Sub-band Coding and Scalar Quantization - Essay Example

- The aim of this project was the comparison of two techniques for data compression. These two data compression techniques are known as Sub-band Coding and Scalar Quantization. The project also aimed to determine the best conditions for which each of these two techniques were suited. The sub-band coder and scalar quantization were implemented with success. From this, it was found that sub-band coding produced the best signal quality when equipped with a specific input signal in mind. Moreover, through the use of adaptive bit allocation, it was possible for the Sub-band Coder to be able to generate a compression of a higher quality for any input signal if compared with Scalar Quantization. I. INTRODUCTION This project was actualized for the purpose of comparing the performance of two different algorithms used for data compression, namely Sub-band Coding and Scalar Quantization as applied in audio and speech data. It is a scientific fact that between weak and strong sounds, the weaker sounds cannot be perceived at all by the human ear. This is the principle behind the practice of digitally compressing audio and speech. Thus, if digital compression removes the weaker sounds that cannot be heard anyway, then this process will never affect the quality of the sound in general. This is the principle of the Simultaneous Masking effect. Therefore, it is the signal processing techniques that make it possible to reduce the bit rate while not causing any damaging quality to the sound that is being perceived. The method of digitally compressing sound becomes most effective in such a case where both the sound the perceived and the removed sounds are in the same frequency band. Thus, if one uses sub-band coders in this situation, then one can expect the separation and individual quantization of low and high frequency bands. Thus, sub-band coders are useful. However, just like in all data compression techniques, there must be a balance that should exist between quality and bit rate of the signal. Overdoing the compression of the signal will only result in poorer output quality, and vice versa. Thus, the sub-band coding technique is also popularly known as the lossy compression method. 2]. The principle of Sub-band coding for audio was conceived by R. E. Crochiere. Through the use of a filter bank, the input signal is basically split up into various bands. What follows next is the downsampling of the outputs of these filters and their coding for transmission. At the receiver end, there is decoding of the signals. These signals are then upsampled and then passed through a separate filter bank. This filter bank is the one responsible for the reconstruction of the signals. This is followed by the addition of the signals and their amplification for the purpose of reviving the original signal [ HYPERLINK \l "REC80" 3 ]. These systems can possibly be distorted produced during the coding process as well as during the other stages when the signal is filtered. However, such distortion caused by the filters in the system can be reduced through the use of Quadrature Mirror Filters. 4] Sub-band coding systems are used in many applications such as Audio, Video and Image Compression. Popular audio compression formats include the MPEG-1 Layer 3 (mp3) coding and the Musepack (MPC). As to Scalar Quantization, there is a separate treatment for every input symbol in producing the output. The output signal quality is usually considerably lower when compared with a Sub-band Coder which is specifically designed for that input signal. The reason for this is the constancy of the number of bits involved in the quantization over the entire frequency band of the input signal. However, in case the input signal varies, the sub-band coder may not be able to generate the output of the highest quality, where the Scalar Quantizer would be capable of generating better quality signals. Sub-band coders that possess adaptive bit allocation systems make possible the generation of the best possible quality outputs that arise from any input signal. In such a case, the scalar quantizer does not perform as efficiently as sub-band coders intended for any input data. II. Theory & implementation Three different divisions comprise the entire system, with each of these divisions performing a very important step in the final sub-band coding. Both the Block Diagram of the Entire System are shown below: a) Quadrature Mirror Filters This particular section is made up of two separate sections called the Deconstruction and Reconstruction Filters. The Deconstruction filters function for the isolation of specific frequency bands. As soon as there is performance of Quantization, and the reconstruction of the final signal from the individual quantized bands [ HYPERLINK \l "Joh80" 5 ] The purpose of performing this is for the removal of any quantization noise that the system might have wrongly included. The coefficients of the impulse response for many low-pass filters were found and are presented in Table 1. As shown in Figure 1, H2(z) is considered a high pass filter implemented by making negative every alternative value which is found in the coefficients. Moreover, K2(z) is actually designed to make negative also every value in the high pass filter coefficients. TABLE 1: IMPULSE RESPONSE OF THE QMF LOW PASS FILTER n h(n) 0 0.0089874495 1 -0.0681367500 2 0.0669402090 3 0.4906729800 4 0.4906729800 5 0.0669402090 6 -0.0681367500 7 0.0089874495 For the purpose of deriving the desired filter response as well as the required frequency response, the input signal must be convolved together with the impulse response. Therefore, H1(z) = H(z) H2(z) = H(-z) K1(z) = H(z) K2(z) = - H(-z) Through the implementation of the above coefficients in various ways, there is a possibility of creating a Quadrature Mirror Filter System. b) Down and Up Sampler This section is necessary for the adjustment of the sampling rate of the quantizer. The Downsampler is utilized for the reduction of the effective sampling rate of the signal. The Upsampler is used to reconstruct the signal through the addition of zeros within the samples in order to match the actual size of data of the original file. In this particular experiment, there is the downsampling and upsampling by a factor of 2. c) Quantizer Straightforward Quantization is the simplest possible method that can be used to compress digital data. The quantizer takes samples from the input data and based on the decision levels that are used, generates a discrete time signal. In this experiment we use a Uniform Mid-Riser Quantizer. In this type of Quantizer, the decision levels are spaced evenly and the representation levels are in between the two decision levels. Hence, the step size is uniform. In a uniform mid-riser quantizer, there will not be a representation level at 0.6] The simplest possible method that be utilized in order to compress digital data is the Straightforward Quantization. The quantizer derives the input data from samples and based also on the decision levels being used, the quantizer generates a discrete signal of time. In this particular experiment, we used a Uniform Mid-Riser Quantizer. This particular type of Quantizer makes it a fact that the decision levels are evenly spaced, and the representation levels are in the middle of two decision levels. Thus, there is a uniform step size. In this uniform mid-rise quantizer, there is no representation. The first step was to feed the input signal into the deconstruction QMF low pass and high pass filters. The next step is to feed the output of the filters into the Downsampler. The purpose of this is to remove every second value, thus the sampling rate is effectively halved in value. The third step was to feed this signal into the quantizer. The next step was to quantize the signal and then upsampled, through the use of inserting a zero in between every sample. The second to the last step was to finally reconstruct and added together. While the very last step, in order to obtain the final output signal, was to amplify the signal using a factor of 2. d) Adaptive bit Allocation Within the context of the basic system, the Signal to Noise Ratio, or SNR, of the sub-band coder is as its maximum value based on the energy level of the band. With adaptive bit allocation, the system finds the energy of every specific band immediately after H1(z) and H2(z). The purpose of this is for the system to be able to automatically computer the best possible SNR. This means that the system compares the bands in order to make sure which possible band has the most information. After which, it is the system that allocates bits to each of the bands accordingly. The reason behind this is to obtain the best possible SNR for any specific given input signal. Read More