Slides
Audio signals are generally referred to as signals that are audible to humans. Audio signals usually come from a sound source which vibrates in the audible frequency range. The vibrations push the air to form pressure waves that travels at about 340 meters per second. Our inner ears can receive these pressure signals and send them to our brain for further recognition.
所謂「聲音訊號」（Audio Signals）簡稱「音訊」，泛指由人耳聽到的各種聲音的訊號。一般來說，發音體會產生震動，此震動會對空氣產生壓縮與伸張的效果，形成聲波，以每秒大約 340 公尺的速度在空氣中傳播，當此聲波傳遞到人耳，耳膜會感覺到一伸一壓的壓力訊號，內耳神經再將此訊號傳遞到大腦，並由大腦解析與判讀，來分辨此訊號的意義。
There are numerous ways to classify audio signals. If we consider the source of audio signals, we can classify them into two categories:
- Sounds from animals: Such as human voices, dog's barking, cat's mewing, frog's croaking. (In particular, Bioacoustics is a cross-disciplinary science, which investigates sound production and reception in animals.)
- Sounds from non-animals: Sounds from car engines, thunder, door slamming, music instruments, etc.
音訊可以有很多不同的分類方式，例如，若以發音的來源，可以大概分類如下：
- 生物音：人聲、狗聲、貓聲等。
- 非生物音：引擎聲、關門聲、打雷聲、樂器聲等。
If we consider repeated patterns within audio signals, we can classify them into another two categories:
- Quasi-periodic sound: The waveforms consist of similar repeated patterns such that we can perceive the pitch. Examples of such sounds include monophonical playback of most music instruments (such as pianos, violins, guitars, etc) and human's singing/speaking.
- Aperiodic sound: The waveforms do not consists of obvious repeated patterns so we cannot perceive a stable pitch. Examples of such sounds include thunder pounding, hand clapping, unvoiced part in a human's utterance, and so on.
若以訊號的規律性，又可以分類如下：
- 準週期音：波形具有規律性，可以看出週期的重複性，人耳可以感覺其穩定音高的存在，例如單音絃樂器、人聲清唱等。
- 非週期音：波形不具規律性，看不出明顯的週期，人耳無法感覺出穩定音高的存在，例如打雷聲、拍手聲、敲鑼打鼓聲、人聲中的氣音等。
In principle, we can divide each short segment (also known as frame, with a length of about 20 ms) of human's voices into two types:
- Voiced sound: These are produced by the vibration of vocal cords. Since they are produced by the regular vibration of the vocal cords, you can observe the fundamental periods in a frame. Moreover, due to the existence of the fundamental period, you can also perceive a stable pitch.
- Unvoiced sound: These are not produced by the vibration of vocal cords. Instead, they are produced by the rapid flow of air through the mouse, the nose, or the teeth. Since these sounds are produced by the noise-like rapid air flow, we can not observed the fundamenta period and no stable pitch can be perceived.
以人聲而言，我們可以根據其是否具有音高而分為兩類，如下：
- Voiced sound: 由聲帶振動所發出的聲音，例如一般的母音等。由於聲帶振動，造成規律性的變化，所以我們可以感覺到音高的存在。
- Unvoiced sound: 由嘴唇所發出的氣音，並不牽涉聲帶的震動。由於波形沒有規律性，所以我們通常無法感受到穩定音高的存在。
The following figure shows the voiced sound of "ay" in the utterance "sunday".
下圖顯示在 "sunday" 發音中的 "ay" 部分波形，這是一個 voiced sound。
You can easiy identify the fundamental period in the closeup plot.
你可以輕易地由目視來看出在放大波形中的基本頻率。
On the other hand, we can also observe the unvoiced sound of "s" in the utterance "sunday", as shown in the following example:
此外，你也可以觀察在發音 "sunday" 中的 unoviced sound "s"，如以下範例所示：
In contract, there is no fundamental periods and the waveform is noise-like.
我們在其放大波形中並無法觀察到基本週期的存在，其波形比較像是雜訊，並無週期性。
Audio signals actually represent the air pressure as a function of time, which is a continuous in both time and signal amplitude. When we want to digitize the signals for storage in a computer, there are several parameter to consider.
- Sample rate: This is the number of sample points per second, in the unit of Hertz (abbreviated as Hz). A higher sample rate indicate better sound quality, but the storage space is also bigger. Commonly used sample rates are listed next:
- 8 kHz: Voice quality for phones and toys
- 16 KHz: Commonly used for speech recognition
- 44.1 KHz: CD quality
- Bit resolution: The number of bits used to represent each sample point of audio signals. Commonly used bit resolutions are listed next:
- 8-bit: The corresponding range is 0~255 or -128~127.
- 16-bit: The corresponding range is -32768~32767.
- Channels: We have mono for single channel and stereo for double channels.
聲音代表了空氣的密度隨時間的變化，基本上是一個連續的函數，但是若要將此訊號儲存在電腦裡，就必須先將此訊號數位化。一般而言，當我們將聲音儲存到電腦時，有下列幾個參數需要考慮：
- 取樣頻率（sample Rate）：每秒鐘所取得的聲音資料點數，以 Hertz（簡寫 Hz）為單位。點數越高，聲音品質越好，但是資料量越大，常用的取樣頻率如下：
- 8 kHz：電話的音質、一般玩具內語音 IC 的音質
- 16 KHz：一般語音辨識所採用
- 44.1 KHz：CD 音質
- 取樣解析度（Bit Resolution）：每個聲音資料點所用的位元數，常用的數值如下：
- 8-bit：可表示的數值範圍為 0~255 或 -128~127
- 16-bit：可表示的數值範圍為 -32768~32767
- 聲道：一般只分單聲道（Mono）或立體聲（Stereo），立體音即是雙聲道。
Let take my utterance of sunday for example. It is a mono recording with a sample rate of 16000 (16 KHz) and a bit resolution of 16 bits (2 bytes). It also contains 15716 sample points, corresponding to a time duration of 15716/16000 = 0.98 seconds. Therefore the file size is about 15716*2 = 31432 bytes = 31.4 KB. In fact, the file size for storing audio signals is usually quite big without compression. For instance:
- If we used the same parameters for a one-minute recording, the file size will be 60 sec x 16 KHz x 2 Byte = 1920 KB, close to 2 MB.
- For audio music in a CD, we have stereo recordings with a sample rate of 44.1 KHz, a bit resolution of 16 Bits. Therefore for a 3-minute audio music, the file size is 180 sec x 44.1 KHz x 2 Byte x 2 = 31752 KB = 32 MB. (From here you will also know the MP3 compression ratio is about 10.)
以我所錄的「sunday」來說，這是單聲道的聲音，取樣頻率是 16000（16 KHz），解析度是 16 Bits（2 Byte），總共包含了 15716 點（等於 15716/16000 = 0.98 秒），所以檔案大小就是 15716*2 = 31432 bytes = 31.4 KB 左右。由此可以看出聲音資料的龐大，例如：
- 如果我以相同的參數來進行錄音一分鐘，所得到的檔案大小大約就是 60 秒 x 16 KHz x 2 Byte = 1920 KB 或將近 2 MB。
- 以一般音樂 CD 來說，大部分是立體聲，取樣頻率是 44.1 KHz，解析度是 16 Bits，所以一首三分鐘的音樂，資料量的大小就是 180 秒 x 44.1 KHz x 2 Byte x 2 = 31752 KB = 32 MB。（由此可知，MP3 的壓縮率大概是10倍左右。）
Audio Signal Processing and Recognition (音訊處理與辨識)
