I would like to implement a filter in the time domain based on a desired frequency response that changes over time. The initial goal is a bandpass filter with a time-varying center frequency, where the bandpass filter has a shape that is defined in the frequency domain. I will illustrate with a simple example.
Here we have 2 gaussians, one centered at 1000Hz and the second centered at 8000Hz. I would like to design a filter in the time domain that can perform a linear sweep between these 2 center frequencies for some fixed duration.
Another way of stating this is that I would like to be able to do the following:
- Define a shape for a bandpass filter in the frequency domain for timepoints 1 and 2
- Define the morph between the filter shapes at the 2 timepoints (in the example the shape is constant and it is only center frequency that varies)
- Given that desired frequency domain information and a duration, I want to design a time-varying time domain filter.
I understand that the resulting filter will have time-varying coefficients. It is okay if the frequency response does not exactly match what I have outlined in the frequency domain as long as it is close.
I am looking for strategies to approach this type of problem, although if the solutions are highly dependent on the shape of the filter in the frequency domain, then a strategy to solve the provided example would be a helpful starting point.