在C＃中绘制快速傅里叶变换 [英] Plotting Fast Fourier Transform in C#
问题描述
您好，
我是电子工程专业的最后一年学生我建立了一个从串口接收输入的软件绘制它。我已完成这一部分，困扰我的是我想绘制该数据的快速傅立叶变换。通过互联网我无法在C＃中找到任何FFT实现，或者我无法理解实施，如果有人会解雇我，我会很高兴提前感谢...
Hi there,
I'm final year student of electronics engineering i build a software with takes input from serial port and plots it. i'm done with this part, the thing that bugging me is that i want to plot Fast Fourier Transform of that data. over the internet i cannot find any implementation of FFT in C# or i cannot understand the implementation if anyone will sort me out i will glad thanks in advance...
<pre lang="c#">
//My serial port receiving code
string _myData;
_myData = serialPort1.ReadExisting();
// i want to plot That _myData string in FFT
问候
Sajid
Regards
Sajid
推荐答案
我在C＃中找不到任何FFT实现
你看起来不太难，那么 - 你呢？
一个非常非常快的谷歌快速傅里叶变换C＃给出了85,000次点击： Google [ ^ ]
你不理解他们是你的问题，而不是我们的问题：而不是我们可以解决的问题。您可能不需要理解它们 - 只需使用它们。
" i cannot find any implementation of FFT in C#"
You didn't look too hard, then - did you?
A very, very quick Google for "Fast Fourier Transform C#" gave 85,000 hits: Google[^]
That you don't understand them is your problem, not ours: and not something we can resolve. You may not need to understand them - just use them.
public class FFT
{
public static Boolean IsPowerOfTwo(UInt32 x)
{
return ((x != 0) && (x & (x - 1)) == 0);
}
public static UInt32 NextPowerOfTwo(UInt32 x)
{
x = x - 1;
x = x | (x >> 1);
x = x | (x >> 2);
x = x | (x >> 4);
x = x | (x >> 8);
x = x | (x >> 16);
return x + 1;
}
public static UInt32 NumberOfBitsNeeded(UInt32 PowerOfTwo)
{
if (PowerOfTwo > 0)
{
for (UInt32 i = 0, mask = 1; ; i++, mask <<= 1)
{
if ((PowerOfTwo & mask) != 0)
return i;
}
}
return 0; // error
}
public static UInt32 ReverseBits(UInt32 index, UInt32 NumBits)
{
UInt32 i, rev;
for (i = rev = 0; i < NumBits; i++)
{
rev = (rev << 1) | (index & 1);
index >>= 1;
}
return rev;
}
public struct Complex
{
public double Re, Im;
public Complex(double x, double y)
{
this.Re = x; this.Im = y;
}
public Complex Mul(Complex C2)
{
Complex aux = new Complex();
aux.Re = this.Re * C2.Re - this.Im * C2.Im;
aux.Im = this.Re * C2.Im + this.Im * C2.Re;
return aux;
}
public Complex Add(Complex C2)
{
Complex aux = new Complex();
aux.Re = this.Re + C2.Re;
aux.Im = this.Im + C2.Im;
return aux;
}
public Complex Sub(Complex C2)
{
Complex aux = new Complex();
aux.Re = this.Re - C2.Re;
aux.Im = this.Im - C2.Im;
return aux;
}
public double Magnitude()
{
double Len = Math.Sqrt(this.Re * this.Re + this.Im * this.Im);
double bb = Math.Abs(Math.Tan(this.Re / Len)) / Math.Tan(this.Re / Len);
return (Len * bb );
}
public Complex Rev()
{
Complex aux = new Complex();
aux.Re = this.Re;
aux.Im = -1.0d * this.Im;
return aux;
}
}
public List<Complex> Cos_Fun(int N)
{
List<Complex> cc = new List<Complex>(N);
Complex aux;
double c = 2.0d * DDC_PI / (double)N;
for (int i = 0; i < N; i++)
{
aux = new Complex(
Math.Cos((double)(3 * i) * c)
, Math.Sin((double)(6 * i * i) * c)
);
cc.Add(aux);
}
return cc;
}
public const Double DDC_PI = 3.14159265358979323846;
UInt32 Block_Size = 2;
public Complex Get_W(int block_size, int index)
{
Complex c = new Complex(1.0d, 1.0d);
c.Re = c.Re * Math.Cos((-2 * DDC_PI / block_size) * index);
c.Im = c.Im * Math.Sin((-2 * DDC_PI / block_size) * index);
return c;
}
public List<Complex> Init_FFT(List<Complex> x)
{
Complex auxx = new Complex(0.0d, 0.0d);
List<Complex> aux = new List<Complex>(x.Count);
UInt32 count;
if (IsPowerOfTwo((UInt32)x.Count))
{
count = (UInt32)x.Count;
}
else
{
count = NextPowerOfTwo((UInt32)x.Count);
}
UInt32 b = NumberOfBitsNeeded(count);
aux = new List<Complex>((int)count);
Complex cccc= new Complex();
for (int i = 0; i < (int)count; i++)
{
aux.Add(cccc);
}
for (int i = x.Count; i < count; i++)
{
x.Add(auxx);
}
for (int i = 0; i < count; i++)
{
aux[i] = (x[(int)ReverseBits((UInt32)i, b)]);
}
x.Clear();
return aux;
}
public List<Complex> FFT_Calc(List<Complex> Xx)
{
Block_Size = 2; int index = 0; int indexx = 0;
int Block_num = Xx.Count / (int)Block_Size;
Complex auxx = new Complex(0.0d, 0.0d);
List<Complex> aux = new List<Complex>(Xx.Count);
for (int i = 0; i < Xx.Count; i++)
aux.Add(auxx);
int test = 0;
while (Block_Size <= Xx.Count)
{
index = 0;
Block_num = Xx.Count / (int)Block_Size;
for (int i = 0; i < Block_num; i++)
{
indexx = 0; index = i * (int)Block_Size;
for (int j = 0; j < (int)Block_Size / 2; j++)
{
//first
auxx = Get_W((int)Block_Size, indexx);
aux[index] = Xx[index];
auxx = auxx.Mul(Xx[index + (int)Block_Size / 2]);
