Audio Representation - Multimedia Computing - Lecture Slides, Slides of Multimedia Applications

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Audio Representation and

Processing

Fundamentals of Audio Signals

• Two signals of different amplitudes
• A greater amplitude represents a louder sound.

Fundamentals of Audio Signals

• Any sound, no matter how complex, can be represented by a waveform.
• For complex sounds, the waveform is built up by the superposition of less complex waveforms
• The component waveforms can be discovered by applying the Fourier Transform - Converts the signal to the frequency domain - Inverse Fourier Transform converts back to the time domain

Sampling

• Sounds can be thought of as functions of a single variable ( t ) which must be sampled and quantized
• The sampling rate is given in terms of samples per second, or, kHz - During the sampling process, an analog signal is sampled at discrete intervals - At each interval, the signal is momentarily “held” and represents a measurable voltage rate

Quantization

• The accuracy of the digital encoding can be

approximated by considering the word length

per sample

• This accuracy is known as the signal-to-error

ratio (S/E) and is given by:

• S/E = 6 n + 1.8 dB
• n is the number of bits per sample

Quantization

• When a coarse quantization is used, it may be useful to add a high-frequency signal (analog white noise) to the signal before it is quantized - This will make the coarse quantization less perceptible when the signal is played back - This technique is known as dithering
• During the sampling process, an analog signal is sampled at discrete intervals
• At each interval, the signal is momentarily “held” and represents a measurable voltage rate

Digital Audio Data

• A complete description of digital audio data

includes (at least):

• sampling rate;
• number of bits per sample;
• number of channels (1 for mono, 2 for stereo, etc.)
• Type of quantization (linear, logarithmic, etc.)

Analog to Digital Conversion

• Nyquist’s theorem states that if an arbitrary

signal has been run through a low-pass filter of

bandwidth H , the filtered signal can be

completely reconstructed by taking only 2 H

(exact) samples per second.

• So, a low-pass filter is placed before the

sampling circuitry of the analog-to-digital

(A/D) converter.

Analog to Digital Conversion

• The low-pass filter can cause side effects.
  • One way that these side effects can be overcome is through the use of oversampling - a signal-processing function that raises the sample rate of a digitally encoded signal.
  • Consumer and professional 16-bit D/A converters often use up to 8- and 12-times oversampling, raising the sampling rate of a CD (for example) from 44.1 kHz to 352.8 kHz or 529.2 kHz.
  • By altering the signal’s noise characteristics, it is possible to shift much of the overall bandwidth noise out of the range of human hearing.

Pulse Code Modulation

• The method that has been discussed for storing audio is known as pulse code modulation (PCM).

1 5 14 12 5

Analog Input

0 0 0 1 0 1 0 1 1 1 1 0 1 1 0 0 0 1 0 1

Transmitted Code

Pulse Code Modulation

• D/A conversion process
  • parallelize the serial bit stream
  • generate an analog voltage analogous to the voltage level at the original time of sampling
  • An output sample and hold circuit is used to minimize spurious signal glitches
  • a final low-pass filter is inserted into the path
    • Smooths out the non-linear steps introduced by digital sampling

Pulse Code Modulation

• Other PCM topics:
  • mu-law and A-law companding
  • DPCM
  • DM
  • ADPCM

Digital Signal Processing

• Addition of two signals is accomplished by adding the sample values of the signals at each sampling point: h(t)=f(t)+g(t) - We can add as many signals as desired together
• Multiplication of a given signal is represented as: g(t)=m*f(t) , where m is the multiplication factor. - Multiplication is used to increase or decrease the gain (loudness) of a signal. If m>1 , g is louder than f. If m<1 , g is less loud than f - Note that when adding signals together or multiplying by a number greater than one, care must be taken when the signal reaches the upper limit of the sample size

Digital Signal Processing

• Delay is an important effect described as follows: g(t)=f(t+d) , where d is a delay time - Use delay and addition to model echo: - f(t) = HELLO - g(t) = f(t + d 1 ) , where 0 < d (^1) - g(t) = HELLO - h(t) = f(t + d 2 ) , where 0 < d 1 < d (^2) - h(t) = HELLO - F(t) = f(t) + g(t) + h(t) - = HELLO HELLO HELLO