Signals
Analog signal digitalization

Analog signal digitalisation is a procedure in which the analog signal (usually representing the specific media) is transformed into digital form. The signal is sampled, quantized and coded. The result is then a sequence of binary digits which is further processed.

Analog signal conversion to digital form (PCM method)

The main methods of multimedia signal coding in the time domain used in multimedia telecommunications are as follows:

- Pulse Code Modulation (PCM),
- Differential PCM (DPCM),
- Adaptive DPCM (ADPCM).

The signal is after low pass filtering (antialiasing filter) sampled in a sampling circuit and a sequence of samples is obtained.

Sampling is the reduction of a continuous signal to a discrete signal. Samples are taken in defined time periods; a sample refers to a value or set of values at a point in time and/or space. The value of sampling rate is given by the sampling theorem (known as Shannon-Kotelnik theorem), e.g. the sampling rate must be at least two times of the highest frequency in the sampled multimedia signal.

The value of sampling rate is given by the bandwidth of the sampled signal. For example a telephone speech has a frequency bandwidth 300 – 3400 Hz (4000 Hz), therefore the sampling rate is = 8 kHz.

Sampling theorem can be mathematically defined as .

The minimum sampling frequency is called the Nyquist frequency.

Sampled signal, let’s mark it as y(t), can be defined as a product of the original signal x(t) and sampling function s(t) represented as an infinite series of the Dirac impulses. Distance of impulses in the time domain is . In the frequency domain spectrum of signal (which is periodic) is discrete with distance of frequency components .

Sampling function in time and frequency

Spectrum Y(ω) of a sampled signal y(t) is a result of the convolution of the spectrum X(ω) and S(ω).

a)spectrum of original signal X(ω), b)sampled signal y(t )in time domain , c) spectrum of sampled signal Y(ω)

Sampling signal with smaller frequency than is signal’s maximum frequency ( ) causes overlapping of spectral components. This is called aliasing. Aliasing can happen also in case when signal has unlimited spectrum. Result is that the signal reconstructed from samples is different from the original continuous signal.

Each sample of the signal is substituted by corresponding quantization level (fixed set of numbers such as integers, or natural numbers), which results in a sequence of the quantized samples, a process known as quantization. Quantization levels are obtained by dividing of the amplitude into small intervals. Interval length is called quantization step. In case the steps are equal the quantization process is linear, in other case the process is non linear.

The main disadvantage of this process is quantization error or noise. It is the difference between the analog input to the ADC (analog-digital convertor) and the output digitized value. The noise is non-linear and signal-dependent. This error causes problems during conversion of digital signal back to analog. The signal is never converted back to the original form; it can be only approximated from the quantization values.

The next step in digitalization process is coding.

The coding of quantized samples is performed by assigning a binary code word to each quantized sample. In this way a sequence of the code words is obtained.

PCM method is an international standard for multimedia signals coding and transmission. The principle of this method is depicted on picture below.

The first systems based on PCM have used 7 bits code words N, e.g. the number of quantization levels has been 128. If we consider a sampling rate = 8 kHz and N = 8, then the required bit rate for speech transmission in telephone bandwidth is 8·103·8 = 64 kb/s.

The advantage of PCM coding in comparison to analog methods of transmission is the resistance of transmitted signal against distortion.

On the other side the disadvantage of this method is the broader frequency bandwidth that is required for signal transmission.

The waveforms of signals coded by using PCM are shown in picture below.

Waveforms in PCM coding of multimedia signals

Linear PCM uses the same constant quantization step in the whole range of the quantization. Therefore the range (dynamic) of quantized signal depends upon number and size of quantization steps. The number of quantization levels for a particular signal determines the size of quantization error. Higher number of quantization levels provides smaller quantization error, but the requirements on the transfer rate are higher. These disadvantages of the method can be solved by non-linear arrangement of quantization levels, which is the idea of non-linear PCM.

Non-linear PCM uses non-linear arrangement of quantization levels. The size of quantization steps for higher signal amplitudes gets larger. A modification of this method uses compression of dynamics of input signal at the transmitter side and expansion of dynamics at the receiver side. In this way small samples are amplified and large one are reduced by a compressor. At the receiver side the expander returns the samples in their original range.

Decoding process is the same process as coding but in reverse order. The output of the decoder is the sequence of quantized samples.