aux[index] = aux[index].Add(auxx);
test++;
//second
auxx = Get_W((int)Block_Size, indexx + (int)Block_Size / 2);
aux[index + (int)Block_Size / 2] = Xx[index];
auxx = auxx.Mul(Xx[index + (int)Block_Size / 2]);
aux[index + (int)Block_Size / 2] = aux[index + (int)Block_Size / 2].Add(auxx);
test++;
indexx++;
index++;
}
}
for (int k = 0; k < aux.Count; k++)
Xx[k] = aux[k];
Block_Size <<= 1;
}
//for (int k = 0; k < aux.Count; k++)
// Xx[k] = aux[k];
return aux;
}
public List<Complex> Inv_FFT_Calc(List<Complex> Xx)
{
Block_Size = 2; int index = 0; int indexx = 0;
int Block_num = Xx.Count / (int)Block_Size;
Complex auxx = new Complex(0.0d, 0.0d);
List<Complex> aux = new List<Complex>(Xx.Count);
for (int i = 0; i < Xx.Count; i++)
aux.Add(auxx);
int test = 0;
while (Block_Size <= Xx.Count)
{
index = 0;
Block_num = Xx.Count / (int)Block_Size;
for (int i = 0; i < Block_num; i++)
{
indexx = 0; index = i * (int)Block_Size;
for (int j = 0; j < (int)Block_Size / 2; j++)
{
//first
auxx = Get_W((int)Block_Size, -indexx);
aux[index] = Xx[index];
auxx = auxx.Mul(Xx[index + (int)Block_Size / 2]);
aux[index] = aux[index].Add(auxx);
test++;
//second
auxx = Get_W((int)Block_Size, -indexx + (int)Block_Size / 2);
aux[index + (int)Block_Size / 2] = Xx[index];
auxx = auxx.Mul(Xx[index + (int)Block_Size / 2]);
aux[index + (int)Block_Size / 2] = aux[index + (int)Block_Size / 2].Add(auxx);
test++;
indexx++;
index++;
}
}
for (int k = 0; k < aux.Count; k++)
Xx[k] = aux[k];
Block_Size <<= 1;
}
Complex c = new Complex(1.0d / aux.Count, 0.0d);
List<Complex> auxxx = new List<Complex>(aux.Count);
for (int k = 0; k < aux.Count; k++)
{
c.Re = aux[k].Re / (double)aux.Count; c.Im = 0.0d;
auxxx.Add(c);
}
//UInt32 b = NumberOfBitsNeeded((uint)aux.Count);
//for (int k = 0; k < aux.Count; k++)
//{
// Xx[k] = aux[k];
// //Xx[(int)ReverseBits((UInt32)k, b)] = aux[k];
//}
return auxxx;
}
public System.Drawing.Bitmap Draw_Spectral(float[] Percent, int From, int To, Color c, System.Drawing.Size Bitmap_Size)
{
Bitmap bb = new Bitmap(Bitmap_Size.Width, Bitmap_Size.Height);
if (Percent != null)
{
System.Drawing.Graphics g = Graphics.FromImage(bb);
g.SmoothingMode = System.Drawing.Drawing2D.SmoothingMode.HighQuality;
g.Clear(Color.White);
float max = 0.0f;
for (int i = From; i < To; i++)
{
if (max < Percent[i])
max = Percent[i];
}
float xStep = ((float)bb.Width - 10.0f) / (float)(To - From);
System.Drawing.SolidBrush sb1 = new SolidBrush(Color.LightBlue);
System.Drawing.Pen p1 = new Pen(c, 1.5f);
float yStep = 1.0f * ((float)bb.Height - 10.0f) / max;
float x = 5.0f, y = bb.Height - 5.0f;
for (int i = From; i < To; i++)
{
g.DrawLine(p1
, x
, bb.Height - 5.0f
, x
, y - (Percent[i] * yStep));
x += xStep;
}
}
return bb;
}
public void Draw_Wave(List<Complex> Spectral, System.Windows.Forms.Panel p, Color c, float D_Width)
{
if (Spectral != null)
{
System.Drawing.Graphics g = p.CreateGraphics();
g.SmoothingMode = System.Drawing.Drawing2D.SmoothingMode.HighSpeed;
g.Clear(Color.White);
float max = 0.0f;
for (int i = 0; i < Spectral.Count; i++)
{
if (max < Spectral[i].Magnitude())
max = (float)Spectral[i].Magnitude();
}
float xStep = ((float)p.Width - 10.0f) / Spectral.Count;
System.Drawing.Pen p1 = new Pen(c, D_Width);
float yStep = 1.0f * ((float)p.Height - 10.0f) / max;
float x = 5.0f, y = p.Height - 5.0f;
for (int i = 0; i < Spectral.Count; i++)
{
g.DrawLine(p1
, x
, p.Height - 5.0f
, x
, y - ((float)Spectral[i].Magnitude() * yStep));
x += xStep;
}
}
}
public enum Complex_Part
{
Real,
Image,
Magenda
}
public void Draw_Spectral(List<Complex> Spectral, System.Windows.Forms.Panel p,Complex_Part cp, Color c, float D_Width)
{
if (Spectral != null)
{
System.Drawing.Graphics g = p.CreateGraphics();
g.SmoothingMode = System.Drawing.Drawing2D.SmoothingMode.HighSpeed;
g.Clear(Color.White);
float max = 0.0f; float min = 0.0f; ;
int freq_step = (Spectral.Count) * 10 / 100;
int f_s = freq_step;
if (cp == Complex_Part.Image)
{
for (int i = 0; i < (Spectral.Count); i++)
{
if (max < Spectral[i].Im)
max = (float)Spectral[i].Im;
if (min > Spectral[i].Im)
min = (float)Spectral[i].Im;
}
}
else if (cp == Complex_Part.Real)
{
for (int i = 0; i < (Spectral.Count); i++)
{
if (max < Spectral[i].Re)
max = (float)Spectral[i].Re;
if (min > Spectral[i].Re)
min = (float)Spectral[i].Re;
}
}
else if (cp == Complex_Part.Magenda)
{
for (int i = 0; i < (Spectral.Count); i++)
{
if (max < Spectral[i].Magnitude())
max = (float)Spectral[i].Magnitude();
if (min > Spectral[i].Magnitude())
min = (float)Spectral[i].Magnitude();
}
