Design IIR Butterworth Filter

Design a digital Butterworth low-pass filter and return its second-order section coefficients, which is the form you actually want for a fixed-point implementation.

Constraints

• Function: [sos, g] = design_butter(order, fc, fs).
• Cutoff is given in Hz along with the sample rate.
• Return second-order sections, not a single high-order transfer function.
• Must reject a cutoff at or above the Nyquist frequency.
• Use butter with the 'sos' output form.
• Report the overall gain separately.