Subband Coding Jennie Abraham 07/23/2009
Overview Previously, 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 characteristics
Overview – cont’d Source 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’d Decomposing 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 Xn Zn Yn Zn Yn Compression Scheme 1 Compression Scheme 2 Xn
Example – Cont’d Xn = Yn = Xn = Yn + Zn Zn =
Introduction to Subband Coding The 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.
Filters A filter is system that isolates certain frequencies. (i) Low Pass Filters (ii) High Pass Filters (iii) Band Pass Filters
Filters – Cont’d Filter Characteristics Magnitude Transfer Function : the ratio of the magnitude of the input and output of the filter as a function of frequency. f o = 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 Filtering The 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 Filter
Example Filter Coefficients a o = 1.25, a 1 = 0.5 and the input sequence {Xn} is given by – then the output {Yn} is given by
Example Consider a filter with a o = 1 and b 1 = 2. The input sequence is a 1 followed by 0s. Then the output is
Filters in literature Design and analysis of digital filters is detailed in Sections 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 Coding Couple of examples of – Quadrature Mirror Filters (QMF), Johnston Filter Smith-Barnwell Filters Daubechies Filters ….and so on
8-tap Johnston Low-Pass Filter
LP HP
Filter Banks Subband 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 Algorithm
The 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) Analysis Source 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) Analysis Source output analysis filter bank sub- sampled encoded. Analysis Filter Bank Decimation The outputs of the filters are subsampled thus reducing the number of samples.
(1) Analysis Source output analysis filter bank sub- sampled encoded. Analysis Filter Bank Decimation The justification for the subsampling is the Nyquist rule and its extension justifies this downsampling.
(1) Analysis Source output analysis filter bank sub- sampled encoded. Analysis Filter Bank Decimation The amount of decimation depends on the ratio of the bandwidth of the filter output to the filter input.
Subband Coding Algorithm
(1) Analysis Source output analysis filter bank sub- sampled encoded. Analysis Filter Bank Decimation Encoding 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 Allocation Minimizing 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 output
Application The subband coding algorithm has applications in - Speech Coding Audio Coding Image Compression
Application to Image Compression LLLH HL HH
Example – Decomposing and Image
Coding the Subbands SQ LLLH HL HH DiscardDPCM Some bands VQ
Example – Coding the Subbands
Coding the Subbands SQ LLLH HL HH DiscardDPCM Some bands VQ
Summary Subband coding is another approach to decompose the source output into components based on frequency. Each of these components can then be encoded using one of the techniques described in the previous chapters.
Summary The general subband encoding procedure can be summarized as follows: Select a set of filters for decomposing the source. Using the filters, obtain the subband signals. Decimate the output of the filters. Encode the decimated output. The decoding procedure is the inverse of the encoding procedure.