}
float xStep = ((float)p.Width - 10.0f) / (Spectral.Count);
System.Drawing.Pen p1 = new Pen(c, D_Width);
System.Drawing.Pen p2 = new Pen(Color.Black, 1.0f);
float yStep = 1.0f * ((float)p.Height - 20.0f) / (max - min);
float x = 5.0f, y = p.Height - (10.0f - yStep * min);
Font f = new Font("Tahoma", 6.5f, FontStyle.Regular);
SolidBrush b = new SolidBrush(Color.Black);
for (int i = 0; i < (Spectral.Count); i++)
{
if (i == f_s)
{
g.DrawString(f_s + "", f, b, x - 25.0f, 5.0f);
f_s += freq_step;
}
g.DrawLine(p2
, x - xStep
, p.Height - (10.0f - yStep * min)
, x + xStep
, p.Height - (10.0f - yStep * min));
if (cp == Complex_Part.Image)
{
g.DrawLine(p1
, x
, p.Height - (10.0f - yStep * min)
, x
, y - (((float)Spectral[i].Im) * yStep));
}
else if (cp == Complex_Part.Real)
{
g.DrawLine(p1
, x
, p.Height - (10.0f - yStep * min)
, x
, y - (((float)Spectral[i].Re) * yStep));
}
else if (cp == Complex_Part.Magenda)
{
g.DrawLine(p1
, x
, p.Height - (10.0f - yStep * min)
, x
, y - (((float)Spectral[i].Magnitude()) * yStep));
}
x += xStep;
}
}
}
public void Draw_Spectral(List<Complex> Spectral, System.Windows.Forms.Panel p, Color c, float D_Width)
{
if (Spectral != null)
{
System.Drawing.Graphics g = p.CreateGraphics();
g.SmoothingMode = System.Drawing.Drawing2D.SmoothingMode.HighSpeed;
g.Clear(Color.White);
float max = 0.0f; float min = 0.0f; ;
int freq_step = (Spectral.Count / 2) * 10 / 100;
int f_s = freq_step;
for (int i = 0; i < (Spectral.Count/2); i++)
{
if (max < Spectral[i].Magnitude())
max = (float)Spectral[i].Magnitude();
if (min > Spectral[i].Magnitude())
min = (float)Spectral[i].Magnitude();
}
float xStep = ((float)p.Width - 10.0f) / (Spectral.Count / 2);
System.Drawing.Pen p1 = new Pen(c, D_Width);
System.Drawing.Pen p2 = new Pen(Color.Black, 1.0f);
float yStep = 1.0f * ((float)p.Height - 20.0f) / (max - min);
float x = 5.0f, y = p.Height - (10.0f - yStep * min);
Font f = new Font("Tahoma", 6.5f, FontStyle.Regular);
SolidBrush b = new SolidBrush(Color.Black);
for (int i = 0; i < (Spectral.Count / 2); i++)
{
if (i == f_s)
{
g.DrawString(f_s + "", f, b, x - 25.0f, 5.0f);
f_s += freq_step;
}
g.DrawLine(p1
, x
, p.Height - (10.0f - yStep * min)
, x
, y - (((float)Spectral[i].Magnitude()) * yStep ));
g.DrawLine(p2
, x - xStep
, p.Height - (10.0f - yStep * min)
, x + xStep
, p.Height - (10.0f - yStep * min));
x += xStep;
}
}
}
public void Draw_Spectral(double[] Spectral, System.Windows.Forms.Panel p, Color c, float D_Width)
{
if (Spectral != null)
{
System.Drawing.Graphics g = p.CreateGraphics();
g.SmoothingMode = System.Drawing.Drawing2D.SmoothingMode.HighSpeed;
g.Clear(Color.White);
float max = 0.0f;
int freq_step = (Spectral.Length) * 5 / 100;
int f_s = freq_step;
for (int i = 0; i < Spectral.Length; i++)
{
if (max < Math.Abs(Spectral[i]))
max = (float)Math.Abs(Spectral[i]);
}
float xStep = ((float)p.Width - 10.0f) / (Spectral.Length);
System.Drawing.Pen p1 = new Pen(c, D_Width);
float yStep = 1.0f * ((float)p.Height - 10.0f) / max;
float x = 5.0f, y = p.Height - 5.0f;
Font f = new Font("Tahoma", 6.5f, FontStyle.Regular);
SolidBrush b = new SolidBrush(Color.Black);
for (int i = 0; i < (Spectral.Length); i++)
{
if (i == f_s)
{
g.DrawString(f_s + "", f, b, x - 25.0f, 5.0f);
f_s += freq_step;
}
g.DrawLine(p1
, x
, p.Height - 5.0f
, x
, y - ((float)Math.Abs(Spectral[i]) * yStep));
x += xStep;
}
}
}
public List<Complex> InitRSine(int n)
{
List<Complex> Data_In = new List<Complex>();
Complex aux = new Complex();
for (int i = 0; i < n; i++)
{
aux = new Complex();
aux.Re =
Math.Cos((double)(45.0) * i * (0.5 * Math.PI / n))
+ 4.0d * Math.Cos((double)(60.0) * i * (0.1 * Math.PI / n))
//+ Math.Cos((double)(20.0) * i * (2.0 * Math.PI / n))
//+ Math.Cos((double)(10.0) * i * (2.0 * Math.PI / n))
//+ Math.Cos((double)(5.0) * i * (2.0 * Math.PI / n))
;
aux.Im = 0.0d;
Data_In.Add(aux);
}
return Data_In;
}
}
公共类FFT
{
public static Boolean IsPowerOfTwo（UInt32 x）
{
return（（x！= 0）&&（x&（x - 1））== 0）;
}
public static UInt32 NextPowerOfTwo（UInt32 x）
{
x = x - 1;
x = x | （x>> 1）;
x = x | （x>> 2）;
x = x | （x>> 4）;
x = x | （x>> 8）;
x = x | （x>> 16）;
返回x + 1;
}
公共静态UInt32 NumberOfBitsNeeded（UInt32 PowerOfTwo）
{
if（PowerOfTwo> 0）
{
for（UInt32 i = 0，mask = 1 ;; i ++，mask<< = 1）
{
if（（PowerOfTwo& mask）！= 0）
return i;
}
}
返回0; //错误
}
公共静态UInt32 ReverseBits（UInt32索引，UInt32 NumBits）
{
UInt32 i ，rev;
for（i = rev = 0; i< NumBits; i ++）
{
rev =（rev<< 1）| （index& 1）;
index>> = 1;
}
return rev ;
}
公共结构复合体
{
公共双重Re，Im;
public Complex（双x，双y）
{
this.Re = x; this.Im = y;
