examples/fftw3_example.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# fftw3_example\n",
    "\n",
    "Discrete Fourier transform (DFT) is a widely-used approach of frequency analysis.\n",
    "DFT is defined by\n",
    "\n",
    "$$z_k = \\frac{1}{N} \\sum^{N-1}_{t=0} x_t \\exp\\left( - \\mathrm{i} \\frac{2 \\pi k t}{N} \\right)$$\n",
    "\n",
    "where $N$ is the number of samples,\n",
    "$x_t \\in \\mathbb{C}$ ($t=0,\\dots,N-1$) is a series of time-domain samples, and\n",
    "$z_k \\in \\mathbb{C}$ ($k=0,\\dots,N-1$) is a series of frequency-domain points.\n",
    "The index $k$ is corresponds to frequency $f_k = f_s k / N$ where $f_s$ is a sample rate,\n",
    "and absolute value $|z_k|$ is amplitude of $f_k$.\n",
    "\n",
    "Fast Fourier transform (FFT) is a set of algorithms for efficient computation of DFT.\n",
    "[FFTW3](http://www.fftw.org/) is a major FFT library faster than similar libraries.\n",
    "We show a simple example of [fftw3-ocaml](https://github.com/Chris00/fftw-ocaml), a binding to FFTW3."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/opam/.opam/4.04.1/lib/ocaml/unix.cma: loaded\n",
      "/home/opam/.opam/4.04.1/lib/ocaml/bigarray.cma: loaded\n",
      "/home/opam/.opam/4.04.1/lib/fftw3: added to search path\n",
      "/home/opam/.opam/4.04.1/lib/fftw3/fftw3.cma: loaded\n",
      "/home/opam/.opam/4.04.1/lib/easy-format: added to search path\n",
      "/home/opam/.opam/4.04.1/lib/easy-format/easy_format.cmo: loaded\n",
      "/home/opam/.opam/4.04.1/lib/biniou: added to search path\n",
      "/home/opam/.opam/4.04.1/lib/biniou/biniou.cma: loaded\n",
      "/home/opam/.opam/4.04.1/lib/yojson: added to search path\n",
      "/home/opam/.opam/4.04.1/lib/yojson/yojson.cmo: loaded\n",
      "/home/opam/.opam/4.04.1/lib/ocaml/str.cma: loaded\n",
      "/home/opam/.opam/4.04.1/lib/atd: added to search path\n",
      "/home/opam/.opam/4.04.1/lib/atd/atd.cma: loaded\n",
      "/home/opam/.opam/4.04.1/lib/atdgen: added to search path\n",
      "/home/opam/.opam/4.04.1/lib/atdgen/atdgen.cma: loaded\n",
      "/home/opam/.opam/4.04.1/lib/bytes: added to search path\n",
      "/home/opam/.opam/4.04.1/lib/result: added to search path\n",
      "/home/opam/.opam/4.04.1/lib/result/result.cma: loaded\n",
      "/home/opam/.opam/4.04.1/lib/lwt: added to search path\n",
      "/home/opam/.opam/4.04.1/lib/lwt/lwt.cma: loaded\n",
      "/home/opam/.opam/4.04.1/lib/lwt/lwt-log.cma: loaded\n",
      "/home/opam/.opam/4.04.1/lib/lwt/lwt-unix.cma: loaded\n",
      "/home/opam/.opam/4.04.1/lib/ctypes: added to search path\n",
      "/home/opam/.opam/4.04.1/lib/ctypes/ctypes.cma: loaded\n",
      "/home/opam/.opam/4.04.1/lib/ctypes/ctypes-top.cma: loaded\n",
      "/home/opam/.opam/4.04.1/lib/ctypes/ctypes-foreign-base.cma: loaded\n",
      "/home/opam/.opam/4.04.1/lib/ctypes/ctypes-foreign-unthreaded.cma: loaded\n",
      "/home/opam/.opam/4.04.1/lib/iocaml-kernel: added to search path\n",
      "/home/opam/.opam/4.04.1/lib/iocaml-kernel/iocaml_lib.cma: loaded\n",
      "/home/opam/.opam/4.04.1/lib/cairo2: added to search path\n",
      "/home/opam/.opam/4.04.1/lib/cairo2/cairo2.cma: loaded\n",
      "/home/opam/.opam/4.04.1/lib/ocaml/dynlink.cma: loaded\n",
      "/home/opam/.opam/4.04.1/lib/ocaml/camlp4: added to search path\n",
      "/home/opam/.opam/4.04.1/lib/archimedes: added to search path\n",
      "/home/opam/.opam/4.04.1/lib/archimedes/archimedes_internals.cma: loaded\n",
      "/home/opam/.opam/4.04.1/lib/archimedes/archimedes_toploop.cma: loaded\n",
