#pragma once
#include <complex>
#include <vector>
class Transform
{
public:
static void VandermondeDFT(
int n,
std::vector<std::complex<double>>& a,
std::vector<std::complex<double>>& y);
static void InverseVandermondeDFT(
int n,
std::vector<std::complex<double>>& a,
std::vector<std::complex<double>>& y);
static std::vector<std::complex<double>> DFT(
std::vector<double>& x, std::vector<double>& f);
static std::vector<double> InverseDFT(
std::vector<double>& f,
std::vector<std::complex<double>>& X);
/*
* Reference: "Elementary Numerical Analysis:
* An Algorithmic Approach Third Edition" (c)
* 1980 by S. D. Conte and Carl de Boor
* Section 6.5 pages 268 - 277 and Section 6.6
* pages 277 - 283
* Input to FFT
* Z1, Z2 complex n-vectors
* n the length of the vectors
* inzee
* = 1 transform in Z1
* = 2 transform in Z2
* Constructs the discrete Fourier transform in the Cooley-
* Tukey way, but with a twist.
*/
static void FFT(
std::vector<std::complex<double>>& Z1,
int& after, int& now, int& before, int& inzee,
std::vector<std::complex<double>>& Z2);
/*
* This computes an in - place complex - to - complex FFT
* x and y are the real and imaginary arrays of 2^m points.
* dir = 1 gives forward transform
* dir = -1 gives reverse transform
* see http://astronomy.swin.edu.au/~pbourke/analysis/dft/
* Website no longer exists
*/
static void FFT(short dir, int m,
std::vector<double>& x, std::vector<double>& y);
/*
* Reference: "Introduction to Algorithms" by
* Thomas H. Cormen, Charles E. Leiserson, and
* Ronald L. Rivest, pages 794 - 795
*/
static void IterativeFFT(
std::vector<std::complex<double>>& a,
std::vector<std::complex<double>>& A);
/*
* Reference: "Introduction to Algorithms" by
* Thomas H. Cormen, Charles E. Leiserson, and
* Ronald L. Rivest, page 788
*/
static std::vector<std::complex<double>> RecursiveFFT(
std::vector<std::complex<double>>& a);
};
#include "Transform.h"
void Transform::VandermondeDFT(
int n,
std::vector<std::complex<double>>& a,
std::vector<std::complex<double>>& y)
{
double pi = 4.0 * atan(1.0);
std::complex<double> z(0.0, 2.0 * pi / n);
std::complex<double> omegaN = exp(z);
std::vector<std::vector<std::complex<double>>> V(n);
for (int k = 0; k < n; k++)
{
V[k].resize(n);
for (int j = 0; j < n; j++)
{
V[k][j] = std::pow(omegaN, k * j);
}
}
for (int k = 0; k < n; k++)
{
std::complex<double> sum = 0.0;
for (int j = 0; j < n; j++)
{
sum += V[k][j] * a[j];
}
y[k] = sum;
}
}
void Transform::InverseVandermondeDFT(
int n,
std::vector<std::complex<double>>& a,
std::vector<std::complex<double>>& y)
{
double pi = 4.0 * atan(1.0);
std::complex<double> nc = { static_cast<double>(n), 0.0 };
std::complex<double> z(0.0, 2.0 * pi / n);
std::complex<double> omegaN = exp(z);
std::vector<std::vector<std::complex<double>>> invV(n);
for (int k = 0; k < n; k++)
{
invV[k].resize(n);
for (int j = 0; j < n; j++)
{
invV[k][j] = std::pow(omegaN, -k * j);
}
}
for (int k = 0; k < n; k++)
{
std::complex<double> sum = 0.0;
for (int j = 0; j < n; j++)