}
public Complex Mul（Complex C2）
{
Complex aux = new Complex（）;
aux.Re = this.Re * C2.Re - this.Im * C2.Im;
aux.Im = this.Re * C2 .Im + this.Im * C2.Re;
返回aux;
}
public Complex Add（Complex C2）
{
复合辅助=新复合体（）;
aux.Re = this.Re + C2.Re;
aux .Im = this.Im + C2.Im;
返回辅助;
}
public Complex Sub（Complex C2）
{
复合辅助=新复合体（）;
aux.Re = this.Re - C2.Re;
aux .Im = this.Im - C2.Im;
返回辅助;
}
public double Magnitude（）
{
double Len = Math.Sqrt（this.Re * this.Re + this.Im * this.Im）;
double bb = Math.Abs（Math.Tan（this.Re / Len））/ Math.Tan（this.Re / Len）;
return（Len * bb）; < br $>
}
public Complex Rev（）
{
复合辅助=新复合体（）;
aux.Re = this.Re;
aux.Im = -1.0d * this.Im;
return aux;
}
}
public List< complex> Cos_Fun（int N）
{
List< complex> cc = new List< complex>（N）;
Complex aux;
double c = 2.0d * DDC_PI /（double）N;
for（int i = 0; i< N; i ++）
{
aux = new Complex（
Math.Cos（（ double）（3 * i）* c）
，Math.Sin（（double）（6 * i * i）* c）
）;
cc.Add（aux）;
}
返回cc;
}
public const Double DDC_PI = 3.14159265358979323846;
UInt32 Block_Size = 2;
public Complex Get_W（int block_size，int索引）
{
复杂c =新复合体（1.0d，1.0d）;
c。= c.Re *数学。 Cos（（ - 2 * DDC_PI / block_size）* index）;
c.Im = c.Im * Math.Sin（（ - 2 * DDC_PI / block_size）* index）;
返回c;
}
public List< complex> Init_FFT（List< complex> x）
{
复合auxx =新的Complex（0.0d，0.0d）;
List< complex> aux = new List< complex>（x.Count）;
UInt32 count;
if（IsPowerOfTwo（（UInt32）x.Count））
{
count =（UInt32）x.Count;
}
else
{
count = NextPowerOfTwo（（UInt32）x.Count）;
}
UInt32 b = NumberOfBitsNeeded（count）;
aux = new List< complex>（（int）count）;
Complex cccc = new Complex（）;
for（int i = 0; i<（int ）count; i ++）
{
aux.Add（cccc）;
}
for（int i = x.Count; i< count; i ++）
{
x.Add（auxx）;
}
for（int i = 0; i< count; i ++）
{
aux [i] =（x [（int）ReverseBits（（UInt32）i，b）]）;
}
x.Clear（）;
return aux;
}
public List< complex> FFT_Calc（List< complex> Xx）
{
Block_Size = 2; int index = 0; int indexx = 0;
int Block_num = Xx.Count /（int）Block_Size;
复合auxx = new Complex（0.0d，0.0d）;
列表< complex> aux = new List< complex>（Xx.Count）;
for（int i = 0; i< Xx.Count; i ++）
aux.Add（auxx ）;
int test = 0;
while（Block_Size< = Xx.Count）
{
index = 0;
Block_num = Xx.Count /（int）Block_Size;
for（int i = 0; i< Block_num; i ++）
{
indexx = 0; index = i *（int）Block_Size;
for（int j = 0; j<（int）Block_Size / 2; j ++）
{
$ b$b //first
auxx = Get_W((int)Block_Size, indexx);
aux[index] = Xx[index];
$b $b auxx = auxx.Mul(Xx[index + (int)Block_Size / 2]);
aux[index] = aux[index].Add(auxx);
$b $b test++;
//second
auxx = Get_W((int)Block_Size, indexx + (int)Block_Size / 2);
aux[index + (int)Block_Size / 2] = Xx[index];
auxx = auxx.Mul(Xx[index + (int)Block_Size / 2]);
$b $b aux[index + (int)Block_Size / 2] = aux[index + (int)Block_Size / 2].Add(auxx);
test++;
indexx++;
index++;
}
}
for (int k = 0; k < aux.Count; k++)
Xx[k] = aux[k];
Block_Size <<= 1;
}
//for (int k = 0; k < aux.Count; k++)
// Xx[k] = aux[k];
return aux;
}
public List<complex> Inv_FFT_Calc(List<complex> Xx)
{
Block_Size = 2; int index = 0; int indexx = 0;
int Block_num = Xx.Count / (int)Block_Size;
Complex auxx = new Complex(0.0d, 0.0d);
List<complex> aux = new List<complex>(Xx.Count);
for (int i = 0; i < Xx.Count; i++)
aux.Add(auxx);
int test = 0;
while (Block_Size <= Xx.Count)
{
index = 0;
Block_num = Xx.Count / (int)Block_Size;
for (int i = 0; i < Block_num; i++)
{
indexx = 0; index = i * (int)Block_Size;
for (int j = 0; j < (int)Block_Size / 2; j++)
{
//first
auxx = Get_W((int)Block_Size, -indexx);
aux[index] = Xx[index];
auxx = auxx.Mul(Xx[index + (int)Block_Size / 2]);
aux[index] = aux[index].Add(auxx);
test++;
//second
auxx = Get_W((int)Block_Size, -indexx + (int)Block_Size / 2);
aux[index + (int)Block_Size / 2] = Xx[index];
auxx = auxx.Mul(Xx[index + (int)Block_Size / 2]);
aux[index + (int)Block_Size / 2] = aux[index + (int)Block_Size / 2].Add(auxx);
test++;
indexx++;
index++;
}
}
for (int k = 0; k < aux.Count; k++)
Xx[k] = aux[k];
Block_Size <<= 1;
}
Complex c = new Complex(1.0d / aux.Count, 0.0d);
List<complex> auxxx = new List<complex>(aux.Count);
for (int k = 0; k < aux.Count; k++)
{
c.Re = aux[k].Re / (double)aux.Count; c.Im = 0.0d;
auxxx.Add(c);
}
//UInt32 b = NumberOfBitsNeeded((uint)aux.Count);
//for (int k = 0; k < aux.Count; k++)
//{
// Xx[k] = aux[k];
// //Xx[(int)ReverseBits((UInt32)k, b)] = aux[k];
//}
return auxxx;
}
public System.Drawing.Bitmap Draw_Spectral(float[] Percent, int From, int To, Color c, System.Drawing.Size Bitmap_Size)
{
Bitmap bb = new Bitmap(Bitmap_Size.Width, Bitmap_Size.Height);
if (Percent != null)
