Haasoscope

package com.felhr.serialportexample;

/******************************************************************************
 *  Compilation:  javac FFT.java
 *  Execution:    java FFT n
 *  Dependencies: Complex.java
 *
 *  Compute the FFT and inverse FFT of a length n complex sequence
 *  using the radix 2 Cooley-Tukey algorithm.

 *  Bare bones implementation that runs in O(n log n) time. Our goal
 *  is to optimize the clarity of the code, rather than performance.
 *
 *  Limitations
 *  -----------
 *   -  assumes n is a power of 2
 *
 *   -  not the most memory efficient algorithm (because it uses
 *      an object type for representing complex numbers and because
 *      it re-allocates memory for the subarray, instead of doing
 *      in-place or reusing a single temporary array)
 *
 *  For an in-place radix 2 Cooley-Tukey FFT, see
 *  https://introcs.cs.princeton.edu/java/97data/InplaceFFT.java.html
 *
 ******************************************************************************/

public class FFT {

    class FFTresult{
        public FFTresult(double[] absSignal, int mPeakPos, double mMaxFFTSample) {
            this.absSignal = absSignal;
            this.mPeakPos = mPeakPos;
            this.mMaxFFTSample = mMaxFFTSample;
        }
        public double[] absSignal;
        public int mPeakPos;
        public double mMaxFFTSample;
    }

    public FFTresult calculateFFT(double[] signal) {
        int mNumberOfFFTPoints = signal.length;
        double mMaxFFTSample;
        double temp;
        Complex[] y;
        Complex[] complexSignal = new Complex[mNumberOfFFTPoints];
        double[] absSignal = new double[mNumberOfFFTPoints/2];

        for(int i = 0; i < mNumberOfFFTPoints; i++){
            //temp = (double)((signal[2*i] & 0xFF) | (signal[2*i+1] << 8)) / 32768.0F;
            complexSignal[i] = new Complex(signal[i],0.0);
        }

        y = FFT.fft(complexSignal); // --> Here I use FFT class

        mMaxFFTSample = 0.0;
        int mPeakPos = 0;
        for(int i = 0; i < (mNumberOfFFTPoints/2); i++)
        {
            absSignal[i] = Math.sqrt(Math.pow(y[i].re(), 2) + Math.pow(y[i].im(), 2));
            if(i>0 && i<absSignal.length/2 && absSignal[i] > mMaxFFTSample) // ignore DC component
            {
                mMaxFFTSample = absSignal[i];
                mPeakPos = i;
            }
        }

        return new FFTresult(absSignal, mPeakPos, mMaxFFTSample);
    }

    // compute the FFT of x[], assuming its length is a power of 2
    public static Complex[] fft(Complex[] x) {
        int n = x.length;

        // base case
        if (n == 1) return new Complex[] { x[0] };

        // radix 2 Cooley-Tukey FFT
        if (n % 2 != 0) {
            throw new IllegalArgumentException("n is not a power of 2");
        }

        // fft of even terms
        Complex[] even = new Complex[n/2];
        for (int k = 0; k < n/2; k++) {
            even[k] = x[2*k];
        }
        Complex[] q = fft(even);

        // fft of odd terms
        Complex[] odd  = even;  // reuse the array
        for (int k = 0; k < n/2; k++) {
            odd[k] = x[2*k + 1];
        }
        Complex[] r = fft(odd);

        // combine
        Complex[] y = new Complex[n];
        for (int k = 0; k < n/2; k++) {
            double kth = -2 * k * Math.PI / n;
            Complex wk = new Complex(Math.cos(kth), Math.sin(kth));
            y[k]       = q[k].plus(wk.times(r[k]));
            y[k + n/2] = q[k].minus(wk.times(r[k]));
        }
        return y;
    }

    // compute the inverse FFT of x[], assuming its length is a power of 2
    public static Complex[] ifft(Complex[] x) {
        int n = x.length;
        Complex[] y = new Complex[n];

        // take conjugate
        for (int i = 0; i < n; i++) {
            y[i] = x[i].conjugate();
        }

        // compute forward FFT
        y = fft(y);

        // take conjugate again
        for (int i = 0; i < n; i++) {
            y[i] = y[i].conjugate();
        }

        // divide by n
        for (int i = 0; i < n; i++) {
            y[i] = y[i].scale(1.0 / n);
        }

        return y;

    }

    // compute the circular convolution of x and y
    public static Complex[] cconvolve(Complex[] x, Complex[] y) {

        // should probably pad x and y with 0s so that they have same length
        // and are powers of 2
        if (x.length != y.length) {
            throw new IllegalArgumentException("Dimensions don't agree");
        }

        int n = x.length;

        // compute FFT of each sequence
        Complex[] a = fft(x);
        Complex[] b = fft(y);

        // point-wise multiply
        Complex[] c = new Complex[n];
        for (int i = 0; i < n; i++) {
            c[i] = a[i].times(b[i]);
        }

