I want to apply some nonlinear processing to a signal, namely: I want to implement a tube emulation which adds warmth/harmonic distortion to a digital audio signal. I am worried about aliasing, so I figured out the following processing sequence:
- Upsampling of the sample rate from $f_s$ to $2 \cdot f_s$
- Applying an interpolation lowpass filter with $f_g = 0.5 f_s$ and a passband gain of $2$
- Applying the nonlinear processing to the upsampled signal
- Again applying a filter with with $f_g = 0.5 f_s$
- Decimation back to $fs$.
My question arises at point 2, the interpolation filter. If I google this topic, it results in fascinating concepts like Lagrange interpolation, spline interpolation and polynominal interpolation and the math behind those seem far from trivial. Moreover, I don't understand why this is even needed - what is the reason why one would utilize one of those concepts rather than just running the signal through a run-off-the-mill IIR with sufficient stopband attenuation? The only thing I can understand is why the passband gain needs to be non-unity.
Also, although not main point of my question, feel free to point out any logical flaws that might be in my processing sequence. Thank you!