{
System.Drawing.Graphics g = Graphics.FromImage(bb);
g.SmoothingMode = System.Drawing.Drawing2D.SmoothingMode.HighQuality;
g. Clear(Color.White);
float max = 0.0f;
for (int i = From;我< To; i++)
{
if (max < Percent[i])
max = Percent[i];
}
float xStep = ((float)bb.Width - 10.0f) / (float)(To - From);
System.Drawing.SolidBrush sb1 = new SolidBrush(Color.LightBlue);
System.Drawing.Pen p1 = new Pen(c, 1.5f);
float yStep = 1.0f * ((float)bb.Height - 10.0f) / max;
float x = 5.0f, y = bb.Height - 5.0f;
for (int i = From; i < To; i++)
{
g.DrawLine(p1
, x
, bb.Height - 5.0f
, x
, y - (Percent[i] * yStep));
x += xStep;
}
}
return bb;
}
public void Draw_Wave(List<complex> Spectral, System.Windows.Forms.Panel p, Color c, float D_Width)
{
if (Spectral != null)
{
System.Drawing.Graphics g = p.CreateGraphics();
g.SmoothingMode = System.Drawing.Drawing2D.SmoothingMode.HighSpeed;
g.Clear(Color.White);
float max = 0.0f;
for (int i = 0; i < Spectral.Count; i++)
{
if (max < Spectral[i].Magnitude())
max = (float)Spectral[i].Magnitude();
}
float xStep = ((float)p.Width - 10.0f) / Spectral.Count;
System.Drawing.Pen p1 = new Pen(c, D_Width);
float yStep = 1.0f * ((float)p.Height - 10.0f) / max;
float x = 5.0f, y = p.Height - 5.0f;
$b$ b for (int i = 0;我< Spectral.Count; i++)
{
g.DrawLine(p1
, x
, p.Height - 5.0f
, x
, y - ((float)Spectral[i].Magnitude() * yStep));
x += xStep;
}
}
}
public enum Complex_Part
{
Real,
Image,
Magenda
}
public void Draw_Spectral(List<complex> Spectral, System.Windows.Forms.Panel p,Complex_Part cp, Color c, float D_Width)
{
if (Spectral != null)
{
System.Drawing.Graphics g = p.CreateGraphics();
g.SmoothingMode = System.Drawing.Drawing2D.SmoothingMode.HighSpeed;
g.Clear(Color.White);
float max = 0.0f; float min = 0.0f; ;
int freq_step = (Spectral.Count) * 10 / 100;
int f_s = freq_step;
if (cp == Complex_Part.Image)
{
for (int i = 0; i < (Spectral.Count); i++)
{
if (max < Spectral[i].Im)
max = (float)Spectral[i].Im;
if (min > Spectral[i].Im)
min = (float)Spectral[i].Im;
}
}
else if (cp == Complex_Part.Real)
{
for (int i = 0; i < (Spectral.Count); i++)
{
if (max < Spectral[i].Re)
max = (float)Spectral[i].Re;
if (min > Spectral[i].Re)
min = (float)Spectral[i].Re;
}
}
else if (cp == Complex_Part.Magenda)
{
for (int i = 0; i < (Spectral.Count); i++)
{
if (max < Spectral[i].Magnitude())
max = (float)Spectral[i].Magnitude();
if (min > Spectral[i].Magnitude())
min = (float)Spectral[i].Magnitude();
}
}
float xStep = ((float)p.Width - 10.0f) / (Spectral.Count);
System.Drawing.Pen p1 = new Pen(c, D_Width);
System.Drawing.Pen p2 = new Pen(Color.Black, 1.0f);
float yStep = 1.0f * ((fl oat)p.Height - 20.0f) / (max - min);
float x = 5.0f, y = p.Height - (10.0f - yStep * min);
Font f = new Font(\"Tahoma\", 6.5f, FontStyle.Regular);
SolidBrush b = new SolidBrush(Color.Black);
for (int i = 0;我< (Spectral.Count); i++)
{
if (i == f_s)
{
g.DrawString(f_s + \"\", f, b, x - 25.0f, 5.0f);
f_s += freq_step;
}
g.DrawLine(p2
, x - xStep
, p.Height - (10.0f - yStep * min)
, x + xStep
, p.Height - (10.0f - yStep * min));
if (cp == Complex_Part.Image)
{
g.DrawLine(p1
, x
, p.Height - (10.0f - yStep * min)
, x
, y - (((float)Spectral[i].Im) * yStep));
}
else if (cp == Complex_Part.Real)
{
g.DrawLine(p1
, x
, p.Height - (10.0f - yStep * min)
, x
, y - (((float)Spectral[i].Re) * yStep));
}
else if (cp == Complex_Part.Magenda)
{
g.DrawLine(p1
, x
, p.Height - (10.0f - yStep * min)
, x
, y - (((float)Spectral[i].Magnitude()) * yStep));
}
x += xStep;
}
}
}
public void Draw_Spectral(List<complex> Spectral, System.Windows.Forms.Panel p, Color c, float D_Width)
{
if (Spectral != null)
{
System.Drawing.Graphics g = p.CreateGraphics();
g.SmoothingMode = System.Drawing.Drawing2D.SmoothingMode.HighSpeed;
g.Clear(Color.White);
float max = 0.0f; float min = 0.0f; ;
int freq_step = (Spectral.Count / 2) * 10 / 100;
int f_s = freq_step;
for (int i = 0; i < (Spectral.Count/2); i++)
{
if (max < Spectral[i].Magnitude())
max = (float)Spectral[i].Magnitude();
if (min > Spectral[i].Magnitude())
min = (float)Spectral[i].Magnitude();
}
float xStep = ((float)p.Width - 10.0f) / (Spectral.Count / 2);
System.Drawing.Pen p1 = new Pen(c, D_Width);
System.Drawing.Pen p2 = new Pen(Color.Black, 1.0f);
float yStep = 1.0f * ((float)p.Height - 20.0f) / (max - min);
float x = 5.0f, y = p.Height - (10.0f - yStep * min);
Font f = new Font(\" Tahoma\", 6.5f, FontStyle.Regular);
SolidBrush b = new SolidBrush(Color.Black);
for (int i = 0;我< (Spectral.Count / 2); i++)
{
if (i == f_s)
