【课程】SP Module4 音频滤波器_source-filter model-优快云博客

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本文探讨了周期信号的谐波结构，如人声与非人声的区别在于周期性。脉冲序列是最简单的具有基本频率倍数能量的周期信号。声音的频谱包络变化是说话者传达语言信息的主要方式，而声道共振则影响声音特性。滤波器模型用于模拟声道操作信号的方式，其脉冲响应和频率响应是关键特征。源过滤器模型综合了这些概念，可以生成任何语音音素。关键词包括谐波、脉冲序列、频谱包络、共振管和滤波器模型。

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Harmonics

In the frequency domain, periodic signals have harmonic structure: they contain energy only at multiples of their fundamental frequency.

Voice sounds different from unvoiced sounds, has repeating pattern, in periodicity. So, the peak of the sound in the frequency domain is clear to observe.

Impulse train

An impulse train is the simplest periodic signal that has energy at all multiples of its fundamental frequency (and energy are evenly distributed).

Spectral envelope

Varying the shape of the spectral envelope is the primary means by which a speaker transmits a linguistic message to a listener.

Spectral envelope: The region under the curve in frequency domain.

Resonant tube

The understand how the vocal tract modifies sound, we need to start with the concept of resonance.

Q: Increased damping in a resonant system…

A: increases the bandwidth of the frequency response. Increased damping won’t increase gain (i.e., boosting of amplitude) as increased damping means the vibration of an object fades away sooner (i.e. loses amplitude), so we can rule out that answer. Bandwidth refers to the width of the frequency response curve (see M4: Vocal tract resonance and formants). A decreased bandwidth would indicate that less frequencies around the resonance frequency are boosted (and thus consume energy). This sort of narrow bandwidth is what allows a tuning fork to ring for a long time. An increased bandwidth means that more frequencies get boosted around the resonant frequency. This is associated with a lower peak amplitude (as the energy is spread across a bigger band of frequencies). This is consistent with increased damping: energy is spread over more frequencies so the oscillations due to resonance die out quicker. (M4: Vocal tract resonance and formants, Wayland Chapter 6: Damping. This is a very challenging question!)

Vocal tract resonance & formants

A speaker can vary their vocal tract shape to change its resonant frequencies, and therefore the spectral envelope of the speech they are producing.

Formant frequencies: Frequencies around which acoustic energy is concentrated as a result of the filtering action of the vocal tract, visible as prominent peaks in a spectrum. (resonances of the vocal tract)

The peak is called formant, properties for the vocal tract, and $F_1$ is the first format and $F_2$ is the second formant.

But $F_0$ is is the fundamental frequency of the vocal folds, the rate of the vocal folds, not formant.

Filter

We now shift from an explicit physical model of the vocal tract as a resonating tube, to a more general model of the vocal tract as a filter operating on signals.

Filter is something map from input domain $X$ to output domain $Y$ , like a function in mathematics.

Impulse response

If we want to characterise a filter in the time domain, we need to know its impulse response.

How the filter response to the impulse.

In the image below, we narrow down the analysis frame down to only one period of waveform, we have impulse response of the filter on the left, and the frequency response of the filter on the right.

Source-filter model

Finally, we arrive at a complete model of speech signals that can generate any speech sound.

We find the impulse response/frequency response of the original sounds

Phoneme

The source-filter model brings together our understanding of speech signals, speech production, and phonetics. It can generate any speech sound: any phoneme.