Sound and images are analogue phenomena that can be represented by complex waveforms
s (t) = A sin (wt + f)
| 参数 | 对应意义 |
|---|---|
| f | frequency (Hz) |
| T | period (s) = 1/f |
| A | amplitude |
| w | angular frequency (rad/s) = 2pf |
| f | phase |
Example: Visible Light
The wavelengths of visible light lie roughly between 400 nm and 700
nm.
Spectral Power Distribution (SPD): a description of how the intensity of light from some source varies with wavelength.
Complex Waveforms
- Most waveforms are complex, i.e. their shape is the result of adding 2 or more waveforms.
- Each complex waveform may be described as the sum of a number of simple sine waves, each with a particular amplitude, frequency (or wavelength) and phase.
Fourier analysis
- Fourier analysis attempts to represent a set of data with a series of sines and cosines with different periods, amplitudes, and phases.
- This representation is done by a mathematical process called a transform : the data measurements in the time domain are transformed into the period or frequency domain.（把信号从时间域转到频域）
Analogue-to-digital conversion
converting the continuous phenomena of images, sound, and motion into a discrete representation that can be handled by a computer
- Digitised pictures and sound can now be captured in fine detail.
- Digital data communication is less vulnerable to noise than is analogue.
- Digital data can be communicated more compactly than analogue… when compressed!
Sampling
- Sampling chooses discrete points at which to measure a continuous phenomenon (a signal).
- In the case of images, the sample points are evenly separated in space.
- In the case of sound, the sample points are evenly separated in time.
- The number of samples taken per unit time or unit space is called the sampling rate.
Quantisation
Let n be the number of bits used to quantize a digital sample. Then the maximum number of different values that can be represented, m, is m = 2n
- Quantisation requires that each sample be represented in a fixed
number of bits, called the sample size or the bit depth. - In the case of an image, the bit depth is called the color depth.
- The bit depth limits the precision with which each sample can be represented.
Sampling + Quantisation
- The sampling rate relates directly to the frequency of a wave.
- Quantization, on the other hand, relates more closely to the amplitude of a wave.
Nyquist theorem
Sample twice as often as the highest frequency you want to capture
Let f be the frequency of a sine wave. Let r be the minimum sampling rate that can be used in the digitisation process such that the resulting digitised wave is not aliased. Then:r = 2 f
r is called the Nyquist rate.
Signal to Noise Ratio (SNR)
SNR: the ratio of the meaningful content of a signal versus the associated noise.（信号中有意义的内容与相关噪声的比率。）
- In analog data communication, SNR is defined as the ratio of the average power in the signal versus the power in the noise level.
- For a digitised image or sound, SNR, also called signal-to-quantisation-noise ratio (SQNR), is defined as the ratio of the maximum sample value versus the maximum quantisation error.