Digital Signal Processing

The concept of digital call attention addressing has been widely used these days, as it has provided many an otherwise(prenominal) benefits to the users with its potential of converting analog signals into digital signals to facilitate the process of transmission. The encoding techniques argon available which were developed after a comprehensive research to support and enable the transmission of digital signals to meet the user requirements. Apart from that, the process of ramification of any signal into many oftenness bunchs where ever set has been digit tout ensemble in ally encoded by itself is termed as sub-band coding. Furthermore, it is better to encode lower frequency band with more silicon chips than the elevateder frequency bands because the lower frequencies postulate most of the speech energy. Sub-band coding method is mainly used to solve this particular problem. This paper depicts the benefits and the magnificence of sub-band coding, as well as it explains the blackguards involved in performing sub-band coding.The method of sub-band coding has been widely practiced for the purpose of transmitting digital signals. For efficient signal encoding this particular method has provided many benefits. Moreover, sub-band coding has overly been used for many years in audio industry for high smell digital audio transmission. At first, on that point is only one signal available which is then subdivided in many military issues of smaller sub-bands where every atomic flesh 53 number composed of a fractioned spectral of the developed spectrum from that actual signal. This process of dividing signal into sub-band will further assist each band to be alter through and through and through distinct number of bits for every take, and further every single band is classified check to its step size. By performing the above process resulted in a finer signal role (Proakis and Manolakis, 2007).After complemental the above process, it will outright be possible to encode every single band separately according to the undermentioned set of steps. The starting step of the digital signal processing is to put one over the filtering required for the signal, which might be a high snuff it or a low gag signal. The purpose of filtering is to avoid the noise linked with the signal. The frequency of noise associated with the signal tush be high or low, depends upon the actual signal requirement. Apart from that, to reduce the sub-band sampling rates, filters are used to minimize the bit rate in the signal encoding process. This method helps to reduce the signal on every band from a factor of deuce in sampling rate, which suggests that every second sample must be taken from the signal in the process of digital signal processing (Crochiere, 1981).Furthermore, the above step can be elaborated as if the signal is x0-6, the samples taken from this would be x0, x2, x4, and x6. The major reason of sampling through this method is to make s ure that the reduced number of samples which would be quantized based on the following phase, which makes the quantization step to be as efficient and as quick as possible.The next step includes the quantization of signal on each band. In this process of quantization involves quantization noise to all the bits that are going to be sampled. However, at the receiving end, all those signals which are acquired from the process of quantization are to be sampled from the factor of two. By doing this method if the input signal is x0-6, the create signal would now results in x0, x2, x4, x6. through with(predicate) performing this step, the identical number of samples before stack sampling would be obtained where every substitute sample was missing (Veldhuis, Breeuwer, and Van Der Wall, 1989).The following step in the process of sub-band coding is to apply filters on all signals located at every single band where every filter should be of same vitrine which are used in the previous step s. Moreover, all filters are now used to lessen the number of sub-band sampling rates. These signals already moved through the quantization and the up and down sampling stages which results in puritanical mode of decoding (Schaffer and Rabiner, 1973).The final step requires amalgamating the signals from many sub-bands to achieve the output signal and to produce an change version of the input signal. The following equation shows that there is only one band available from the two bands that will move in the equivalent process.X1 (z) is the signal on the transmitting end, which was acquired after moving from the H1(z) also known as the high-pass filter which isX1 (z)= x1 (0)+ x1 (1) z-1+ x1 (2) z-2+ x1 (3) z-3 _____ 1X1 (-z)= x1 (0)- x1 (1) z-1+ x1 (2) z-2- x1 (3) z-3 _____ 1AIt is therefore proved that Z-transformed is actually a result of brief a high pass filter to the signal which is the actual input xn. X1 (z)= X (z) H1(z) _____ 2The down sampling has been performed by the fact or of two on the signal which is originally X1 (z) will now be presented by Y1(z) signal as shown in the following equationY1(z) = y1 (0)+ y1 (1) z-1+ y1 (2) z-2+ y1 (3) z-3 _____ 3Y1(z) = x1 (0)+ x1 (2) z-1+ x1 (4) z-2+ _____ 4The equation 4 mentioned above, explains that the down sampling effect has removed every single alternate sample available.However, at the other end signals that were previously up sampled, will now be considered as U1(z) at which every single alternate sample is equal to zero value.U1(z) = u1 (0)+ u1 (1) z-1+ u1 (2) z-2+ u1 (3) z-3 U1(z) = y1 (0)+0+ y1 (1) z-2+ 0+y1 (2) z-4+ U1(z) = y1 (0)+ y1 (1) z-2+ y1 (2) z-4+ from 4 U1(z)= Y1(z2)U1(z) = x1 (0)+ x1 (2) z-2+ x1 (4) z-4+ x1 (6) z-6 U1(z) = (X1(z)+X1(-z))/2 = X(z) H1(z)+X(-z) H1(-z)/2__5Besides, the U1(z) signal now move towards the next high pass filter which is K1(z) which is positioned at the receiving point and specified asV1(z)= U1(z) K1(z) = K1(z) X(z) H1(z) )+X(-z) H1(-z) 6Furthermore, the final ou tput signal will now be created after each sub-band output is added which results in the subsequent equationX_out(z)=V1(z)+ V2(z)X_out(z)= K1(z) X(z) H1(z) )+X(-z) H1(-z) + K2(z) X(z) H2(z) )+X(-z) H2(-z) .X_out(z)= H2 (z) H2 (-z) X(z).When the final output is obtained, to make equation more expressive, it will now be altered into the frequency domain of w from the resulted Z domain, which will now be express in the following mannerX out(w)= H2 (w)- H2 (w-p) X(w).X out(w)= e-jw(m-1) Hr2 (w) e-j(m-1)(w-pi) Hr2 (w-p) X(w).In the above equation, m represents that even number which measures the length of the filter.After completing the above procedure, the next phase requires experimentation which includes the implementation of sub-band coding that can be accomplished through two methods. The first method of experimentation is MATLAB, which requires the theory section to be followed from the same phases outlined. There is a file named as subband.dat is provided from the input sig nal in this particular method. This file consists of many values which expresses the file regarding the capacity of the signal in a given time. Moreover, H2(z) was also given as the coefficients of the low pass filters (Croisier, 1974).It is also suggested that the high pass filters H1(z) are used with the low pass filters K2(z) which creates relationship among the filters explained belowH1(z) = H(z), H2(z)= H(-z), K1(z)= 2H(z) and K2(z)= -2H(-z).Apart from that, there is one more value known as the SNR value that is required for the process of quantization where every single value of Q1 will be computed through the following equationSNRdB= xi(n)2 / (xi(n)- xo(n))2 . Where the limits of the summation is from n=0 to N-1.The next method for the implementation of the sub-band coding used is called C6711. It is a device that works as a converter and facilitate users in converting software implementations into the physical results. On the other hand, CRO is used on which the output wil l be connected for the verification of results. Moreover, the sine wave is also generated through connecting the frequency generator to the C6711 device (Rabiner and Gold, 1975).Finally, the results generated through MATLAB for the sub-ban coding reveals that before performing any find of modifications on the signal, it extremely requires the plotting of input signal. Apart from that, result has also shown that the low pass and high pass filters of sub-bands were moved towards an crosswalk point which exactly equals to 0.5 rad/sample.The SNR values used in the process of quantization of distinct number of bits reached at a highest level of 16.5dB at the 5th bit. On the other hand, the SNR value has been calculated for 4 bit PCM system was almost 13.2dB. The value suggests that there is a 0.5dB variation from the value computed at the out bit which is 12.7 dB and is acceptable after the comparison. However, the resulted output signal appeared on the CRO is quite similar to the inp ut signal which explains that as the frequency increases the output signal will move towards zero (Kuester and Mize, 1973).After reviewing the entirely process, it is concluded that the sub-band coding is a method to encode the input signal successfully with maximum efficiency. The two methods used in the process known as MATLAB and C6711 endorse the theory presented in the preceding sections which are considered as valid and reliable.