Analog to digital signal conversion
To convert any analog signal (sound, image) into digital format, three basic operations must be performed: sampling, quantization and encoding.
Sampling
– presentation of a continuous analog signal by means of a sequence of its values (samples). These samples are taken at times separated from each other by an interval called the sampling interval. The reciprocal of the interval between samples is called the sample rate. In Fig. 1 shows the original analog signal and its sampled version. The images below the timing diagrams are obtained assuming that the signals are one line television video signals, the same for the entire television screen.
Analog to digital conversion. Sampling
It is clear that the shorter the sampling interval, and therefore the higher the sampling frequency, the smaller the difference between the original signal and its sampled copy. The stepped structure of the sampled signal can be smoothed with a low-pass filter. This is how the analog signal is restored from the sampled one. But the reconstruction will be accurate only if the sampling frequency is at least 2 times the bandwidth of the original analog signal (this condition is determined by the well-known Kotelnikov theorem). If this condition is not met, the sampling is accompanied by irreversible distortions. The fact is that, as a result of sampling, additional components appear in the frequency spectrum of the signal, which lie around the harmonics of the sampling frequency in the range, equal to twice the bandwidth of the original analog signal. . If the maximum frequency in the frequency spectrum of the analog signal exceeds half the sampling frequency, then the additional components fall within the frequency band of the original analog signal. In this case, it is no longer possible to restore the original signal without distortion. The theory of sampling is covered in many books.
Analog to digital conversion. Distortion sampling
An example of sampling distortions is shown in Fig. 2. An analog signal (again, suppose it is a TV line video signal) contains a wave, the frequency of which first increases from 0.5 MHz to 2.5 MHz and then decreases to 0.5 MHz. This signal is sampled at 3 MHz. In Fig. 2 the images are shown sequentially: the original analog signal, the sampled signal, the restored analog signal after sampling. The low-pass reconstruction filter has a 1.2 MHz bandwidth. As you can see, the low-frequency components (less than 1 MHz) are restored without distortion. The 1.5 MHz wave disappears and becomes a relatively flat field. The 2.5 MHz wave after recovery became a 0.5 MHz wave (this is the difference between the 3 MHz sampling frequency and the original 2.5 MHz frequency). These image diagrams illustrate the distortion associated with an insufficiently high spatial sample rate of the image. If the subject of the television recording is an object that is moving very fast or, for example, a rotating object, then sampling distortions in the time domain may occur. An example of distortion associated with an insufficiently high sample rate (and this is the frame rate of television decay) is an image of a fast moving car on stationary wheels or, for example, slowly turning in one direction or other, the spokes of the wheel (stroboscopic effect). There is no sampling distortion when the bandwidth of the original signal is limited from above and does not exceed half the sampling frequency. associated with insufficiently high spatial sampling rate of the image. If the subject of the television recording is an object that is moving very fast or, for example, a rotating object, then sampling distortions in the time domain may occur. An example of distortion associated with an insufficiently high sample rate (and this is the frame rate of television decay) is an image of a fast moving car on stationary wheels or, for example, slowly turning in one direction or other, the spokes of the wheel (stroboscopic effect). There is no sampling distortion when the bandwidth of the original signal is limited from above and does not exceed half the sampling frequency.
