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## Introduction and motivation

Many speech processing algorithms are resource intensive and require significant computing power or transmission bandwidth. Yet speech is discontinuous such that we often have pauses between sentences and breaks even within sentences. Moreover, in a dialogue, a speaker would typically use polite turn-taking, such that others are silent when one person is speaking. Resource-intensive processing is not necessary during breaks in speech. Consequently, there is great potential in saving resources by deactivating advanced speech processing methods whenever the input signal does not contain speech.

Voice activity detection (VAD) refers to the task of determining whether a signal contains speech or not. It is thus a binary decision. A related task is to determine the probability that an input signal contains speech or not, referred to as the speech presence probability (SPP). The SPP is typically then expressed as the probability in the range 0 to 1. Speech presence probability is typically an intermediate step in voice activity detection, such that the voice activity classification is obtained by thresholding the output of the speech presence probability estimator.

Generally, voice activity detection algorithms are relatively simple, such that the more complex tasks such as speech recognition, need to be applied only when speech is present. Similarly, in speech coding, we need to transmit speech only when speech is present and we can reduce bitrate whenever speech is absent.

## Problem formulation

For an input signal x, our objective is to determine whether it is speech or not. We express the VAD algorithm as a function y=VAD(x), where the desired target output is

$y^* := \begin{cases} 0, & x \text{ is not speech,} \\ 1, & x \text{ is speech.} \end{cases}$

Correspondingly, the speech presence probability is the probability that x is speech, SPP(x)=P(x is speech). A possible definition for the VAD is then

$VAD(x) := \begin{cases} 0, & SPP(x) < \theta\\ 1, & SPP(x) \geq \theta, \end{cases}$

where θ is a scalar threshold. An example of speech presence probability is illustrated in the following section.

## Naïve approach 1 - Energy thresholding

A speech signal is not a stationary signal. Most prominently, sometimes we speak energetically and sometimes we do not speak. It is then obvious that signal energy can be used as an indicator of speech presence. Speech adds energy to the signal, such that high-energy regions of the signal are likely speech. For example, we can set a threshold $$\theta_{SILENCE}$$ such that when the energy of the signal $$\sigma^2(x)$$ is above the threshold, the VAD indicates speech activity

$VAD(x) := \begin{cases} 0, & \sigma^2(x) < \theta_{SILENCE}\\ 1, & \sigma^2(x) \geq \theta_{SILENCE}. \end{cases}$

To implement this approach, we first apply windowing to the input signal with 30 ms windows and 50 % overlap. For each window, we calculate signal energy as

$\sigma^2(x) := \|x\|^2 = \sum_{k=0}^{N-1} x_k^2.$

To choose a suitable threshold, in the figure on the right, we plot the energy over a speech signal $$\sigma^2(x)$$ over a speech signal. We can observe that areas in the speech signal with little activity have an energy below 17 dB, whereby we can set the threshold at $$\theta_{SILENCE}:=17dB.$$ The resulting voice activity estimate is illustrated in the lowest pane.

The result does seem reasonable. High-amplitude speech sounds are clearly identified as speech. However, in the middle of the sentence, the VAD frequently identifies non-speech frames. Is this correct?

In fact, it is not entirely clear what the output should be. It is a matter of definition. On a heuristic level, we can define that speech starts at the beginning of a sentence and finishes when the sentence ends. But how should the VAD then handle sentences like "What if ... we would go on a holiday?." where there is a break in the middle of a grammatically correct sentence. Should the break be identified as non-speech? How long breaks do we allow? What about grammatically incorrect sentence like "We could go to..."?

Moreover, sentences often have a trail-off, where the signal energy decreases. For example in the figure on the right, the last word diminishes in energy up to about the time 2.7 s, where the signal energy goes below 10 dB. However, with the threshold of 17 dB, we have cut of the VAD already before 2.6 s. If we would lower the threshold to 10dB, then everything between 0.2 s and 1 s would be labelled incorrectly as speech.

It is then clear that even in this simple example, it is not easy to set a threshold which gives a good result. To make things worse, often speech signals are corrupted by background noises, which makes energy-thresholding even more difficult. To avoid labelling everything as speech, the threshold must be higher, but then less of the speech frames are labelled correctly. Which leads to the question, is it more important to label speech or non-speech correctly?

