TABLE OF CONTENTS The cosine-modulated filter banks are an attractive choice for the design and implementation of filter banks with a large number of sub-bands. Their main features are:
Simple design procedure, consisting of generating a lowpass prototype whose impulse response satisfies some constraints required to achieve perfect reconstruction.
Low cost of implementation measured in terms of multiplication count, since the resulting analysis and synthesis filter banks rely on a type of DCT, which is amenable to fast implementation and can share the prototype implementation cost with each sub-filter.
In the cosine-modulated filter bank design, we begin by finding a linear-phase prototype lowpass filter H( z) of order N, with passband edge ? p = ( 
- ?) and stopband edge ? r = ( 
+ ?), where 2 ? is the width of the transition band. For convenience, we assume that the length N + 1 is an even multiple of the number M of sub-bands, that is, N = (2 LM - 1). Although the actual length of the prototype can be arbitrary, this assumption greatly simplifies our analysis. [3]
Given the prototype filter, we can generate cosine-modulated versions of it in order to obtain the analysis and synthesis filter banks as follows:
| (9.79) |  |
| (9.80) |  |
for n = 0, ..., N and m = 0, ..., M - 1, with N = (2 LM -...
