QMF - In many applications, a discrete-time signal x[n] is...

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1 Copyright © S. K. Mitra • 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 ]
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2 Copyright © S. K. Mitra • 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
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3 Copyright © S. K. Mitra
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4 Copyright © S. K. Mitra • 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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5 Copyright © S. K. Mitra
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6 Copyright © S. K. Mitra • Figure below shows the basic two-channel QMF bank-based subband codec ( coder/ decoder )
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7 Copyright © S. K. Mitra • The analysis filters and have typically a lowpass and highpass frequency responses, respectively, with a cutoff at Q /2
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8 Copyright © S. K. Mitra • 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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9 Copyright © S. K. Mitra • 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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10 Copyright © S. K. Mitra • In practice, various errors are generated in this scheme • In addition to the coding error and errors caused by transmission of the coded signals through the channel, the QMF bank itself introduces several errors due to the sampling rate alterations and imperfect filters • We ignore the coding and the channel errors
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11 Copyright © S. K. Mitra • We investigate only the errors caused by the sampling rate alterations and their effects on the performance of the system • To this end, we consider the QMF bank structure without the coders and the decoders as shown below
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12 Copyright © S. K. Mitra • Making use of the input-output relations of the down-sampler and the up-sampler in the z -domain we arrive at k = 0, 1 ^
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13 Copyright © S. K. Mitra • From the first and the last equations we obtain after some algebra • The reconstructed output of the filter bank is given by ^ ^ ^
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14 Copyright © S. K. Mitra
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Copyright © S. K. Mitra
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This note was uploaded on 02/19/2012 for the course ECE 538 taught by Professor Zoltolski during the Fall '08 term at Purdue University-West Lafayette.

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QMF - In many applications, a discrete-time signal x[n] is...

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