Multiple Static Designs/Coefficient Interpolation

• In this method, we sample the desired multidimensional frequency response, design filters at the sample points, then interpolate between the design locations to get coefficients when running

• Multidimensional Frequency Responses represent the desired frequency response as a function of the desired parameters $\Psi_i$ :
  $$H_{\hbox{\small des}}(\omega,\Psi_1,\dots,\Psi_n)$$

• The sampled response (sampling across $\Psi_i$ ) can be viewed as a multidimensional matrix:
  $$H[k,m_1,\ldots,m_n] = H_{\hbox{\small des}}(\omega_k,m_1\Delta_1,\dots,m_n\Delta_n)$$
  where, e.g., $n_i\Delta_i=\Psi_i^{\mbox{\small max}}$ .