Theory of Subband Decomposition

Abstract

One of the most practical and successful applications of multirate filters is in video or audio compression using subband coding. Consider an example of audio subband coding shown in Figure 5.1.1. Let us say that one needs to sample the signal at a 10-kHz rate which corresponds to a bandwidth of 5 kHz.* If we need an accuracy of 16 bits, then we need to transmit or store a total of 160 Kb/s. As shown in Figure 5.1.1, in practice, the energy near the cutoff frequency is very small. Hence, we can take the time signal and, using multirate filters, split the signal into two bands, one containing the signal components below 5 kHz and the other band containing the components in the 5 kHz to 10 kHz change. Note that due to downsampling by 2, the total number of samples still remains the same. We can now use 16-bit accuracy for the lower subband with more energy and 8-bit accuracy for the higher band without losing any fidelity, as the high pass band has very little energy. Thus, for this case, we need only a total of 80 Kb/s + 40 Kb/s = 120 Kb/s. Thus, we have achieved, for this example, a compression ratio of 4/3. Of course, one need not be limited to only two subbands. Actually, for speech signals, which need 8 kHz sampling, 16 Kb/s is enough or, on the average 2 bit/sample.