{
sum += invV[k][j] * y[j];
}
a[k] = sum / nc;
}
}
std::vector<std::complex<double>> Transform::DFT(
std::vector<double>& x, std::vector<double>& f)
{
int length = static_cast<int>(x.size());
double pi = 4.0 * atan(1.0);
double pi2oN = 2.0 * pi / length;
int k, n;
std::vector<double> X(length);
std::vector<double> Y(length);
std::vector<std::complex<double>> Z(length);
f.resize(length);
for (k = 0; k < length; k++)
{
X[k] = Y[k] = 0;
for (n = 0; n < length; n++)
{
X[k] += x[n] * cos(pi2oN * k * n);
Y[k] -= x[n] * sin(pi2oN * k * n);
}
f[k] = pi2oN * k;
X[k] /= length;
Y[k] /= length;
Z[k] = { X[k], Y[k] };
}
return Z;
}
std::vector<double> Transform::InverseDFT(
std::vector<double>& f,
std::vector<std::complex<double>>& X)
{
double imag = 0.0;
int length = static_cast<int>(X.size());
std::vector<double> x(length);
for (int n = 0; n < length; n++)
{
imag = x[n] = 0.0;
for (int k = 0; k < length; k++)
{
x[n] += X[k]._Val[0] * cos(f[k] * n)
- X[k]._Val[1] * sin(f[k] * n);
imag += X[k]._Val[0] * sin(f[k] * n)
+ X[k]._Val[1] * cos(f[k] * n);
}
}
return x;
}
static void FFTStep(
std::vector<std::complex<double>>& Zinp,
int after, int now, int before,
std::vector<std::complex<double>>& Zout)
{
double angle = 0.0, ratio = 0.0;
double twoPi = 2.0 * 4.0 * atan(1.0);
int ia = 0, ib = 0, inp = 0, j = 0;
std::complex<double> arg = 1.0, omega = 0, value = 0;
angle = twoPi / ((now + 1) * (after + 1));
omega = std::complex<double>(cos(angle), -sin(angle));
int address = 1;
for (int i = 1; i <= now; i++)
{
for (int j = 1; j <= after; j++)
{
for (int k = 1; k <= before; k++)
{
address = i * j * k;
if (address < Zout.size())
Zout[address] = { 0.0, 0.0 };
}
}
}
address = 1;
for (int j = 1; j <= now; j++)
{
for (ia = 1; ia <= after; ia++)
{
for (ib = 1; ib <= before; ib++)
{
int address = j * ia * ib;
if (address < Zinp.size())
value = Zinp[address];
for (inp = now - 1; inp >= 1; inp--)
{
address = ia * ib * inp;
if (address < Zinp.size())
value = value * arg + Zinp[address];
}
address = ia * j * ib;
if (address < Zout.size())
Zout[address] = value;
}
arg *= omega;
}
}
}
void Transform::FFT(
std::vector<std::complex<double>>& Z1,
int& after, int& now, int& before, int& inzee,
std::vector<std::complex<double>>& Z2)
{
std::vector<int> prime =
{ 0, 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43,
47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97 };
int next = 1, nextmx = 25;
after = 1;
before = (int)Z1.size();
now = 1;
Label10:
if (before / prime[next] * prime[next] < before)
{
next++;
if (next <= nextmx)
goto Label10;
else
{
now = before;
before = 1;
}
}
else
{
now = prime[next];
before /= prime[next];
}
if (inzee == 1)
FFTStep(Z1, after, now, before, Z2);
else
FFTStep(Z2, after, now, before, Z1);
inzee = 3 - inzee;
if (before == 1)
return;
after *= now;
goto Label10;
}
void Transform::FFT(short dir, int m,
std::vector<double>& x, std::vector<double>& y)
{
int n, i, i1, j, k, i2, l, l1, l2;
double c1, c2, tx, ty, t1, t2, u1, u2, z;
