/// <summary>
/// Applies the Fast Fourier Transform in 2 dimensions to a Signal in 2 dimensions
/// </summary>
/// <param name="signal">The Signal2D to apply FFT2D to</param>
/// <returns>The Fourier Transform of the Signal2D</returns>
public static Signal2D FFT2D(Signal2D signal)
{
Signal2D result = new Signal2D(signal.Height, signal.Width);
for (int i = 0; i < result.Height; i++)
{
result[i] = new ComplexNumber[signal[i].Length];
}
//rows
for (int n = 0; n < signal.Height; n++)
{
result[n] = FFT(signal[n]);
}
//columns
for (int i = 0; i < signal[0].Length; i++)
{
ComplexNumber[] col = new ComplexNumber[signal.Height];
for (int j = 0; j < col.Length; j++)
{
col[j] = result[j][i];
}
col = FFT(col);
for (int j = 0; j < col.Length; j++)
{
result[j][i] = col[j];
}
}
return(result);
}
/// <summary>
/// Gets the Conjugate for each frequency in the Signal2D
/// </summary>
/// <returns>A new Signal2D containing the Conjugate for each frequency</returns>
public Signal2D GetConjugate()
{
Signal2D result = new Signal2D(Height, Width);
for (int i = 0; i < Height; i++)
{
result[i] = this[i].GetConjugate();
}
return(result);
}
/// <summary>
/// Creates a new Image based on a Signal2D
/// </summary>
/// <param name="matrix">The Signal2D to base off of</param>
public Image(Signal2D matrix)
{
BMap = new Bitmap(matrix.Width, matrix.Height);
for (int i = 0; i < matrix.Height; i++)
{
for (int j = 0; j < matrix[0].Length; j++)
{
Set(j, i, Color.FromArgb((int)matrix[i][j].Real));
}
}
}
/// <summary>
/// Multiplies a Signal2D by a scalar
/// </summary>
/// <param name="a">The Signal2D to multiply</param>
/// <param name="scalar">The scalar to multiply</param>
/// <returns>The product of the Signal2D and the scalar</returns>
public static Signal2D operator*(Signal2D a, ComplexNumber scalar)
{
Signal2D result = new Signal2D(a.Height, a.Width);
for (int y = 0; y < a.Height; y++)
{
for (int x = 0; x < a.Width; x++)
{
result[y][x] = a[y][x] * scalar;
}
}
return(result);
}
/// <summary>
/// Applies the Inverted Fast Fourier Transform algorithm in 2 dimensions to a Signal
/// </summary>
/// <param name="signal">The Signal2D to apply IFFT2D to</param>
/// <returns>The Inverted Fourier Transform of the Signal2D</returns>
public static Signal2D InverseFFT2D(Signal2D signal)
{
Signal2D result = signal.GetConjugate();
result = FFT2D(result);
for (int i = 0; i < signal.Height; i++)
{
for (int j = 0; j < signal.Width; j++)
{
result[i][j] /= signal.Width * signal.Height;
}
}
return(result);
}
/// <summary>
/// Deconstructs the Image into 3 Signal2Ds: red, green, and blue
/// </summary>
/// <returns>A Signal2D array with 3 Signal2Ds for each color</returns>
public Signal2D[] Deconstruct()
{
Signal2D[] rgb = new Signal2D[] { new Signal2D((int)Height, (int)Width), new Signal2D((int)Height, (int)Width), new Signal2D((int)Height, (int)Width) };
for (int i = 0; i < Height; i++)
{
for (int j = 0; j < Width; j++)
{
rgb[0][i][j] = BMap.GetPixel(i, j).R;
rgb[1][i][j] = BMap.GetPixel(i, j).G;
rgb[2][i][j] = BMap.GetPixel(i, j).B;
}
}
return(rgb);
}
/// <summary>
/// Gets all blue values in a Signal2D of the Image
/// </summary>
/// <returns>The blue values in a Signal2D</returns>
public Signal2D GetBlueMatrix()
{
Signal2D matrix = new Signal2D((int)Height, (int)Width);
for (int i = 0; i < Height; i++)
{
matrix[i] = new Signal(matrix.Width);
for (int j = 0; j < Width; j++)
{
matrix[i][j] = BMap.GetPixel(i, j).B;
}
}
return(matrix);
}
/// <summary>
/// Subtracts a Signal2D from another
/// </summary>
/// <param name="a">The first Signal2D</param>
/// <param name="b">The second Signal2D</param>
/// <returns>The difference of the two Signals</returns>
public static Signal2D operator-(Signal2D a, Signal2D b)
{
if (a.Height != b.Height || a.Width != b.Width)
{
throw new ArgumentException("Sizes must be equal");
}
Signal2D result = new Signal2D(a.Height, a.Width);
for (int y = 0; y < a.Height; y++)
{
for (int x = 0; x < a.Width; x++)
{
result[y][x] = a[y][x] - b[y][x];
}
}
return(result);
}
/// <summary>
/// Reconstructs the Image from 3 Signal2Ds each representing R G or B
/// </summary>
/// <param name="red">The red signal</param>
/// <param name="green">The green signal</param>
/// <param name="blue">The blue signal</param>
/// <returns>An Image created from the rgb signals</returns>
public static Image Reconstruct(Signal2D red, Signal2D green, Signal2D blue)
{
Image image = new Image(red.Width, red.Height);
for (int i = 0; i < image.Height; i++)
{
for (int j = 0; j < image.Width; j++)
{
int r = (int)red[i][j].Real;
if (red[i][j].Real > 255)
{
red[i][j] = 255;
}
if (green[i][j].Real > 255)
{
green[i][j] = 255;
}
if (blue[i][j].Real > 255)
{
blue[i][j] = 255;
}
if (red[i][j].Real < 0)
{
red[i][j] = 0;
}
if (green[i][j].Real < 0)
{
green[i][j] = 0;
}
if (blue[i][j].Real < 0)
{
blue[i][j] = 0;
}
Color c = Color.FromArgb((int)red[i][j], (int)green[i][j], (int)blue[i][j]);
image.Set(i, j, c);
}
}
return(image);
}
/// <summary>
/// Scales the Signal2D based on the max value between 0-255
/// </summary>
/// <returns>A scaled version of the Signal2D</returns>
public Signal2D Scale()
{
Signal2D mag = this;
int[] maxIndex = Max();
int[] minIndex = Min();
double max = this[maxIndex[0]][maxIndex[1]].Real;
double min = this[minIndex[0]][minIndex[1]].Real;
double scalar = 255.0 / max;
for (int i = 0; i < mag.Height; i++)
{
for (int j = 0; j < mag.Width; j++)
{
mag[i][j] *= scalar;
}
}
maxIndex = Max();
minIndex = Min();
max = this[maxIndex[0]][maxIndex[1]].Real;
min = this[minIndex[0]][minIndex[1]].Real;
return(mag);
}
/// <summary>
/// Calculates the cross correlation of 2 dimensional Signals
/// </summary>
/// <param name="signal">The response Signal</param>
/// <param name="pulse">The pulse Signal</param>
/// <returns>The cross correlation</returns>
public static Signal2D CrossCorrelation2D(Signal2D signal, Signal2D pulse)
{
return(InverseFFT2D(FFT2D(pulse).GetConjugate() * FFT2D(signal)));
}