QMF - Quadrature-Mirror Filter Bank In many applications, a...

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Copyright © S. K. 1 Quadrature-Mirror Filter Bank Quadrature-Mirror Filter Bank In many applications, a discrete-time signal x [ n ] is split into a number of subband signals by means of an analysis filter bank The subband signals are then processed Finally, the processed subband signals are combined by a synthesis filter bank resulting in an output signal y [ n ] ]} [ { n v k
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Copyright © S. K. 2 Quadrature-Mirror Filter Bank Quadrature-Mirror Filter Bank If the subband signals are bandlimited to frequency ranges much smaller than that of the original input signal x [ n ] , they can be down-sampled before processing Because of the lower sampling rate, the processing of the down-sampled signals can be carried out more efficiently ]} [ { n v k
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Copyright © S. K. 3 Quadrature-Mirror Filter Bank Quadrature-Mirror Filter Bank After processing, these signals are then up- sampled before being combined by the synthesis filter bank into a higher-rate signal The combined structure is called a quadrature-mirror filter quadrature-mirror filter ( ( QMF QMF ) ) bank bank
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Copyright © S. K. 4 Quadrature-Mirror Filter Bank Quadrature-Mirror Filter Bank If the down-sampling and up-sampling factors are equal to or greater than the number of bands of the filter bank, then the output y [ n ] can be made to retain some or all of the characteristics of the input signal x [ n ] by choosing appropriately the filters in the structure
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Copyright © S. K. 5 Quadrature-Mirror Filter Bank Quadrature-Mirror Filter Bank If the up-sampling and down-sampling factors are equal to the number of bands, then the structure is called a critically critically sampled filter bank sampled filter bank The most common application of this scheme is in the efficient coding of a signal x [ n ]
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Copyright © S. K. 6 Two-Channel QMF Bank Two-Channel QMF Bank Figure below shows the basic two-channel QMF bank-based subband codec ( coder/decoder )
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Copyright © S. K. 7 Two-Channel QMF Bank Two-Channel QMF Bank The analysis filters and have typically a lowpass and highpass frequency responses, respectively, with a cutoff at π /2 ) ( z H 0 ) ( z H 1
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Copyright © S. K. 8 Two-Channel QMF Bank Two-Channel QMF Bank Each down-sampled subband signal is encoded by exploiting the special spectral properties of the signal, such as energy levels and perceptual importance It follows from the figure that the sampling rates of the output y [ n ] and the input x [ n ] are the same
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Copyright © S. K. 9 Two-Channel QMF Bank Two-Channel QMF Bank The analysis and the synthesis filters are chosen so as to ensure that the reconstructed output y [ n ] is a reasonably close replica of the input x [ n ] Moreover, they are also designed to provide good frequency selectivity in order to ensure that the sum of the power of the subband signals is reasonably close to the input signal power
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Copyright © S. K. 10
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QMF - Quadrature-Mirror Filter Bank In many applications, a...

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