Why do we need filter banks

Signal Theory pp 169-226 | Cite as

Summary

Filter banks are arrangements of low, band and high pass filters with which signals can be spectrally broken down or composed from their spectral components. Figure 7.1 shows an example of this. The input signal is transmitted by means of a Analysis filter bank in M. so-called Subband signals yk(m), each of which contains the information about the input signal in a specific frequency band. In the filter bank shown in Figure 7.1, the sampling rate of the subband signals is reduced by a factor Nk instead of. Because of these Downsampling, which is symbolized in the picture by blocks with arrows pointing downwards, the filter bank is also referred to as a Multirate system. The sampling rate reduction is usually used to reduce the M. Redundancy contained in subband signals to reduce or completely remove. Since only then can one expect a signal x(n) to be able to recover error-free from sub-sampled sub-band signals if the total number of all sub-band samples per unit of time is greater than or equal to the number of input values, one speaks of a sampling rate ratio of μ = (1/ N0 + 1/ N1 + + 1/ NM − 1) = 1 of one critical scanning.

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