cscの作法 その188

# 概要
cscの作法、調べてみた。
練習問題やってみた。

# 練習問題
fm波に、fft掛けて、グラフ化せよ。

# 写真

![image.png](https://qiita-image-store.s3.ap-northeast-1.amazonaws.com/0/18104/967fdde5-ea75-4e69-5e60-11caf72f730a.png)


# サンプルコード

```

using System;
using System.Collections.Generic;
using System.Drawing;
using System.Windows.Forms;

namespace app
{
	class form1: Form {
		public static void FFT(double[] inputRe, double[] inputIm, out double[] outputRe, out double[] outputIm, int bitSize) {
			int dataSize = 1 << bitSize;
			int[] reverseBitArray = BitScrollArray(dataSize);
			outputRe = new double[dataSize];
			outputIm = new double[dataSize];
			for (int i = 0; i < dataSize; i++)
			{
				outputRe[i] = inputRe[reverseBitArray[i]];
				outputIm[i] = inputIm[reverseBitArray[i]];
			}
			for (int stage = 1; stage <= bitSize; stage++)
			{
				int butterflyDistance = 1 << stage;
				int numType = butterflyDistance >> 1;
				int butterflySize = butterflyDistance >> 1;
				double wRe = 1.0;
				double wIm = 0.0;
				double uRe = System.Math.Cos(System.Math.PI / butterflySize);
				double uIm = -System.Math.Sin(System.Math.PI / butterflySize);
				for (int type = 0; type < numType; type++)
				{
					for (int j = type; j < dataSize; j += butterflyDistance)
					{
						int jp = j + butterflySize;
						double tempRe = outputRe[jp] * wRe - outputIm[jp] * wIm;
						double tempIm = outputRe[jp] * wIm + outputIm[jp] * wRe;
						outputRe[jp] = outputRe[j] - tempRe;
						outputIm[jp] = outputIm[j] - tempIm;
						outputRe[j] += tempRe;
						outputIm[j] += tempIm;
					}
					double tempWRe = wRe * uRe - wIm * uIm;
					double tempWIm = wRe * uIm + wIm * uRe;
					wRe = tempWRe;
					wIm = tempWIm;
				}
			}
		}
		private static int[] BitScrollArray(int arraySize) {
			int[] reBitArray = new int[arraySize];
			int arraySizeHarf = arraySize >> 1;
			reBitArray[0] = 0;
			for (int i = 1; i < arraySize; i <<= 1)
			{
				for (int j = 0; j < i; j++)
					reBitArray[j + i] = reBitArray[j] + arraySizeHarf;
				arraySizeHarf >>= 1;
			}
			return reBitArray;
		}
		private double[] po = new double[256];
		private double[] data = new double[256];
		public form1() {
			this.Text = "fft";
			this.ClientSize = new Size(400, 400);
			Button btn1 = new Button();
			btn1.Location = new Point(320, 360);
			btn1.Text = "run";
			btn1.Click += btn1_Click;
			Controls.AddRange(new Control[] {
				btn1
			});
		}
		void btn1_Click(object sender, System.EventArgs e) {
			const int size = 256;
			double[] re = new double[size];
			double[] im = new double[size];
			for (int i = 0; i < size; i++)
			{
				data[i] = Math.Sin(2 * Math.PI * Math.Cos(2 * 10 * i * Math.PI / 1800) + 2 * 200 * i * Math.PI / 1800);
			}
			FFT(data, im, out re, out im, 8);
			for (int i = 0; i < size; i++)
			{
				po[i] = Math.Sqrt(re[i] * re[i] + im[i] * im[i]);
			}
			this.Invalidate();
		}
		protected override void OnPaint(PaintEventArgs e) {
			Graphics g = e.Graphics;
			Pen pen0 = new Pen(Color.Red, 2);
			Pen pen1 = new Pen(Color.Black, 2);
			SolidBrush brush = new SolidBrush(Color.Yellow);
			float y2 = 250;
			for (int i = 0; i < 256; i++)
			{
				float y0 = (float)(50 + po[i] * 1.0);
				if (i < 128)
					g.DrawLine(pen0, 50 + i, 50, 50 + i, y0);
				float y1 = (float)(250 + data[i] * 100);
				g.DrawLine(pen1, 50 + i, y2, 50 + i, y1);
				y2 = y1;
			}
		}
		[STAThread]
		public static void Main() {
			Application.Run(new form1());
		}
	}
}


```


以上。