      "Module Archimedes loaded and aliased as A.\n",
      "/home/opam/.opam/4.04.1/lib/archimedes/archimedes_cairo.cma: loaded\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "module Archimedes_iocaml : sig  end\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"color:slategray;max-height:100px;overflow:hidden\" \n",
       "onclick=\"\n",
       "if (this.style.maxHeight === 'none') \n",
       "    this.style.maxHeight = '100px';\n",
       "else\n",
       "    this.style.maxHeight = 'none'; \n",
       "\">module FFT = Fftw3.D\n",
       "</pre>"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#require \"fftw3\" ;;\n",
    "#use \"archimedes_iocaml.ml\" ;;\n",
    "open Bigarray ;;\n",
    "module FFT = Fftw3.D ;;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<pre style=\"color:slategray;max-height:100px;overflow:hidden\" \n",
       "onclick=\"\n",
       "if (this.style.maxHeight === 'none') \n",
       "    this.style.maxHeight = '100px';\n",
       "else\n",
       "    this.style.maxHeight = 'none'; \n",
       "\">val pi : float = 3.14159265358979\n",
       "</pre>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"color:slategray;max-height:100px;overflow:hidden\" \n",
       "onclick=\"\n",
       "if (this.style.maxHeight === 'none') \n",
       "    this.style.maxHeight = '100px';\n",
       "else\n",
       "    this.style.maxHeight = 'none'; \n",
       "\">val n : int = 1000\n",
       "</pre>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"color:slategray;max-height:100px;overflow:hidden\" \n",
       "onclick=\"\n",
       "if (this.style.maxHeight === 'none') \n",
       "    this.style.maxHeight = '100px';\n",
       "else\n",
       "    this.style.maxHeight = 'none'; \n",
       "\">val sample_rate : int = 100\n",
       "</pre>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"color:slategray;max-height:100px;overflow:hidden\" \n",
       "onclick=\"\n",
       "if (this.style.maxHeight === 'none') \n",
       "    this.style.maxHeight = '100px';\n",
       "else\n",
       "    this.style.maxHeight = 'none'; \n",
       "\">val xdata : (Complex.t, FFT.complex_elt, Bigarray.c_layout) Bigarray.Array1.t =\n",
       "  &lt;abstr&gt;\n",
       "</pre>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"color:slategray;max-height:100px;overflow:hidden\" \n",
       "onclick=\"\n",
       "if (this.style.maxHeight === 'none') \n",
       "    this.style.maxHeight = '100px';\n",
       "else\n",
       "    this.style.maxHeight = 'none'; \n",
       "\">val ydata : (Complex.t, FFT.complex_elt, Bigarray.c_layout) Bigarray.Array1.t =\n",
       "  &lt;abstr&gt;\n",
       "</pre>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"color:slategray;max-height:100px;overflow:hidden\" \n",
       "onclick=\"\n",
       "if (this.style.maxHeight === 'none') \n",
       "    this.style.maxHeight = '100px';\n",
       "else\n",
       "    this.style.maxHeight = 'none'; \n",
       "\">val plan : Fftw3.D.c2c Fftw3.D.plan = &lt;abstr&gt;\n",
       "</pre>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "let pi = 3.14159265358979 ;;\n",
    "let n = 1000 ;; (* # of samples *)\n",
    "\n",
    "let xdata = Array1.create FFT.complex C_layout n ;; (* source memory for time-domain data *)\n",
    "let ydata = Array1.create FFT.complex C_layout n ;; (* destination memory for frequency-domain data *)\n",
    "let plan = FFT.Array1.dft FFT.Forward xdata ydata ;; (* FFTW3 plan *)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1. Time-domain input data\n",
    "\n",
