Human speeches may be captured as signals representing speech or speech signals using transducers, e.g., microphones, and be further processed for a wide range of applications, e.g., noise reduction or denoising, speech recognition, speaker recognition, speech synthesis, hearing aids, cochlear implants, and speech compression. The speech signals may be captured in the form of analog signals or digital signals and may be stored in electronic media, e.g., memory or disks. The speech signals may be processed using analog or digital processors.
One commonly used scheme in speech signal processing may include transforming speech signals from a time domain representation, e.g., signal waveforms as a function of time, into a frequency domain representation, e.g., spectrums or spectrograms, using the Fourier transformation. However, the Fourier transform may have a fixed time-frequency resolution. Thus, frequency distribution is limited to a linear scale. This limitation may require additional processing, e.g., converting a linear frequency distribution to a non-linear frequency distribution, e.g., as in the basilar membrane. Additionally, the fixed window size of the Fourier transform may cause undesirable harmonics in spectrograms.
This problem may be illustrated by the following example. In most speech processing systems, speech signals are first converted into digital signals on which, for example, short-time Fourier transform via Fast Fourier Transforms (FFT) may be applied for computing spectrograms of the speech signals. The intensity of a spectrogram represents the amplitude of the signal at a particular time and at a particular frequency. FIG. 1 shows speech signals of a male voice recorded under two different scenarios. FIG. 1(A) shows the speech signal recorded using a close-talking microphone, and FIG. 1(B) shows the same speech signal simultaneously recorded using a hands-free microphone in a moving vehicle. The close-talking microphone is placed near the speaker's mouth, while the hands-free microphone is placed, e.g., on a sun visor of the vehicle. Due to the distance between the mouth and the microphone in the hands-free scenario, the recorded speech signal in FIG. 1(B) may include substantial background noise compared to the speech signal as shown in FIG. 1(A). Both speech signals in this example are recorded at a sampling rate of 8 KHz.
FIG. 2 shows the spectrograms of speech signals shown in FIG. 1. Specifically, FIG. 2(A) shows a spectrogram of the clean speech signal recorded using a close-talking microphone as shown in FIG. 1(A), and FIG. 2(B) shows a spectrogram of the noisy speech signal recorded using a hand-free microphone as shown in FIG. 1(B). The spectrograms are computed in the standard way, as in traditional feature extraction for speaker or speech recognition. It may include using a window of, e.g., the length of 30 ms shifted every 10 ms with an overlap of 20 ms, of a type of Hamming window before applying FFT to the speech signals. To facilitate further analysis and feature extraction, the frequency distribution is mapped from linear scales to the Bark scale after the FFT computation.
The spectrograms of FIG. 2 shows two types of distortions: (1) the pitch harmonics as periodical waves along the frequency axis; and (2) the background noise in the frequency domain in the form of “snow” noise (which is different from environmental noise). Both types of distortions are caused by FFT computation.
Additional processing steps may be needed to remove effects of these undesirable distortions. FIG. 3 shows a schematic diagrams of such a Fourier transform based system 300 for extracting features from speech signals. A speech signal may first undergo pre-processing steps of frame blocking 302 and windowing 304. Then at 306 FFT may be applied to the pre-processed speech signal for computing a spectrum. As discussed above, the spectrum may include unwanted harmonics and noise. In this method, triangular filters 308, a non-linear filter 310, and discrete cosine transform (DCT) 312 may be applied to reduce the effects of harmonics and noises caused by FFT. However, while these steps may reduce the harmonic distortions, they may also remove useful and real pitch information. It is commonly known that humans identify peoples' voices by the voice characteristics, represented mainly by pitch information.
Speech signal processing based on wavelet transforms may provide flexible time-frequency resolution. However, it may have other noticeable problems. First, the existing wavelet does not have the capabilities of mimicking the impulse responses of the basilar membrane. Thereby, it may not be used directly for modeling the human hearing system, e.g., cochlea. Second, there is no discrete formula to approximate inverse continuous wavelet transforms even though forward and inverse transforms for continuous wavelet based are well defined.