In the above example, "fs" is the sample rate which is 16000 in this case. This indicates that there are 16000 samples per second when the clip was recorded. The vector "y" is a column vector containing the samples of the speech signals. We can use "sound(y, fs)" to play the audio signals read from the file. "time" is a time vector in which each element corresponds to the time of each sample. Therefore we can plot "y" against "t" to show the waveform directly.
Most audio signals are digitized to have a bit resolution of 8 or 16 bits. If we want to know the bit resolution of the input wave file, we can use an extra output arguments to "wavread" to obtain the information, such as
From the above example, it can be observed that all the audio signals are between -1 and 1. However, each sample point is represented by an 8-bit interger. How are they related? First of all, we need to know the following convention:
- If a wave file has a bit resolution of 8 bits, then each sample point is stored as an unsigned integer between 0 and 255 (= 2^8-1).
- If a wave file has a bit resolution of 16 bits, then each sample point is stored as an unsigned integer between -32768 (= 2^16/2) and 32767 (= 2^16/2-1).
- For 8-bit resolution, we can multiply "y" (the value obtained by wavread) by 128 and then plus 128.
- For 16-bit resolution, we can multiply "y" (the value obtained by wavread) by 32768.
In the above example, the difference is zero, indicating the retrived y0 contains no fractional parts. Moreover, to increase code generality, we use 2^nbits/2 instead of 128.
We can also use the command "wavread" to read a stereo wave file. The returned variable will be a matrix of 2 columns, each containing the audio signals from a single channel. Example follows.
In the above example, MATLAB will read the wave file "flanger.wav", play the stereo sound, and plot two streams of audio signals in two subplots. Since the intensities of these two channels are more or less complemntary to each other, which gives an illusion that the sound source is moving back and forth between two speakers. (A quiz: how do you create such effect given a single stream of audio signals?)
If the wave file is too large to be read into memory directly, we can also use "wavread" to read a part of the audio signals directly. See the following example.
The waveform in the above example represent the vowel part of the second Chinese character "迎" in the original utterance of "歡迎光臨" (welcome). It is obvious that the waveform contain a fundamental period of about 100 samples, corresponding to a time duration of 100/fs = 0.0091 seconds = 9.1 ms. This corresponds to a pitch frequency of 11025/100 = 110.25 Hz. This pitch is very close to two octave down the central la, or the 5th white key counting from the left.
The perception of pitch of human ear is proportional to the logrithm of the fundamental frequency. The central la of a piano has a fundamental frequency of 440 Hz. One octave above it is 880 Hz, while one octave below it is 220 Hz. Each octave in the piano keyboard contains 12 keys, including 7 white keys and 5 black ones, corresponding to 12 semitones within a octave. If we adopt the standard of MIDI files, the semitone of the central la is 69 with a fundamental frequency of 440. Therefore we can have a formula to convert a frequency into a semitone:
If we want to obtain more information about a wave file, we can retrieve it from the 4th output arguments of the command "wavread", as follows.
In the above example, some quantities are explained next.
- wFormatTag is the format tag of the wave file.
- nChannels is the number of channels.
- nSamplePerSec is the number of samples per second, which is equal to the samping rate 22050.
- nAveBytesPerSec is the number of bytes per second. In this case, since we have two channels and the bit resolution is 2 bytes, therefore we have 22050*4 = 88200.
- nBlockAlign is equal to the rato between nAveBytesPerSec and nSamplePerSec.
- nBitsPerSample is the bit resolution.
Audio Signal Processing and Recognition (音訊處理與辨識)
