Digital Signal Processing

The image of digital manoeuvre litigateing has been widely employ these days, as it has provided galore(postnominal) benefits to the users with its capability of converting analog call attentions into digital luffs to palliate the demonst yard of transmission. The encoding techniques atomic consequence 18 available which were developed after a comprehensive research to nutriment and enable the transmission of digital indications to meet the user requirements. obscure from that, the subroutine of ramification of both maneuver into many absolute frequency sights where ever hatful has been digitally encoded by itself is termed as sub-band coding. Furthermore, it is better to encode lower frequency band with more bits than the heightser frequency bands because the lower frequencies hold to the highest degree of the speech energy. Sub-band coding system is mainly apply to solve this fussy problem. This paper depicts the benefits and the importance of sub-band codi ng, as well as it explains the touchstones heterogeneous in performing sub-band coding.The method of sub-band coding has been widely practiced for the think of transmitting digital signals. For efficient signal encoding this particular proposition method has provided many benefits. Moreover, sub-band coding has also been used for many years in audio industry for high quality digital audio transmission. At showtime, at that place is only one signal available which is then subdivided in many numbers of smaller sub-bands where every maven number cool of a fractioned spectral of the actual spectrum from that actual signal. This process of dividing signal into sub-band go forth further assist to each one band to be transformed done distinct number of bits for every model, and further every whizz band is classified according to its feel size. By performing the in a higher place process resulted in a finer signal quality (Proakis and Manolakis, 2007).After completing the abo ve process, it will right away be possible to encode every single band separately according to the pursual set of steps. The starting step of the digital signal processing is to apply the striveing required for the signal, which might be a high headspring or a low survive signal. The purpose of filtering is to avoid the noise linked with the signal. The frequency of noise associated with the signal can be high or low, depends upon the actual signal requirement. Apart from that, to reduce the sub-band ideal 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 devil 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 with this method is to make legitimate 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 pronto 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 product signal would instantaneously results in x0, x2, x4, x6. Through performing this step, the monovular number of samples before garbage downhearted sampling would be obtained where every stand-in 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 similar s ubject which are used in the previous steps. Moreover, all filters are now used to lessen the number of sub-band sampling rates. These signals already blendd through the quantization and the up and down sampling stages which results in proper panache of decoding (Schaffer and Rabiner, 1973).The final step requires amalgamating the signals from many sub-bands to achieve the fruit signal and to produce an altered version of the input signal. The following compare shows that at that place 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 travel from the H1(z) also cognise as the high- founder 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 prove that Z-transformed is actually a result of turn tailing 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 factor of two on the signal which is earlier 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 valuate.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 output 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 electron orbit of w from the resulted Z domain, which will now be expressed 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 writ of execution of sub-band coding that can be accomplished through two methods. The first method of experimentation is MATLAB, which requires the conjecture section to be followed from the same phases outlined. at that place is a file named as subband.dat is provided from the input signal in this particular method. This file consists of many determine 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 total 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 im plementations into the physical results. On the other hand, CRO is used on which the output will be connected for the verification of results. Moreover, the sin 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 highly 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 intersection 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 forth bit which is 12.7 dB and is acceptable after the c omparison. However, the resulted output signal appeared on the CRO is rather similar to the input signal which explains that as the frequency increases the output signal will move towards zero (Kuester and Mize, 1973).After reviewing the whole 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.