    "This example shows the FFT of the [hamming window](https://en.wikipedia.org/wiki/Window_function#Hamming_window) given by\n",
    "\n",
    "$$w(x) = 0.54 - 0.46 \\cos(2 \\pi x).$$\n",
    "\n",
    "We append zeros at the beginning and the end of the signal for simulation of masking by the window function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<pre style=\"color:slategray;max-height:100px;overflow:hidden\" \n",
       "onclick=\"\n",
       "if (this.style.maxHeight === 'none') \n",
       "    this.style.maxHeight = '100px';\n",
       "else\n",
       "    this.style.maxHeight = 'none'; \n",
       "\">- : unit = ()\n",
       "</pre>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "let min = n / 10 in\n",
    "let max = n - min in\n",
    "for i = 0 to n - 1 do\n",
    "  if min <= i && i <= max then begin\n",
    "    let x = float (i - min) /. float (max - min) in\n",
    "    let y = 0.54 -. 0.46 *. cos (2.0 *. pi *. x) in  (* the hamming window between `min` and `max` *)\n",
    "    xdata.{i} <- Complex.({ re = y; im = 0.0; })\n",
    "  end else begin\n",
    "    xdata.{i} <- Complex.zero\n",
    "  end\n",
    "done"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
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"
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"color:slategray;max-height:100px;overflow:hidden\" \n",
       "onclick=\"\n",
       "if (this.style.maxHeight === 'none') \n",
       "    this.style.maxHeight = '100px';\n",
       "else\n",
       "    this.style.maxHeight = 'none'; \n",
       "\">- : unit = ()\n",
       "</pre>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "let vp = A.init ~w:600. ~h:300. [\"iocaml\"] in\n",
    "A.Axes.box vp ;\n",
    "A.Viewport.title vp \"Time domain\" ;\n",
    "A.Viewport.ylabel vp \"Amplitude\" ;\n",
    "A.Viewport.yrange vp 0.0 1.0 ;\n",
    "A.set_color vp A.Color.red ;\n",
    "A.Array.y vp ~style:`Lines (Array.init n (fun i -> xdata.{i}.Complex.re)) ;\n",
    "A.close vp"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2. Frequency-domain series"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<pre style=\"color:slategray;max-height:100px;overflow:hidden\" \n",
       "onclick=\"\n",
       "if (this.style.maxHeight === 'none') \n",
       "    this.style.maxHeight = '100px';\n",
       "else\n",
       "    this.style.maxHeight = 'none'; \n",
       "\">- : unit = ()\n",
       "</pre>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "FFT.exec plan ;; (* Execute FFT *)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"color:slategray;max-height:100px;overflow:hidden\" \n",
       "onclick=\"\n",
       "if (this.style.maxHeight === 'none') \n",
       "    this.style.maxHeight = '100px';\n",
       "else\n",
       "    this.style.maxHeight = 'none'; \n",
       "\">- : unit = ()\n",
       "</pre>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "let spectrum = Array.init (n / 2) (fun i -> 10. *. log10 (Complex.norm2 ydata.{i})) in\n",
    "\n",
    "let vp = A.init ~w:600. ~h:300. [\"iocaml\"] in\n",
    "A.Axes.box vp ;\n",
    "A.Viewport.title vp \"Frequency domain\" ;\n",
    "A.Viewport.ylabel vp \"Magnitude (dB)\" ;\n",
    "A.set_color vp A.Color.red ;\n",
    "A.Array.y vp ~style:`Lines spectrum ;\n",
    "A.close vp"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "OCaml 4.04.1",
   "language": "ocaml",
   "name": "iocaml-kernel"
  },
  "language_info": {
   "name": "ocaml",
   "version": "4.1.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}