analog_filters.hpp

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// toolboxes/signal/include/nk/signal/filter_design/analog_filters.hpp
//
// Analog filter prototypes + lowpass-to-X frequency transformations +
// bilinear z-transform + analog freq response. Together these form the
// machinery underneath cheby1 / cheby2 / ellip / besself; the
// top-level filters compose prototype → lp2X → bilinear.
 
#pragma once
 
#include <memory_resource>
#include <nk/value/value.hpp>
 
#include <tuple>
 
namespace nk::signal {

 
 
// ─────────────────────────────────────────────────────────────────────
// Analog lowpass prototypes (cutoff Ω = 1 rad/s)
//
// Each returns (z, p, k) — zeros, poles, gain. `z` may be empty
// (all-pole filters); `p` is always a COMPLEX column vector; `k` is a
// real DOUBLE scalar.
// ─────────────────────────────────────────────────────────────────────

std::tuple<Value, Value, Value>
buttap(int N, std::pmr::memory_resource *mr = nullptr);

std::tuple<Value, Value, Value>
cheb1ap(int N, double Rp, std::pmr::memory_resource *mr = nullptr);

std::tuple<Value, Value, Value>
cheb2ap(int N, double Rs, std::pmr::memory_resource *mr = nullptr);

std::tuple<Value, Value, Value>
besselap(int N, std::pmr::memory_resource *mr = nullptr);

std::tuple<Value, Value, Value>
ellipap(int N, double Rp, double Rs, std::pmr::memory_resource *mr = nullptr);
 
// ─────────────────────────────────────────────────────────────────────
// Lowpass → X frequency transformations on (z, p, k)
// ─────────────────────────────────────────────────────────────────────

std::tuple<Value, Value, Value>
lp2lp(const Value &                z,
      const Value &                p,
      double                       k,
      double                       Wo,
      std::pmr::memory_resource *  mr = nullptr);

std::tuple<Value, Value, Value>
lp2hp(const Value &                z,
      const Value &                p,
      double                       k,
      double                       Wo,
      std::pmr::memory_resource *  mr = nullptr);

std::tuple<Value, Value, Value>
lp2bp(const Value &                z,
      const Value &                p,
      double                       k,
      double                       Wo,
      double                       Bw,
      std::pmr::memory_resource *  mr = nullptr);

std::tuple<Value, Value, Value>
lp2bs(const Value &z, const Value &p, double k,
      double Wo, double Bw,
      std::pmr::memory_resource *mr = nullptr);
 
// ─────────────────────────────────────────────────────────────────────
// Analog → digital
// ─────────────────────────────────────────────────────────────────────

std::tuple<Value, Value>
bilinear(const Value &                b,
         const Value &                a,
         double                       fs,
         double                       fp = 0.0,
         std::pmr::memory_resource *  mr = nullptr);

std::tuple<Value, Value>
impinvar(const Value &                b,
         const Value &                a,
         double                       fs,
         double                       tol = 1e-3,
         std::pmr::memory_resource *  mr  = nullptr);

Value freqs(const Value &                b,
            const Value &                a,
            const Value &                w,
            std::pmr::memory_resource *  mr = nullptr);
 

} // namespace nk::signal