package FFT1;

public class Fourier {

	public Fourier() {

	}

	public Complex[] dft(double[] x) {
		int n = x.length;
		Complex[] xX = new Complex[n]; // FFT-bins
		for (int k = 0; k < n; k++) {
			Complex accum = new Complex(0.0, 0.0);
			for (int nn = 0; nn < n; nn++) {
				Complex wnkN = Complex.expjphi(-2 * Math.PI * nn * k / n);
				Complex prod = wnkN.multiply(x[nn]);
				accum = accum.add(prod);
			}
			xX[k] = accum;
		}
		return xX;
	}

	public Complex[] idft(Complex[] X) {
		int n = X.length;
		Complex[] x = new Complex[n];
		for (int k = 0; k < n; k++) {
			Complex accum = new Complex(0.0, 0.0);
			for (int nn = 0; nn < n; nn++) {
				Complex wnkN = Complex.expjphi(2 * Math.PI * nn * k / n);
				Complex prod = wnkN.multiply(X[nn]);
				accum = accum.add(prod);
			}
			x[k] = accum.multiply((double) (1.0 / n));
		}
		return x;
	}
}

package FFT1;

import java.text.DateFormat;
import java.util.Calendar;
import java.util.Date;

import util.FileIO;
import util.ShowPlot2d;

public class Engine {

	DateFormat f = DateFormat.getDateTimeInstance(DateFormat.MEDIUM,
			DateFormat.MEDIUM);
	DateFormat ff = DateFormat.getDateTimeInstance(DateFormat.MEDIUM,
			DateFormat.MEDIUM);
	double time1;
	int numSam = (int) Math.pow(2, 10);
	double[] inBuffer;

	public Engine() {
	}
	
	public void startTimer(){
		Calendar cal = Calendar.getInstance();
		time1 = cal.getTimeInMillis();
		Date now = cal.getTime();
		System.out.println("start " + "\t" + " " + f.format(now));	
	}	

	public void stopTimer(){
		Calendar cal = Calendar.getInstance();
		double time2 = cal.getTimeInMillis();
		System.out.println("stop " + "\t" + " " + ff.format(time2));
		double dif = time2 - time1;
		System.out.println("runtime (msec): " + dif + "\n");		
	}

	public double[] readSamples(int number) {
		FileIO inputfile = new FileIO();
		inputfile.FileSetup("output");
		int kar;
		double inputSamples[] = new double[number];
		for (int k = 0; k < number; k++) {
			kar = inputfile.readByte();
			if (kar > 127) {
				kar = kar - 256;
			}
			inputSamples[k] = kar;
		}
		return inputSamples;
	}

	public void testFFT1(String title) {
		System.out.println(title);
		System.out.println("numSam = " + numSam);
		inBuffer = readSamples(numSam);
		Fourier myFourier = new Fourier();
		
		startTimer();
		Complex[] outBuffer = myFourier.dft(inBuffer);
		stopTimer();
		
		double[] plotBuffer = new double[numSam];
		for (int i = 0; i < outBuffer.length; i++) {
			plotBuffer[i] = outBuffer[i].magnitude();
		}
		ShowPlot2d myPlot = new ShowPlot2d(1);
		myPlot.add(plotBuffer, 1, "myPlot");
		myPlot.showFigure();
	}
}

package FFT2;

/*************************************************************************
 *  Compilation:  javac FFT.java
 *  Execution:    java FFT N
 *  Dependencies: Complex.java
 *
 *  Compute the FFT and inverse FFT of a length N complex sequence.
 *  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)
 *  
 *************************************************************************/

public class FFT {

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

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

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

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

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

        // combine
        Komplex[] y = new Komplex[N];
        for (int k = 0; k < N/2; k++) {
            double kth = -2 * k * Math.PI / N;
            Komplex wk = new Komplex(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 Komplex[] ifft(Komplex[] x) {
        int N = x.length;
        Komplex[] y = new Komplex[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].times(1.0 / N);
        }

        return y;

    }

    // compute the circular convolution of x and y
    public static Komplex[] cconvolve(Komplex[] x, Komplex[] 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 RuntimeException("Dimensions don't agree"); }

        int N = x.length;

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

        // point-wise multiply
        Komplex[] c = new Komplex[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 Komplex[] convolve(Komplex[] x, Komplex[] y) {
        Komplex ZERO = new Komplex(0, 0);

        Komplex[] a = new Komplex[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;

        Komplex[] b = new Komplex[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);
    }

    // display an array of Complex numbers to standard output
    public static void show(Komplex[] x, String title) {
        System.out.println(title);
        System.out.println("-------------------");
        for (int i = 0; i < x.length; i++) {
            System.out.println(x[i]);
        }
        System.out.println();
    } 
}

package DSP;

import src_old.Complex;


/*************************************************************************
 *  Compilation:  javac InplaceFFT.java
 *  Execution:    java InplaceFFT N
 *  Dependencies: Complex.java
 *
 *  Compute the FFT of a length N complex sequence in-place.
 *  Uses a non-recursive version of the Cooley-Tukey FFT.
 *  Runs in O(N log N) time.
 *
 *  Reference:  Algorithm 1.6.1 in Computational Frameworks for the
 *  Fast Fourier Transform by Charles Van Loan.
 *
 *
 *  Limitations
 *  -----------
 *   -  assumes N is a power of 2
 *
 *  
 *************************************************************************/

public class InplaceFFT {

    // compute the FFT of x[], assuming its length is a power of 2
    public static void fft(Complex[] x) {

        // check that length is a power of 2
        int N = x.length;
        if (Integer.highestOneBit(N) != N) {
            throw new RuntimeException("N is not a power of 2");
        }

        // bit reversal permutation
        int shift = 1 + Integer.numberOfLeadingZeros(N);
        for (int k = 0; k < N; k++) {
            int j = Integer.reverse(k) >>> shift;
            if (j > k) {
                Complex temp = x[j];
                x[j] = x[k];
                x[k] = temp;
            }
        }

        // butterfly updates
        for (int L = 2; L <= N; L = L+L) {
            for (int k = 0; k < L/2; k++) {
                double kth = -2 * k * Math.PI / L;
                Complex w = new Complex(Math.cos(kth), Math.sin(kth));
                for (int j = 0; j < N/L; j++) {
                    Complex tao = w.times(x[j*L + k + L/2]);
                    x[j*L + k + L/2] = x[j*L + k].minus(tao); 
                    x[j*L + k]       = x[j*L + k].plus(tao); 
                }
            }
        }
    }
    public static void ifft(Complex[] x) {
    	
    	// inverse FFT using above FFT
    	
    	for(int i=0;i