{
g.DrawString(f_s + \"\", f, b, x - 25.0f, 5.0f);
f_s += freq_step;
}
g.DrawLine(p1
, x
, p.Height - (10.0f - yStep * min)
, x
, y - (((float)Spectral[i].Magnitude()) * yStep ));
g.DrawLine(p2
, x - xStep
, p.Height - (10.0f - yStep * min)
, x + xStep
, p.Height - (10.0f - yStep * min));
x += xStep;
}
}
}
public void Draw_Spec tral(double[] Spectral, System.Windows.Forms.Panel p, Color c, float D_Width)
{
if (Spectral != null)
{
System.Drawing.Graphics g = p.CreateGraphics();
g.SmoothingMode = System.Drawing.Drawing2D.SmoothingMode.HighSpeed;
g.Clear(Color.White);
float max = 0.0f;
int freq_step = (Spectral.Length) * 5 / 100;
int f_s = freq_step;
for (int i = 0;我< Spectral.Length; i++)
{
if (max < Math.Abs(Spectral[i]))
max = (float)Math.Abs(Spectral[i]);
}
float xStep = ((float)p.Width - 10.0f) / (Spectral.Length);
System.Drawing.Pen p1 = new Pen(c, D_Width);
float yStep = 1.0f * ((float)p.Height - 10.0f) / max;
float x = 5.0f, y = p.Height - 5.0f;
Font f = new Font(\"Tahoma\", 6.5f, FontStyle.Regular);
SolidBrush b = new SolidBrush(Color.Black);
for (int i = 0; i < (Spectral.Length); i++)
{
if (i == f_s)
{
g.DrawString(f_s + \"\", f, b, x - 25.0f, 5.0f);
f_s += freq_step;
}
g.DrawLine(p1
, x
, p.Height - 5.0f
, x
, y - ((float)Math.Abs(Spectral[i]) * yStep));
x += xStep;
}
}
}
public List<complex> InitRSine(int n)
{
List<complex> Data_In = new List<complex>();
Complex aux = new Complex();
for (int i = 0; i < n; i++)
{
aux = new Complex();
aux.Re =
Math.Cos((double)(45.0) * i * (0.5 * Math.PI / n))
+ 4.0d * Math.Cos((double)(60.0) * i * (0.1 * Math.PI / n))
//+ Math.Cos((double)(20.0) * i * (2.0 * Math.PI / n))
//+ Math.Cos((double)(10.0) * i * (2.0 * Math.PI / n))
//+ Math.Cos((double)(5.0) * i * (2.0 * Math.PI / n))
;
aux.Im = 0.0d;
Data_In.Add(aux);
}
return Data_In;
}
}
public class FFT
{
public static Boolean IsPowerOfTwo(UInt32 x)
{
return ((x != 0) && (x & (x - 1)) == 0);
}
public static UInt32 NextPowerOfTwo(UInt32 x)
{
x = x - 1;
x = x | (x >> 1);
x = x | (x >> 2);
x = x | (x >> 4);
x = x | (x >> 8);
x = x | (x >> 16);
return x + 1;
}
public static UInt32 NumberOfBitsNeeded(UInt32 PowerOfTwo)
{
if (PowerOfTwo > 0)
{
for (UInt32 i = 0, mask = 1; ; i++, mask <<= 1)
{
if ((PowerOfTwo & mask) != 0)
return i;
}
}
return 0; // error
}
public static UInt32 ReverseBits(UInt32 index, UInt32 NumBits)
{
UInt32 i, rev;
for (i = rev = 0; i < NumBits; i++)
{
rev = (rev << 1) | (index & 1);
index >>= 1;
}
return rev;
}
public struct Complex
{
public double Re, Im;
public Complex(double x, double y)
{
this.Re = x; this.Im = y;
}
public Complex Mul(Complex C2)
{
Complex aux = new Complex();
aux.Re = this.Re * C2.Re - this.Im * C2.Im;
aux.Im = this.Re * C2.Im + this.Im * C2.Re;
return aux;
}
public Complex Add(Complex C2)
{
Complex aux = new Complex();
aux.Re = this.Re + C2.Re;
aux.Im = this.Im + C2.Im;
return aux;
}
public Complex Sub(Complex C2)
{
Complex aux = new Complex();
aux.Re = this.Re - C2.Re;
aux.Im = this.Im - C2.Im;
return aux;
}
public double Magnitude()
{
double Len = Math.Sqrt(this.Re * this.Re + this.Im * this.Im);
double bb = Math.Abs(Math.Tan(this.Re / Len)) / Math.Tan(this.Re / Len);
return (Len * bb );
}
public Complex Rev()
{
Complex aux = new Complex();
aux.Re = this.Re;
aux.Im = -1.0d * this.Im;
return aux;
}
}
public List<complex> Cos_Fun(int N)
{
List<complex> cc = new List<complex>(N);
Complex aux;
double c = 2.0d * DDC_PI / (double)N;
for (int i = 0; i < N; i++)
{
aux = new Complex(
Math.Cos((double)(3 * i) * c)
, Math.Sin((double)(6 * i * i) * c)
);
cc.Add(aux);
}
return cc;
}
public const Double DDC_PI = 3.14159265358979323846;
UInt32 Block_Size = 2;
public Complex Get_W(int block_size, int index)
{
Complex c = new Complex(1.0d, 1.0d);
c.Re = c.Re * Math.Cos((-2 * DDC_PI / block_size) * index);
c.Im = c.Im * Math.Sin((-2 * DDC_PI / block_size) * index);
return c;
}
public List<complex> Init_FFT(List<complex> x)
{
Complex auxx = new Complex(0.0d, 0.0d);
List<complex> aux = new List<complex>(x.Count);
UInt32 count;
if (IsPowerOfTwo((UInt32)x.Count))
{
count = (UInt32)x.Count;
}
else
{
count = NextPowerOfTwo((UInt32)x.Count);
}
UInt32 b = NumberOfBitsNeeded(count);
aux = new List<complex>((int)count);
Complex cccc= new Complex();
for (int i = 0; i < (int)count; i++)
{
aux.Add(cccc);
}
for (int i = x.Count; i < count; i++)
{
x.Add(auxx);
}
for (int i = 0; i < count; i++)
{
aux[i] = (x[(int)ReverseBits((UInt32)i, b)]);
}
x.Clear();
return aux;
}
public List<complex> FFT_Calc(List<complex> Xx)
{