Input sound sample

sound_example.wav ## Performance criteria

The task of voice activity detection (VAD) is seemingly straightforward, but even evaluation of performance is more difficult than one perhaps would expect. As with the definition of correct labels, also the performance criteria depend on the application;

• In speech transmission (i.e. speech coding), we would like to save bandwidth by shutting off transmission when there is no speech present. However, turning off transmission during a speech segment would leave to severe degradations.
• Some speech enhancement algorithms can estimate noise-statistics during non-speech segments, which are identified using a VAD. During speech segments, the algorithm can then remove everything which looks like noise. If however speech is present in the segment where we estimate characteristics of the noise, then we would remove also such features which appear during noise segments. This would lead to a degradation of the desired speech signal.
• In speech recognition, we would like to limit CPU usage by activating the algorithm only during speech segments. We would then like to be sure that no speech segments are omitted, because that would severely degrade output quality.
• In wake-word spotting, we want to activate a device when a specific word is pronounced, such that the device can be in a sleep mode when the wake-word has not been pronounced. We can also turn the wake-word algorithm off for further reductions when there is no speech present. The latter functionality is achieved with the VAD. Overall, if some wake-words are missed, the user just has to say it again - no big deal. We can therefore allow some speech segments to be identified as non-speech. However, assuming that the wake-word spotting is not a too big load on the CPU, we can allow the VAD to be more sensitive. Detailed CPU cost vs. performance -optimization can however be complicated.

We can observe that different applications emphasise different types of errors. Speech transmission and recognition prefer a sensitive VAD where we are certain that no speech-segments are lost. In contrast, speech enhancement and wake-word spotting tend to prefer that the VAD is conservative and labels audio to speech only when certain.

To quantify such differences, we can label performance with the following attributes:

Input=SpeechTrue positive (TP)False negative (FN)
Input=Non-speechFalse positive (FP)True negative (TN)

Then for example for speech recognition, we would penalise less for false positives and penalise more for false negatives. In comparison, in wake-word spotting, we would perhaps penalise equally for both false positives and negatives. It really depends on your overall design.

In the above example of thresholding energy, we can then choose different values for the threshold and plot the values for true positive and negatives for each threshold (see figure on the right). Performance for a threshold of 17 dB is indicated with a red cross. We can readily see that there, all non-speech segments are correctly identified (TN=1 and FP=0), however, speech segments are not all correct (TP=0.72 and FN=0.28). In fact, by reducing the threshold to 14.6 dB (yellow circle in the figure), we would retain perfect false positives, (TN=1 and FP=0), but we would improve false negatives (TP=0.80 and FN=0.20).

VAD performance in terms of percentage of true positives and true negatives (left) and false negatives and false positives (right). ## Naïve approach 2 - More features

To improve performance of the voice activity detector (VAD), we can analyse more properties of the speech signal, which we usually call features. For example,

• Linear predictors describe the spectral shape of speech signals efficiently. In other words, if the modelling error of a linear predictor is small, then the signal is likely a speech signal.
• Alternatively, if we prefer a lower-complexity solution instead of linear prediction, we can analyse the normalised autocorrelation $$c_k/c_0$$ at lag k=1. Speech signals are highly correlated over time, such that if the absolute value  $$|c_1|/c_0$$ is high, then it is likely a speech signal. However, noise signals can also have a negative correlation which is close to -1, such
that we can prefer to omit the absolute value.
An alternative which is roughly equivalent to the covariance at lag-1, is to use to zero-crossing rate.

• Signals with a prominent fundamental frequency in the range which is typical to humans (approx 80 to 450 Hz) are likely to be voiced speech signals. However, unvoiced speech signals have by definition no fundamental frequency and would not be detected by this method.
• Mel-frequency cepstral coefficients (MFCCs) have been shown to give excellent performance as features in many classification tasks.

These features can be further augmented by their trends over time. A classic method is to measure time-derivatives, known as the deltas and delta-deltas, defined for a feature  $$f_k(t)$$ at time t as

$\begin{cases} \Delta_k(t) &= f_k(t) - f_k(t-1) \\ \Delta\Delta_k(t) &= \Delta_k(t) - \Delta_k(t-1). \end{cases}$

Alternatively, we can just consider features explicitly over time $$f_k(t-N) ... f_k(t).$$

We can use all these parameters and many more to effectively characterize speech signals. The question however is how we can merge the information from a vector of features into a single output value? A naïve approach would be to implement a binary decision tree, such that for example,

• If energy is sufficiently high, then output is speech and we return VAD(x)=1.
• If covariance is sufficiently high, then output is speech and we return VAD(x)=1.
• If there is a prominent fundamental frequency in the range 80 to 450 Hz, then return VAD(x) = 1.
• Otherwise return VAD(x) = 0.

