feat: add iir high-pass design routine

pasada-lib/include/pd_signal.h

@@ -7,8 +7,11 @@
 
 #include <vector>
 #include <deque>
+#include <complex>
 
 namespace pd_signal {
+    using cplx = std::complex<double>;
+
     /** `num` evenly spaced numbers over interval [start,stop] */
     void linspace(std::vector<double>& data, double start, double stop, int num);
     /** `num` evenly spaced numbers over interval [start,stop] with endpoint=true or [start,stop) with endpoint=false */
@@ -37,6 +40,34 @@ namespace pd_signal {
     /** two-dimensional mean of a collection of signals */
     void mean(std::vector<double> &out, std::deque<std::vector<double> >& m);
 
+    /**
+     * Convolution of two polynomials given in ASCENDING power order.
+     * If <c>p = p_0 + p_1 x + ... + p_{P-1} x^{P-1}</c> and likewise for q,
+     * then <c>out = p * q</c> in ascending power order, of length P+Q-1.
+     */
+    void polymul(std::vector<cplx>& out,
+                 const std::vector<cplx>& p, const std::vector<cplx>& q);
+
+    /**
+     * Build a monic polynomial from its roots:
+     * <c>(x - r_0) (x - r_1) ... (x - r_{N-1})</c>.
+     * Returned in DESCENDING power order, i.e. <c>out[0]=1, ..., out[N]</c>
+     * is the constant term. Length is <c>roots.size() + 1</c>.
+     */
+    void poly(std::vector<cplx>& out, const std::vector<cplx>& roots);
+
+    /**
+     * Design an N-th order Butterworth IIR high-pass digital filter via the
+     * bilinear transform. The passband is normalized to unit gain at Nyquist.
+     *
+     * @param b  numerator coefficients in DESCENDING powers of z (length N+1)
+     * @param a  denominator coefficients in DESCENDING powers of z (length N+1)
+     * @param N  filter order (>= 1)
+     * @param fc cutoff frequency of the digital filter in Hz (0 < fc < fs/2)
+     * @param fs sampling frequency in Hz
+     */
+    void iirHighpass(std::vector<double>& b, std::vector<double>& a,
+                     int N, double fc, double fs);
 }
 
 #endif //PASADASUPERPROJECT_SIGNAL_H