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Published in: Education. Full Name Comment goes here. To solve this last issue, it is possible to use the Short Time Fourier Transform STFT , which consists of performing a Fourier transform for each part the sliced windowed signal. Figure 3: Time-Frequency transform Magnitude of the signal Glockenspiel. The vertical lines are the precise timing where the bar of glockenspiel is hit.
The long horizontal line represents the base frequency of the bar resonating. The small horizontal lines are the harmonics. The TF representation solves most of the issues that were discussed previously as it is:. With this in mind, it can be surprising to notice that, when it comes to sound, most generative models still use the time representation Wavenet , WaveGAN .
In fact, the problem mainly comes from the phase.
While it can basically be dropped for a discrimination task, it has to be recovered or produced, for a generation task as it is needed to eventually reconstruct the time representation. Figure 4: Raw phase of the signal. The phase structure is not easily understandable. One reason why this representation is hard to grasp is that the phase is wrapped between and.
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In practice, there are mainly three issues when it comes to handling the phase. The TF representation is usually redundant, meaning that it is a larger representation than time. For a signal of size L, the representation we have elements, with being the redundancy having typically a value of 2,4 or 8. As the set of TF representation is larger than the set of time signals, there exist some TF representations that do not have a corresponding signal.
These TF representations are called inconsistent. While, in the discrete case, the phase recovery is still an unsolved problem, in the continuous case, there exist a particular TF transform that has an analytic relation linking its phase and its magnitude See the math box. Our work defines some practical rules to build a TF representation for generative models making them optimally work with PGHI.
Speech Time-Frequency Representations | Michael D. Riley | Springer
Following these rules, the phase can be reconstructed efficiently from the amplitudes without undesired artifacts. This solves the phase reconstruction problem. The math box The rules we propose are geared towards allowing the network to generate consistent spectrogram, but we still need to make sure that this is the case. Even PGHI will not generate a good phase for an inconsistent spectrogram.
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This allows the quality assessment of the produced magnitudes and is a good proxy for the final audio quality of the signals. In grey, is a failling network. First we design an appropriate TF transform and compute its representation for the dataset. Eventually, we recover the phase using PGHI and reconstruct the audio signal. To evaluate our network, we performed a psychoacoustic experiment where the subjects were asked to choose the most realistic audio signal from two candidates.
This allows comparing our network with other methods and with respect of real audio signals. Numerical results can be found in Table 1, that we took directly from  Hence eq. Auditory scenes contain valuable information, including speech, source location, music, and emergency alerts such as a passing police car.
Humans with normal hearing naturally analyze auditory scenes, but computer systems and humans with hearing impairments struggle to perform this task. My goal as a researcher is to develop algorithms that address this problem in realistic and challenging auditory environments. Generally speaking, I am interested in the following broad research areas: Speech Processing separation, recognition, identification, etc. Speech separation systems usually operate on the short-time Fourier transform STFT of noisy speech, and enhance only the magnitude spectrum while leaving the phase spectrum unchanged.
This is done because there was a belief that the phase spectrum is unimportant for speech enhancement. Recent studies, however, suggest that phase is important for perceptual quality, leading some researchers to consider magnitude and phase spec- trum enhancements. We present a supervised monaural speech separation approach that simultaneously enhances the magni- tude and phase spectra by operating in the complex domain.
HOW TO GENERATE AUDIO USING TIME-FREQUENCY REPRESENTATIONS?
Our approach uses a deep neural network to estimate the real and imaginary components of the ideal ratio mask defined in the complex domain. We report separation results for the pro- posed method and compare them to related systems. As a means of speech separation, time-frequency masking applies a gain function to the time-frequency representation of noisy speech.