smart_signal_processing 2.0.3

Provides useful functions for signal processing such as Fast Fourier Transform, windowing (apodization), variance/standard deviation and others.

example/example.dart

// Copyright (c) 2019, Dr. Bruno Guigas. All rights reserved. Use of this source
// code is governed by a BSD-style license that can be found in the LICENSE file.
import 'package:smart_signal_processing/smart_signal_processing.dart';
import 'dart:typed_data';
import 'dart:math' as math;

/// Signal processing example:
/// - Computes 8 periods of a cosine shape filling an array of 256 points.
/// - Applies an exponential function, resulting in a decaying oscillation
/// - Applies a real Fourier transform, resulting in a complex-valued line shape
///   whose real part is an absorption mode Lorentzian, and whose imaginary
///   part is a dispersion mode Lorentzian. The real part's maximum is at
///   index 8, corresponding to the number of periods.
/// Paste the printed output into MS Excel, OpenOffice calc, Google tables or
/// similar to view result as a curve.
main() {
  // Generate sine wave consisting of [npoints] with [amplitude] and [phase],
  // and [nperiods] periods within [npoints]. Make the sine "noisy" by adding
  // [noise] a fraction of [amplitude].
  Float64List genSine(
      int npoints, double amplitude, double phase, int nperiods, double noise) {
    math.Random rand = math.Random();
    double xmax = 2 * math.pi * nperiods, x, y;
    Float64List sine = new Float64List(npoints);
    for (int i = 0; i < npoints; i++) {
      x = (i * xmax) / npoints;
      y = amplitude * math.sin(x + phase);
      // add noise between -1 and 1
      sine[i] = y + noise * amplitude * (2 * rand.nextDouble() - 1.0).sign;
    }
    return sine;
  }

  // Generate cosine
  final int NPOINTS = 256, NPERIODS = 8;
  Float64List reals = genSine(NPOINTS, 100.0, math.pi / 2, NPERIODS, 0.0);
  Float64List imags = Float64List(reals.length);

  // Make cosine exponentially decaying
  double decayFactor = -3.0 / (reals.length - 1);
  WinFunc.expMult(reals, decayFactor, false, "0");

  // In-place transform: initally [imags] has only zeroes. After transform,
  // [reals] contains absorption mode and [imags] dispersion mode Lorentzian shape.
  FFT.transform(reals, imags);

  // Print result: Due to the symmetry properties of the FFT only the first
  // halfs play a role. The second halfs contain identical information
  // (corresonding to "negative frequencies")
  for (int i = 0; i < reals.length ~/ 2; i++) {
    print("$i\t ${reals[i].toStringAsFixed(2)}");
  }
  for (int i = 0; i < imags.length ~/ 2; i++) {
    print("$i\t ${imags[i].toStringAsFixed(2)}");
  }
}