Block_Size = 2; int index = 0; int indexx = 0;
int Block_num = Xx.Count / (int)Block_Size;
Complex auxx = new Complex(0.0d, 0.0d);
List<complex> aux = new List<complex>(Xx.Count);
for (int i = 0; i < Xx.Count; i++)
aux.Add(auxx);
int test = 0;
while (Block_Size <= Xx.Count)
{
index = 0;
Block_num = Xx.Count / (int)Block_Size;
for (int i = 0; i < Block_num; i++)
{
indexx = 0; index = i * (int)Block_Size;
for (int j = 0; j < (int)Block_Size / 2; j++)
{
//first
auxx = Get_W((int)Block_Size, indexx);
aux[index] = Xx[index];
auxx = auxx.Mul(Xx[index + (int)Block_Size / 2]);
aux[index] = aux[index].Add(auxx);
test++;
//second
auxx = Get_W((int)Block_Size, indexx + (int)Block_Size / 2);
aux[index + (int)Block_Size / 2] = Xx[index];
auxx = auxx.Mul(Xx[index + (int)Block_Size / 2]);
aux[index + (int)Block_Size / 2] = aux[index + (int)Block_Size / 2].Add(auxx);
test++;
indexx++;
index++;
}
}
for (int k = 0; k < aux.Count; k++)
Xx[k] = aux[k];
Block_Size <<= 1;
}
//for (int k = 0; k < aux.Count; k++)
// Xx[k] = aux[k];
return aux;
}
public List<complex> Inv_FFT_Calc(List<complex> Xx)
{
Block_Size = 2; int index = 0; int indexx = 0;
int Block_num = Xx.Count / (int)Block_Size;
Complex auxx = new Complex(0.0d, 0.0d);
List<complex> aux = new List<complex>(Xx.Count);
for (int i = 0; i < Xx.Count; i++)
aux.Add(auxx);
int test = 0;
while (Block_Size <= Xx.Count)
{
index = 0;
Block_num = Xx.Count / (int)Block_Size;
for (int i = 0; i < Block_num; i++)
{
indexx = 0; index = i * (int)Block_Size;
for (int j = 0; j < (int)Block_Size / 2; j++)
{
//first
auxx = Get_W((int)Block_Size, -indexx);
aux[index] = Xx[index];
auxx = auxx.Mul(Xx[index + (int)Block_Size / 2]);
aux[index] = aux[index].Add(auxx);
test++;
//second
auxx = Get_W((int)Block_Size, -indexx + (int)Block_Size / 2);
aux[index + (int)Block_Size / 2] = Xx[index];
auxx = auxx.Mul(Xx[index + (int)Block_Size / 2]);
aux[index + (int)Block_Size / 2] = aux[index + (int)Block_Size / 2].Add(auxx);
test++;
indexx++;
index++;
}
}
for (int k = 0; k < aux.Count; k++)
Xx[k] = aux[k];
Block_Size <<= 1;
}
Complex c = new Complex(1.0d / aux.Count, 0.0d);
List<complex> auxxx = new List<complex>(aux.Count);
for (int k = 0; k < aux.Count; k++)
{
c.Re = aux[k].Re / (double)aux.Count; c.Im = 0.0d;
auxxx.Add(c);
}
//UInt32 b = NumberOfBitsNeeded((uint)aux.Count);
//for (int k = 0; k < aux.Count; k++)
//{
// Xx[k] = aux[k];
// //Xx[(int)ReverseBits((UInt32)k, b)] = aux[k];
//}
return auxxx;
}
public System.Drawing.Bitmap Draw_Spectral(float[] Percent, int From, int To, Color c, System.Drawing.Size Bitmap_Size)
{
Bitmap bb = new Bitmap(Bitmap_Size.Width, Bitmap_Size.Height);
if (Percent != null)
{
System.Drawing.Graphics g = Graphics.FromImage(bb);
g.SmoothingMode = System.Drawing.Drawing2D.SmoothingMode.HighQuality;
g.Clear(Color.White);
float max = 0.0f;
for (int i = From; i < To; i++)
{
if (max < Percent[i])
max = Percent[i];
}
float xStep = ((float)bb.Width - 10.0f) / (float)(To - From);
System.Drawing.SolidBrush sb1 = new SolidBrush(Color.LightBlue);
System.Drawing.Pen p1 = new Pen(c, 1.5f);
float yStep = 1.0f * ((float)bb.Height - 10.0f) / max;
float x = 5.0f, y = bb.Height - 5.0f;
for (int i = From; i < To; i++)
{
g.DrawLine(p1
, x
, bb.Height - 5.0f
, x
, y - (Percent[i] * yStep));
x += xStep;
}
}
return bb;
}
public void Draw_Wave(List<complex> Spectral, System.Windows.Forms.Panel p, Color c, float D_Width)
{
if (Spectral != null)
{
System.Drawing.Graphics g = p.CreateGraphics();
g.SmoothingMode = System.Drawing.Drawing2D.SmoothingMode.HighSpeed;
g.Clear(Color.White);
float max = 0.0f;
for (int i = 0; i < Spectral.Count; i++)
{
if (max < Spectral[i].Magnitude())
max = (float)Spectral[i].Magnitude();
}
float xStep = ((float)p.Width - 10.0f) / Spectral.Count;
System.Drawing.Pen p1 = new Pen(c, D_Width);
float yStep = 1.0f * ((float)p.Height - 10.0f) / max;
float x = 5.0f, y = p.Height - 5.0f;
for (int i = 0; i < Spectral.Count; i++)
{
g.DrawLine(p1
, x
, p.Height - 5.0f
, x
, y - ((float)Spectral[i].Magnitude() * yStep));
x += xStep;
}
}
}
public enum Complex_Part
{
Real,
Image,
Magenda
}
public void Draw_Spectral(List<complex> Spectral, System.Windows.Forms.Panel p,Complex_Part cp, Color c, float D_Width)
{
if (Spectral != null)
{
System.Drawing.Graphics g = p.CreateGraphics();
g.SmoothingMode = System.Drawing.Drawing2D.SmoothingMode.HighSpeed;
g.Clear(Color.White);
float max = 0.0f; float min = 0.0f; ;
int freq_step = (Spectral.Count) * 10 / 100;
int f_s = freq_step;
if (cp == Complex_Part.Image)
