Filterbanks are configurations of digital filters that process signals by separating them into multiple frequency subbands or reconstructing them back into a single broadband signal. They form the backbone of modern Digital Signal Processing (DSP) architectures, driving technologies like audio compression (MP3/AAC), speech recognition, and wavelet transforms. 1. The Analysis Filterbank (Signal Decomposition)
The analysis bank acts as a signal channelizer. It takes a single broadband input signal,
, and passes it through an array of parallel bandpass filters (
Frequency Splitting: The first filter H₀(z) is typically a lowpass prototype filter. The remaining filters are modulated, higher-frequency versions that cover adjacent parts of the spectrum.
Downsampling (Decimation): Because each subband now occupies only a fraction of the original bandwidth, the sample rate can be reduced. The filtered signals are downsampled by a factor of M (retaining every M-th sample).
Critical Subsampling: If the downsampling factor matches the number of channels (M), the filterbank is maximally decimated. This ensures the total number of subband samples equals the number of original signal samples, maximizing storage and transmission efficiency. 2. The Synthesis Filterbank (Signal Reconstruction)
The synthesis bank reverses the analysis process to reconstruct the original signal. It accepts the processed subband signals and merges them back into a unified broadband output,
Upsampling (Expansion): The subband signals are first upsampled by inserting M-1 zeros between each existing sample to restore the original sample rate.
Interpolation Filtering: The expanded signals pass through synthesis filters (
). These filters eliminate the unwanted imaging artifacts introduced by upsampling.
Summation: The outputs of all synthesis filters are summed together to create the final reconstructed signal. 3. The Resolution Trade-off (Time vs. Frequency) Filter Bank – an overview | ScienceDirect Topics
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