        // compute inverse FFT
        return ifft(c);
    }

    // compute the linear convolution of x and y
    public static Complex[] convolve(Complex[] x, Complex[] y) {
        Complex ZERO = new Complex(0, 0);

        Complex[] a = new Complex[2 * x.length];
        for (int i = 0; i < x.length; i++) a[i] = x[i];
        for (int i = x.length; i < 2 * x.length; i++) a[i] = ZERO;

        Complex[] b = new Complex[2 * y.length];
        for (int i = 0; i < y.length; i++) b[i] = y[i];
        for (int i = y.length; i < 2 * y.length; i++) b[i] = ZERO;

        return cconvolve(a, b);
    }
}


/*
 *  Data type for complex numbers.
 *
 *  The data type is "immutable" so once you create and initialize
 *  a Complex object, you cannot change it. The "final" keyword
 *  when declaring re and im enforces this rule, making it a
 *  compile-time error to change the .re or .im instance variables after
 *  they've been initialized.
 *
 *  % java Complex
 *  a            = 5.0 + 6.0i
 *  b            = -3.0 + 4.0i
 *  Re(a)        = 5.0
 *  Im(a)        = 6.0
 *  b + a        = 2.0 + 10.0i
 *  a - b        = 8.0 + 2.0i
 *  a * b        = -39.0 + 2.0i
 *  b * a        = -39.0 + 2.0i
 *  a / b        = 0.36 - 1.52i
 *  (a / b) * b  = 5.0 + 6.0i
 *  conj(a)      = 5.0 - 6.0i
 *  |a|          = 7.810249675906654
 *  tan(a)       = -6.685231390246571E-6 + 1.0000103108981198i
 *
*/

class Complex {
    private final double re;   // the real part
    private final double im;   // the imaginary part

    // create a new object with the given real and imaginary parts
    public Complex(double real, double imag) {
        re = real;
        im = imag;
    }

    // return a string representation of the invoking Complex object
    public String toString() {
        if (im == 0) return re + "";
        if (re == 0) return im + "i";
        if (im <  0) return re + " - " + (-im) + "i";
        return re + " + " + im + "i";
    }

    // return abs/modulus/magnitude
    public double abs() {
        return Math.hypot(re, im);
    }

    // return angle/phase/argument, normalized to be between -pi and pi
    public double phase() {
        return Math.atan2(im, re);
    }

    // return a new Complex object whose value is (this + b)
    public Complex plus(Complex b) {
        Complex a = this;             // invoking object
        double real = a.re + b.re;
        double imag = a.im + b.im;
        return new Complex(real, imag);
    }

    // return a new Complex object whose value is (this - b)
    public Complex minus(Complex b) {
        Complex a = this;
        double real = a.re - b.re;
        double imag = a.im - b.im;
        return new Complex(real, imag);
    }

    // return a new Complex object whose value is (this * b)
    public Complex times(Complex b) {
        Complex a = this;
        double real = a.re * b.re - a.im * b.im;
        double imag = a.re * b.im + a.im * b.re;
        return new Complex(real, imag);
    }

    // return a new object whose value is (this * alpha)
    public Complex scale(double alpha) {
        return new Complex(alpha * re, alpha * im);
    }

    // return a new Complex object whose value is the conjugate of this
    public Complex conjugate() {
        return new Complex(re, -im);
    }

    // return a new Complex object whose value is the reciprocal of this
    public Complex reciprocal() {
        double scale = re*re + im*im;
        return new Complex(re / scale, -im / scale);
    }

    // return the real or imaginary part
    public double re() { return re; }
    public double im() { return im; }

    // return a / b
    public Complex divides(Complex b) {
        Complex a = this;
        return a.times(b.reciprocal());
    }

    // return a new Complex object whose value is the complex exponential of this
    public Complex exp() {
        return new Complex(Math.exp(re) * Math.cos(im), Math.exp(re) * Math.sin(im));
    }

    // return a new Complex object whose value is the complex sine of this
    public Complex sin() {
        return new Complex(Math.sin(re) * Math.cosh(im), Math.cos(re) * Math.sinh(im));
    }

    // return a new Complex object whose value is the complex cosine of this
    public Complex cos() {
        return new Complex(Math.cos(re) * Math.cosh(im), -Math.sin(re) * Math.sinh(im));
    }

    // return a new Complex object whose value is the complex tangent of this
    public Complex tan() {
        return sin().divides(cos());
    }

    // a static version of plus
    public static Complex plus(Complex a, Complex b) {
        double real = a.re + b.re;
        double imag = a.im + b.im;
        Complex sum = new Complex(real, imag);
        return sum;
    }

    // See Section 3.3.
    public boolean equals(Object x) {
        if (x == null) return false;
        if (this.getClass() != x.getClass()) return false;
        Complex that = (Complex) x;
        return (this.re == that.re) && (this.im == that.im);
    }
}