From 9852b855db2a65ea6eb5e877411634820214ddf0 Mon Sep 17 00:00:00 2001
From: John Denker <jsd@av8n.com>
Date: Sat, 16 Mar 2024 11:21:23 -0700
Subject: initial setup

---
 src/iir_bp.cxx | 133 +++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 133 insertions(+)
 create mode 100644 src/iir_bp.cxx

(limited to 'src/iir_bp.cxx')

diff --git a/src/iir_bp.cxx b/src/iir_bp.cxx
new file mode 100644
index 0000000..b742dd1
--- /dev/null
+++ b/src/iir_bp.cxx
@@ -0,0 +1,133 @@
+#include "iir_bp.h"
+
+////////////////////////////////////////
+// negative of a vector, component-by-component:
+//
+std::vector<C> neg(const std::vector<C>& foo) {
+  using namespace std;
+  int siz = foo.size();
+  vector<C> rslt(siz);
+  for (int ii = 0; ii < siz; ii++) {
+    rslt[ii] = -foo[ii];
+  }
+  return rslt;
+}
+
+////////////////////////////////////////
+//  expand_poly - multiplies a set of binomials together and returns
+//  the coefficients of the resulting polynomial.
+//
+//  All polynomials (input and output) are represented using the
+//  /reduced/ representation, meaning the coefficient of the highest
+//  power of x is assumed to be 1, and is not included in the
+//  representation.
+//
+//  The multiplication has the following form:
+//
+//  (x+c[0]) * (x+c[1]) *...* (x+c[n-1])
+//
+//  On input, the c[i] is the coefficient of x^0 in the ith binomial.
+//  Each c[i] is a complex number.
+//
+//  The resulting polynomial has the following form:
+//
+//  x^n + a[0]*x^n-1 + a[1]*x^n-2 +...+ a[n-2]*x + a[n-1]
+//
+//  The a[i] coefficients can in general be complex but in typical
+//  digital-filter applications should turn out to be real.
+//
+std::vector<C> expand_poly(const std::vector<C>& cvec) {
+    int n = cvec.size();
+
+    std::vector<C> a(n);
+    for (int ii = 0; ii < n; ii++) a[ii] = 0.;
+
+    for (int i = 0; i < n; ++i) {
+      for (int j = i; j > 0; --j) a[j] += cvec[i] * a[j-1];
+      a[0] += cvec[i];
+    }
+    return a;
+}
+
+////////////////////////////////////////
+// Calculate poles for Butterworth low pass filter.
+//
+std::vector<C> dpole_bwlp (int n, double fcf, double extraPole)
+{
+    using namespace std;
+
+    int needed(n);
+    if (extraPole) needed += 2;
+    vector<C> dpole(needed);
+
+    double theta = 2. * M_PI * fcf;
+    double st = sin(theta);
+    double ct = cos(theta);
+
+    for (int k = 0; k < n; ++k) {
+        // angle, as seen from (1,0)
+        // as we go around the small circlet of poles:
+        double polang = M_PI * (double)(2*k+1)/(double)(2*n);
+        double denom = 1.0 + st*sin(polang);
+        dpole[k] = C(ct/denom, st*cos(polang)/denom);
+    }
+    if (extraPole) {
+      double thetaZero = 2. * M_PI * extraPole;
+      dpole[n]   = C(cos(thetaZero),  sin(thetaZero));
+      dpole[n+1] = C(cos(thetaZero), -sin(thetaZero));
+    }
+    return dpole;
+}
+
+////////////////////////////////////////
+// return the real part of a vector of complex numbers
+// also convert from reduced to non-reduced representation,
+// by inserting rslt[0] = 1 and shifting everything one place
+std::vector<double> rxpoly(const std::vector<C>& foo){
+    std::vector<double> rslt(1+foo.size());
+
+    rslt[0] = 1.;
+    for (unsigned int k = 0; k < foo.size(); ++k)
+       rslt[1+k] = foo[k].real();
+    return (rslt);
+}
+
+
+////////////////////////////////////////
+//  calculate the d coefficients for a butterworth lowpass  filter.
+//
+//  Returns result in the non-reduced representation,
+//  i.e. a vector of n+1 doubles,
+//  where dcof[0] is the coefficient in front of x^n
+//  However, dcof[0] will always be 1.0.
+//
+std::vector<double> dcof_bwlp (int n, double fcf, double extraPole)  {
+    return rxpoly(expand_poly(neg(dpole_bwlp(n, fcf, extraPole))));
+}
+
+////////////////////////////////////////
+//  calculate the c coefficients for a butterworth lowpass filter.
+//  details same as above.
+//
+std::vector<double> ccof_bwlp(const int n, const double extraZero) {
+    return rxpoly(expand_poly(neg(croot_bwlp(n, extraZero))));
+}
+
+////////////////////////////////////////
+std::vector<C> croot_bwlp (int n, double extraZero) {
+    using namespace std;
+
+    int needed(n);
+    if (extraZero) needed += 2;
+    vector<C> dpole(needed);
+
+    for (int k = 0; k < n; ++k)  {
+        dpole[k] = -1;
+    }
+    if (extraZero) {
+      double thetaZero = 2. * M_PI * extraZero;
+      dpole[n]   = C(cos(thetaZero),  sin(thetaZero));
+      dpole[n+1] = C(cos(thetaZero), -sin(thetaZero));
+    }
+    return dpole;
+}
-- 
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