Subband CodingOverviewOverview – cont’dOverview - cont’dExample 14.2.1Example 14.2.1 – Cont’dIntroduction to Subband CodingSubband CodingFiltersFilters – Cont’dDigital FiltersDigital FilteringExample 14.3.1Example 14.3.2Filters in literatureFilters used in Subband Coding8-tap Johnston Low-Pass FilterSlide 18Filter BanksSubband Coding AlgorithmSlide 21(1) AnalysisSlide 23Slide 24Slide 25Slide 26Slide 27Slide 28(2) Quantization and CodingBit Allocation(3) SynthesisApplicationApplication to Image CompressionExample 14.12.2 – Decomposing and ImageSlide 35Slide 36Coding the SubbandsExample 14.12.3 – Coding the SubbandsSlide 39Slide 40SummarySlide 42Subband CodingJennie Abraham 07/23/2009OverviewPreviously, different compression schemes were looked into – (i)Vector Quantization Scheme(ii)Differential Encoding Scheme(iii)Scalar Quantization Scheme- Most efficient when the data exhibit certain characteristicsOverview – cont’dSource data characteristics - Unfortunately, most source outputs exhibit a combination of characteristics. difficult to select a compression scheme exactly suited to the source output.Overview - cont’dDecomposing the source output into constituent parts using some method. Each constituent part is encoded using one or more of the methods described previously. enables the use of these compression schemes more effectively.Example 14.2.1XnZnYnZnYnCompression Scheme 1Compression Scheme 2XnExample 14.2.1 – Cont’dXn = 10 14 10 12 14 8 14 12 10 8 10 12Yn = Xn = Yn + ZnZn =Introduction to Subband CodingThe source output can be decomposed into its constituent parts using digital filters. Each of these constituent parts will be different bands of frequencies which make up the source.Subband Coding A compression approach where digital filters are used to separate the source output into different bands of frequencies. Each part then can be encoded separately.FiltersA filter is system that isolates certain frequencies.(i) Low Pass Filters(ii) High Pass Filters(iii) Band Pass FiltersFilters – Cont’dFilter Characteristics Magnitude Transfer Function : the ratio of the magnitude of the input and output of the filter as a function of frequency.fo = Cutoff Frequency.Digital Filters Sampling and Nyquist rule :If fo is the highest frequency of the signal then the sampling rate > 2fo per second can accurately represent the continuous signal in digital form. Extension of Nyquist rule: For signal with frequency components between frequencies f1and f2 then, sampling rate = 2(f2 — f1) per second.Violation of Nyquist rule: Distortion due to aliasing.Digital FilteringThe general form of the input-output relationships of the filter is given by where, {Xn}= input, {Yn}=output of the filter,Values {ai} and {bi} = filter coefficients, N is called the taps in the filter. FIR Filter IIR FilterExample 14.3.1Filter Coefficients ao = 1.25, a1= 0.5 and the input sequence {Xn} is given by – then the output {Yn} is given byExample 14.3.2Consider a filter with ao = 1 and b1 = 2. The input sequence is a 1 followed by 0s. Then the output isFilters in literatureDesign and analysis of digital filters is detailed in Sections 14.5-14.8 of the textbook.A useful approach is to make use of the available literature to select the necessary filters rather than design them.Filters used in Subband CodingCouple of examples of –Quadrature Mirror Filters (QMF),Johnston FilterSmith-Barnwell FiltersDaubechies Filters….and so on8-tap Johnston Low-Pass Filter8-tap Johnston Low-Pass FilterLPHPFilter BanksSubband coding uses filter banks.Filter banks are essentially a cascade of stages, where each stage consists of a low-pass filter and a high-pass filter.Subband Coding AlgorithmSubband Coding AlgorithmThe three major components of this system are - the analysis and synthesis filters, the bit allocation scheme, and the encoding scheme. A substantial amount of research has focused on each of these components.(1) AnalysisSource output  analysis filter bank  sub-sampled encoded.Analysis Filter BankThe source output is passed through a bank of filters.This filter bank covers the range of frequencies that make up the source output.The passband of each filter specifies each set of frequencies that can pass through.Subband Coding Algorithm(1) AnalysisSource output  analysis filter bank  sub-sampled encoded.Analysis Filter BankDecimationThe outputs of the filters are subsampled thus reducing the number of samples.(1) AnalysisSource output  analysis filter bank  sub-sampled encoded.Analysis Filter BankDecimationThe justification for the subsampling is the Nyquist rule and its extension justifies this downsampling.(1) AnalysisSource output  analysis filter bank  sub-sampled encoded.Analysis Filter BankDecimationThe amount of decimation depends on the ratio of the bandwidth of the filter output to the filter input.Subband Coding Algorithm(1) AnalysisSource output  analysis filter bank  sub-sampled encoded.Analysis Filter BankDecimationEncodingThe decimated output is encoded using one of several encoding schemes, including ADPCM, PCM, and vector quantization.(2) Quantization and CodingSelection of the compression scheme Allocation of bits between the subbandsallocate the available bits among the subbands according to measure of the information content in each subband. This bit allocation procedure significantly impacts quality of the final reconstruction.Bit AllocationMinimizing the distortion i.e. minimizing the reconstruction error drives the bit allocation procedure.Different subbandsdifferent amount of information.Bit allocation procedure can have a significant impact on the quality of the final reconstruction(3) SynthesisQuantized and Coded coefficients are used to reconstruct a representation of the original signal at the decoder. Encoded samples from each subband decoded upsampled  bank of reconstruction filters outputs combined  Final reconstructed outputApplicationThe subband coding algorithm has applications in -Speech CodingAudio CodingImage CompressionApplication to Image CompressionLL LHHLHHExample 14.12.2 – Decomposing and ImageExample 14.12.2 – Decomposing and ImageExample 14.12.2 – Decomposing and ImageCoding the SubbandsSQLL LHHLHHDiscardDPCMSome bands  VQExample 14.12.3 – Coding the