// =================
// || Worksheet 5
// || In this example, we are going be visualizing waves.
// =================

// for another (less detailed example) see,
// http://docs.opencv.org/doc/tutorials/core/discrete_fourier_transform/discrete_fourier_transform.html

#include "program.h"

using namespace std;
using namespace cv;

// In this worksheet, we will be performing DFT's and Inverse DFT's
// (for this exercise, we are going to ignore the image passed in i.e. 'src')
int worksheetfive(Mat& src)
{
    
    // We are going to start with a blank (fourier space) image. I..e
    // a blank image indicates that we are not 'playing' any notes on our 2d piano.
    // we'll make a 400x400 matrix of zeros, with floating point values.
    Mat blankImage = Mat::zeros(400,400, CV_32F);
    
    // now we embed this real image into a complex image
    // this is where fourier transforms live
    // an image where every pixel represents a complex number.
    Mat complexImage = embedInComplexImage(blankImage);
    
    // now, set only a few pixels (i.e. musical notes) to be non-zero.
    // the value we set on the can be any complex number. here we are just using 1+0i
    complexImage.at<complex<float>>(0,6) = complex<float>(1.0,0);
    complexImage.at<complex<float>>(0,12) = complex<float>(1.0,0);
    complexImage.at<complex<float>>(0,18) = complex<float>(1.0,0);
    
    // Now, we are going to compute the magnitude of our complex image.
    // i.e. we want a new image whose values are sqrt( X^2+ Y^2) of our complex image X+iY.
    Mat magnitudeImage = computeMagnitudeImage(complexImage);
    
    // now we rearrange, to make the image look a little better.
    rearrange(magnitudeImage);
    
    // Show the result
    imshow("Spectrum Magnitude", magnitudeImage);
    
    // PERFORM THE INVERSE DISCRETE FOURIER TRANSFORM (IDFT)
    cv::Mat invtransformedImage;
    
    // perform the inverse transform of our complex image.
    cv::dft(complexImage, invtransformedImage, cv::DFT_INVERSE | cv::DFT_REAL_OUTPUT);
    
    /// just normalize our image to be safe.
    normalize(invtransformedImage, invtransformedImage, 0, 1, CV_MINMAX);
    
    // show the IDFT
    imshow("Reconstructed", invtransformedImage);
    
    waitKey();
    
    return 0;
}