This is an entirely heuristic and non-scientific approach which is difficult to design when the number of features increases.

A better way is the classic method of linear estimation, even if it is now considered old-fashioned (with good reasons). In this method we take all features $$f=[f_0\dots f_{N-1}]^T$$ and take their linear combination weights $$w=[w_0\dots w_{N-1}]^T$$ , as

$\hat y = f^T w.$

The objective is to find weights such that the estimate $$\hat y$$ is approximately equal to the desired output $$y\approx\hat y.$$ By collecting the features of a large amount of speech samples in a matrix $$F=[f(t) \dots f(t+T)]$$ , the output is $$\hat y = F^T w$$ and we can minimize the squared estimation error

$\| y -\hat y\|^2 = \|y- F^T w\|^2.$

To find the optimum, we set the derivative to zero

$0=\frac{\partial}{\partial w}\|y- F^T w\|^2 = F(y-F^Tw) = Fy-FF^T w.$

Clearly the optimal weight vector is then

$w^* = (FF^T)^{-1} Fy = F^\dagger y.$

Here the superscript $$\dagger$$ denotes the pseudo-inverse.

Once we have found the optimal weights, for an individual frame we then have

$\hat y = f(t)^T w^*,$

and we can apply thresholding to get the VAD output as

$VAD(x) := \begin{cases} 0, & f^Tw^* < \theta\\ 1, & f^Tw^* \geq \theta. \end{cases}$

The figure on the right illustrates a linear classifier with this approach using the 8 first autocorrelation values as well as their delta and delta-delta values as features. The figure illustrates the desired, raw as well as the thresholded output. Compared to energy thresholding implemented above, the result seems much better. In the false-positives/false-negatives plot, we see a comparison of the two methods, energy thresholding and linear classifier. Both error-types are reduced by an order of magnitude using the improved method.

It is important to note, however, that voice activity detection in silence is a very easy task. The good results we obtained here are therefore not unexpected. Speech distorted by background noises is much more difficult for VAD algorithms.

The problems with this approach include that it hiddenly assumes that the distribution of the input features for speech and non-speech signals are linearly separable. That is, it cannot take into account any non-linear shapes of the distribution, nor can it take into account the fact that speech signals are represented by a multitude of sub-classes such as voiced and unvoiced samples. ## Modern approach - Machine learning

Executive summary: Use machine learning for voice activity detection tasks.

The basic design principle is:

1. Choose a selection of the features described above.
2. Choose the design of your machine learning method.
3. Train the parameters over a large database of speech, which is representative of your intended application.

Unfortunately, the scientific methods for feature-selection and choosing designs of machine learning methods have not yet matured. It is however important to remember that voice activity detection is intended to be a low-complexity method which saves resources. We can therefore accept using a smaller number of parameters and a simpler design, even if that sacrifices quality to some extent.

## Post-processing

In general, speech onsets (when an utterance begins) are relatively easy to detect, whereas it is difficult to determine where an utterance ends, especially when speech trails off slowly. Another typical error in voice activity detectors (VAD) are isolated errors, where one or small number of consecutive frames are incorrectly labelled. And even if onsets are generally easily detected, sometimes the VAD activates a bit too slowly, such that the first frame of the speech segment is incorrectly classified as non-speech.

Such errors can be easily corrected with heuristic methods such as hangover, where we define a modified output as

$VAD'(x) = \max\left(VAD(k-K)..VAD(k)\right).$

In other words, if any of the last K frames was speech, then also this frame is speech. If future frames are available, we can even extend this to the future by defining

$VAD'(x) = \max\left(VAD(k-K)..VAD(k+H)\right).$

Such hangover -type functionalities can reduce false negatives with a substantial amount. A similar approach can be implemented to remove very short segments labelled as speech, since very short speech utterances are both non-informative, but also cannot realistically be speech sounds.

The figure on the right illustrates post-processing applied on the output of the linear model implemented above. In this case, we first remove isolated peaks with $$VAD'(x) = \min\left(VAD(k-1)..VAD(k+1)\right)$$ and then apply a hangout with a two-samples backward and one-sample lookahead as $$VAD''(x) = \max\left(VAD'(k-2)..VAD'(k+1)\right).$$ In this simple case, we get then a perfect output. • No labels