The digital form of an analog signal is a number sequence with finite precision. The A/D converter is the name given the process of conversion (Proakis & Manolakis, 2007). This process is subdivided into the following processes: sampling, quantizing and coding. Sampling entails the conversion of continuous time signals into discrete time signals with the use of samples of continuous time signals at a known frequency. Quantization involves changes to continuous time values of the discrete time signals so as to convert them into discrete time values. The process of coding gives binary numbers to quantized signals depending on their values.
There are various ways of converting analog signals into digital form for both storage and transmission. Sub-band coding happens to be an efficient method for this conversion, especially with medium bit rates (Pirani & Zingarelli, 1984, 645). As the rate of sampling alters with time, either with an increase or decrease, the efficiency of the conversion process can be enhanced by minimizing the energy of transmitting or sending signals, depending, of course, on their sample rates, so that a greater amount of energy is made available for high sampling rates.
It is also possible to compress data in order to reduce the amount of energy required for the process of transmission. This should be achieved without impairing the quality of the signal that is decoded (Crochiere, 1981, 1633). Sub-band coding is an effective technique for data compression. With the Matlab program, sub-band coding can be developed before it is implemented in the C7613. Here, the coder of sub-bands uses sampled signals as inputs. Depending on the energy of different signals, the various subs of the sub-band coder are assigned different numbers of bits.
Thus, sub-band coding is expected to provide output signals that are similar to input signals. (See Sub-band coder in Figure 1, resulting in differing accuracies for output signals. Accuracies are dependent on the different values of bits used in the quantizers. It is preferable to give a greater number of bits for higher energy subs of the signal). Sub-band coding Sub-band coding involves the sub-band coder and sub-band encoded. There are different subs in the sub-band coder responsible for filtering the input sample with both filters, H1 and H2, in addition to down sampling.
Sub-band encoded, on the other hand, entails quantizing, upsampling and filtering with K1 and K2 before the bands are summed for the final signal. (See Figure 1). As shown in this figure, if the rate of sampling the signal is Fs sample per second, the frequencies of each of the subdivisions of the sub-band coder can be computed. The signal spectrum is split into two equal-width parts by the first frequency subdivision: a lowpass signal (0
The signals in both lowpass and highpass frequency bands require interpolation and summation. The filtering step serves to do away with signal noise, which may be lower or higher in frequency than the required signal. Filtering further serves to reduce the rates of sub-band sampling in order to minimize overall bit rates for encoding of signals. Hence, a superior performance in sub-band coding can be achieved by developing an accurate filter design (Crochiere, 1633). Filters that are idle, for example, the Brick wall filters as shown in Figure 2, are suitable for this purpose.
However, such filters are not available outside of theory. Aliasing must be avoided; this is achieved by the decimation of sub-band signals. As actual filters have overlaps, it is best to resolve the problem of aliasing with the use of quadrature mirror filters. These filters have frequency response characteristics as shown in Figure 3 (Proakis & Manolakis). The following equation shows perfect reconstruction: . From this equation we chose . Next, the filtered signal is down sampled with the process of down sampling.
This process involves the deletion of every second sample. If there are three samples, for instance, the second sample would have to be deleted. This deletion reduces the number of samples to be quantized. Using the quantizer, the down sampled signal is quantized following deletion. Through quantization, we add quantization noise to bits being sampled. Thus, every set of two samples is averaged in order to approximate continuous time input signals on each of the bands by discrete numbers of samples (Veldhuis, Breeuwer, & Van Der Wall, 1989).