Subband Coding

mGenXTechno Tags: audio, encoding, subband, coding

Introduction to Subband Coding
Sub-Band Coding (SBC) is a powerful and general method of encoding audio signals efficiently. Unlike source specific methods (like LPC, which works only on speech), SBC can encode any audio signal from any source, making it ideal for music recordings, movie soundtracks, and the like. MPEG Audio is the most popular example of SBC. This document describes the basic ideas behind SBC and discusses some of the issues involved in its use.
Basic Principles
SBC depends on a phenomenon of the human hearing system called masking. Normal human ears are sensitive to a wide range of frequencies. However, when a lot of signal energy is present at one frequency, the ear cannot hear lower energy at nearby frequencies. We say that the louder frequency masks the softer frequencies. The louder frequency is called the masker.
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.
A compression approach where digital filters are used to separate the source output into different bands of frequencies.
àEach 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
Filter Characteristics

• ØMagnitude 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
Components between frequencies f1and f2 then,
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
sampling rate = 2(f2 — f1) per second.
Violation of Nyquist rule:
Distortion due to aliasing.



Subband Coding Algorithm



Above picture shows pyramid decomposition of an image where encoding is shown on the left and decoding is shown on the right. The operators D and I correspond to Decimation and interpolation operators, respectively. For example, D produces an N/2 × N/2 image from an N × N original, while I interpolate an N × N image based on an N/2 × N/2 original.
Analysis
Source output --> analysis filter bank--> sub-sampled-->encoded.
Analysis Filter Bank

• The source output is passed through a bank of filters.
• his 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.

Decimation

• The outputs of the filters are subsampled thus reducing the number of samples.
• The justification for the subsampling is the Nyquist rule and its extension justifies this downsampling.
• The amount of decimation depends on the ratio of the bandwidth of the filter output to the filter input.

Encoding

• The decimated output is encoded using one of several encoding schemes, including ADPCM, PCM, and vector quantization.

Quantization and Coding
Selection of the compression scheme will be done based on the characteristic exhibited by the subbands.
Along with the selection of the compression scheme, the allocation of bits between the subbands is an important design parameter. This is what determines the quantizer parameters.

• 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.
Bit Allocation
This bit allocation procedure significantly impacts quality of the final reconstruction.
Minimizing the distortion i.e. minimizing the reconstruction error drives the bit allocation procedure.
Different subband-->different amount of information.
Bit allocation procedure can have a significant impact on the quality of the final reconstruction
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