Optimal Chebyshev FIR filters

1. What is optimal FIR filter?
2. Is a Chebyshev filter a FIR filter?
3. Are FIR filters always Bibo stable?
4. How do you normalize FIR filter coefficients?

What is optimal FIR filter?

The function designs optimal FIR filters in the least-Pth sense. However the filter is not constrained to have linear-phase, that is, the impulse response has no special symmetry properties. However, the linear-phase constraint also results in filters with larger order than the more general nonlinear-phase designs.

Is a Chebyshev filter a FIR filter?

Both the windowed-sinc and the Chebyshev filters are designed to separate one band of frequencies from another. The windowed-sinc is an FIR filter implemented by convolution, while the Chebyshev is an IIR filter carried out by recursion.

Are FIR filters always Bibo stable?

g) BIBO stability for FIR filters: From f), it immediately follows that FIR filters are always BIBO stable (if |h(t)| < ∞ for all t). This is also reflected in the fact that all the poles of an FIR filter are at z=0 (inside the unit circle), which implies stability.

How do you normalize FIR filter coefficients?

The coefficients are then normalized by dividing by the sum of the coefficients themselves. This is done in order to have a DC gain equal to 1 (0 dB). At this point the FIR filter is a low pass filter. By negating every other coefficient, the FIR filter becomes a high pass filter.