In this presentation, we will show FIR bandpass filters with an unusual spectral variation. We describe why we want that variation and then show how to design and implement it.

We have need for bandpass filters with selectable and different transition bandwidths on its left (lower frequency) and right (higher frequency) sides. Now why would we need that? We need this to build proportional bandwidth filter banks. In such a bank, channel bandwidths are proportional to channel center frequency. This means that the filter above my band has a higher bandwidth with a wider transition bandwidth and the filter below my band has a lower bandwidth and a narrower transition bandwidth.

To obtain a perfect reconstruction filter bank, the transition bandwidths of my band must match the transition bandwidths of the filters below and above my band. Thus, my filter must have a lower transition bandwidth on its lower edge than it has on its upper edge. Can we design a filter to do that? Yes! Why? Ask the hearing aid filter bank designer (or ask me)!

One problem with reduced bandwidth filters with reduced transition bandwidth is they have increased filter length. Increased length means more computational work. We include multirate processing to reduce filter length in the reduced bandwidth filters.