are excited by the signal under analysis. Multirate filter bank A multirate filter bank divides a signal into a number of subbands, which can be analysed at different rates corresponding to the bandwidth of the frequency bands. The implementation makes use of downsampling (decimation) and upsampling (expansion). See and for additional insight into the effects of those operations in the transform domains. Narrow lowpass filter One can define a narrow lowpass filter as a lowpass filter with a narrow passband. In order to create a multirate narrow lowpass FIR filter, one can replace the time-invariant FIR filter with a lowpass antialiasing filter and a decimator, along with an interpolator and lowpass anti-imaging filter. In this way, the resulting multirate system is a time-varying linear-phase filter via the decimator and interpolator. The lowpass filter consists of two polyphase filters, one for the decimator and one for the interpolator. A filter bank divides the input signal into a set of signals . In this way each of the generated signals corresponds to a different region in the spectrum of . In this process it can be possible for the regions overlap (or not, based on application). The generated signals can be generated via a collection of set of bandpass filters with bandwidths and center frequencies (respectively). A multirate filter bank uses a single input signal and then produces multiple outputs of the signal by filtering and subsampling. In order to split the input signal into two or more signals, an analysis-synthesis system can be used. The signal would split with the help of four filters for k =0,1,2,3 into 4 bands of the same bandwidths (In the analysis bank) and then each sub-signal is decimated by a factor of 4. In each band by dividing the signal in each band, we would have different signal characteristics. In synthesis section the filter will reconstruct the original signal: First, upsampling the 4 sub-signals at the output of the processing unit by a factor of 4 and then filter by 4 synthesis filters for k = 0,1,2,3. Finally, the outputs of these four filters are added. Statistically optimized filter bank (Eigen filter bank) A discrete-time filter bank framework allows inclusion of desired input signal dependent features in the design in addition to the more traditional perfect reconstruction property. The information theoretic features like maximized energy compaction, perfect de-correlation of sub-band signals and other characteristics for