{
for (int i = 0; i < (Spectral.Count); i++)
{
if (max < Spectral[i].Im)
max = (float)Spectral[i].Im;
if (min > Spectral[i].Im)
min = (float)Spectral[i].Im;
}
}
else if (cp == Complex_Part.Real)
{
for (int i = 0; i < (Spectral.Count); i++)
{
if (max < Spectral[i].Re)
max = (float)Spectral[i].Re;
if (min > Spectral[i].Re)
min = (float)Spectral[i].Re;
}
}
else if (cp == Complex_Part.Magenda)
{
for (int i = 0; i < (Spectral.Count); i++)
{
if (max < Spectral[i].Magnitude())
max = (float)Spectral[i].Magnitude();
if (min > Spectral[i].Magnitude())
min = (float)Spectral[i].Magnitude();
}
}
float xStep = ((float)p.Width - 10.0f) / (Spectral.Count);
System.Drawing.Pen p1 = new Pen(c, D_Width);
System.Drawing.Pen p2 = new Pen(Color.Black, 1.0f);
float yStep = 1.0f * ((float)p.Height - 20.0f) / (max - min);
float x = 5.0f, y = p.Height - (10.0f - yStep * min);
Font f = new Font("Tahoma", 6.5f, FontStyle.Regular);
SolidBrush b = new SolidBrush(Color.Black);
for (int i = 0; i < (Spectral.Count); i++)
{
if (i == f_s)
{
g.DrawString(f_s + "", f, b, x - 25.0f, 5.0f);
f_s += freq_step;
}
g.DrawLine(p2
, x - xStep
, p.Height - (10.0f - yStep * min)
, x + xStep
, p.Height - (10.0f - yStep * min));
if (cp == Complex_Part.Image)
{
g.DrawLine(p1
, x
, p.Height - (10.0f - yStep * min)
, x
, y - (((float)Spectral[i].Im) * yStep));
}
else if (cp == Complex_Part.Real)
{
g.DrawLine(p1
, x
, p.Height - (10.0f - yStep * min)
, x
, y - (((float)Spectral[i].Re) * yStep));
}
else if (cp == Complex_Part.Magenda)
{
g.DrawLine(p1
, x
, p.Height - (10.0f - yStep * min)
, x
, y - (((float)Spectral[i].Magnitude()) * yStep));
}
x += xStep;
}
}
}
public void Draw_Spectral(List<complex> Spectral, System.Windows.Forms.Panel p, Color c, float D_Width)
{
if (Spectral != null)
{
System.Drawing.Graphics g = p.CreateGraphics();
g.SmoothingMode = System.Drawing.Drawing2D.SmoothingMode.HighSpeed;
g.Clear(Color.White);
float max = 0.0f; float min = 0.0f; ;
int freq_step = (Spectral.Count / 2) * 10 / 100;
int f_s = freq_step;
for (int i = 0; i < (Spectral.Count/2); i++)
{
if (max < Spectral[i].Magnitude())
max = (float)Spectral[i].Magnitude();
if (min > Spectral[i].Magnitude())
min = (float)Spectral[i].Magnitude();
}
float xStep = ((float)p.Width - 10.0f) / (Spectral.Count / 2);
System.Drawing.Pen p1 = new Pen(c, D_Width);
System.Drawing.Pen p2 = new Pen(Color.Black, 1.0f);
float yStep = 1.0f * ((float)p.Height - 20.0f) / (max - min);
float x = 5.0f, y = p.Height - (10.0f - yStep * min);
Font f = new Font("Tahoma", 6.5f, FontStyle.Regular);
SolidBrush b = new SolidBrush(Color.Black);
for (int i = 0; i < (Spectral.Count / 2); i++)
{
if (i == f_s)
{
g.DrawString(f_s + "", f, b, x - 25.0f, 5.0f);
f_s += freq_step;
}
g.DrawLine(p1
, x
, p.Height - (10.0f - yStep * min)
, x
, y - (((float)Spectral[i].Magnitude()) * yStep ));
g.DrawLine(p2
, x - xStep
, p.Height - (10.0f - yStep * min)
, x + xStep
, p.Height - (10.0f - yStep * min));
x += xStep;
}
}
}
public void Draw_Spectral(double[] Spectral, System.Windows.Forms.Panel p, Color c, float D_Width)
{
if (Spectral != null)
{
System.Drawing.Graphics g = p.CreateGraphics();
g.SmoothingMode = System.Drawing.Drawing2D.SmoothingMode.HighSpeed;
g.Clear(Color.White);
float max = 0.0f;
int freq_step = (Spectral.Length) * 5 / 100;
int f_s = freq_step;
for (int i = 0; i < Spectral.Length; i++)
{
if (max < Math.Abs(Spectral[i]))
max = (float)Math.Abs(Spectral[i]);
}
float xStep = ((float)p.Width - 10.0f) / (Spectral.Length);
System.Drawing.Pen p1 = new Pen(c, D_Width);
float yStep = 1.0f * ((float)p.Height - 10.0f) / max;
float x = 5.0f, y = p.Height - 5.0f;
Font f = new Font("Tahoma", 6.5f, FontStyle.Regular);
SolidBrush b = new SolidBrush(Color.Black);
for (int i = 0; i < (Spectral.Length); i++)
{
if (i == f_s)
{
g.DrawString(f_s + "", f, b, x - 25.0f, 5.0f);
f_s += freq_step;
}
g.DrawLine(p1
, x
, p.Height - 5.0f
, x
, y - ((float)Math.Abs(Spectral[i]) * yStep));
x += xStep;
}
}
}
public List<complex> InitRSine(int n)
{
List<complex> Data_In = new List<complex>();
Complex aux = new Complex();
for (int i = 0; i < n; i++)
{
aux = new Complex();
aux.Re =
Math.Cos((double)(45.0) * i * (0.5 * Math.PI / n))
+ 4.0d * Math.Cos((double)(60.0) * i * (0.1 * Math.PI / n))
//+ Math.Cos((double)(20.0) * i * (2.0 * Math.PI / n))
//+ Math.Cos((double)(10.0) * i * (2.0 * Math.PI / n))
//+ Math.Cos((double)(5.0) * i * (2.0 * Math.PI / n))
;
aux.Im = 0.0d;
Data_In.Add(aux);
}
return Data_In;
}
}
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