// Calculate the number of points
n = 1;
for (i = 0; i < m; i++)
n *= 2;
// Do the bit reversal
i2 = n >> 1;
j = 0;
for (i = 0; i < n - 1; i++)
{
if (i < j)
{
tx = x[i];
ty = y[i];
x[i] = x[j];
y[i] = y[j];
x[j] = tx;
y[j] = ty;
}
k = i2;
while (k <= j)
{
j -= k;
k >>= 1;
}
j += k;
}
// Compute the FFT
c1 = -1.0;
c2 = 0.0;
l2 = 1;
for (l = 0; l < m; l++)
{
l1 = l2;
l2 <<= 1;
u1 = 1.0;
u2 = 0.0;
for (j = 0; j < l1; j++)
{
for (i = j; i < n; i += l2)
{
i1 = i + l1;
t1 = u1 * x[i1] - u2 * y[i1];
t2 = u1 * y[i1] + u2 * x[i1];
x[i1] = x[i] - t1;
y[i1] = y[i] - t2;
x[i] += t1;
y[i] += t2;
}
z = u1 * c1 - u2 * c2;
u2 = u1 * c2 + u2 * c1;
u1 = z;
}
c2 = sqrt((1.0 - c1) / 2.0);
if (dir == 1)
c2 = -c2;
c1 = sqrt((1.0 + c1) / 2.0);
}
// Scaling for forward transform
if (dir == 1)
{
for (i = 0; i < n; i++)
{
x[i] /= n;
y[i] /= n;
}
}
}
static void FFTBase(
std::vector<std::complex<double>> a,
std::vector<std::complex<double>> A)
{
double pi = 4.0 * atan(1.0);
int n = static_cast<int>(a.size());
for (int s = 1; s <= log2(n); s++)
{
int m = static_cast<int>(pow(2, s));
std::complex<double> z(0.0, 2.0 * pi / m);
std::complex<double> omegaM = exp(z);
for (int k = 0; k <= n - 1; k += m)
{
std::complex<double> omega = { 1.0, 0.0 };
for (int j = 0; j <= m / 2 - 1; j++)
{
std::complex<double> t = omega * A[k + j + m / 2];
std::complex<double> u = A[k + j];
std::complex<double> jc = { static_cast<double>(j), 0.0 };
A[k + j] = u + jc;
A[k + j + m / 2] = u - t;
omega *= omegaM;
}
}
}
}
static int Reverse(int k)
{
int digits[32] = { 0 }, i = 0;
while (k > 0)
{
int digit = k & 1;
k >>= 1;
digits[i++] = digit;
}
int result = digits[0];
for (int j = 1; j < i; j++)
result = result * 2 + digits[j];
return result;
}
static void BitReverseCopy(
std::vector<std::complex<double>>& a,
std::vector<std::complex<double>>& A)
{
int n = static_cast<int>(a.size());
for (int k = 0; k <= n - 1; k++)
A[Reverse(k)] = a[k];
}
void Transform::IterativeFFT(
std::vector<std::complex<double>>& a,
std::vector<std::complex<double>>& A)
{
BitReverseCopy(a, A);
double pi = 4.0 * atan(1.0);
int n = static_cast<int>(a.size());
for (int s = 1; s <= static_cast<int>(log2(n)); s++)
{
int m = static_cast<int>(pow(2.0, s));
std::complex<double> z(0.0, 2.0 * pi / m);
std::complex<double> omegaM = exp(z);
std::complex<double> omega = { 1.0, 0.0 };
for (int j = 0; j <= m / 2 - 1; j++)
{
for (int k = j; k <= n - 1; k += m)
{
std::complex<double> t = omega * A[k + m / 2];
std::complex<double> u = A[k];
A[k] = u + t;
A[k + m / 2] = u - t;
omega *= omegaM;
}
}
}
}
std::vector<std::complex<double>> Transform::RecursiveFFT(
std::vector<std::complex<double>>& a)
{
int n = static_cast<int>(a.size());
if (n == 1)
return a;
std::vector<std::complex<double>> a0;
std::vector<std::complex<double>> a1;
std::vector<std::complex<double>> y0;
std::vector<std::complex<double>> y1;
for (int i = 0; i <= n - 2; i++)
a0.push_back(a[i]);
for (int i = 1; i <= n - 1; i++)
a1.push_back(a[i]);
y0 = RecursiveFFT(a0);
y1 = RecursiveFFT(a1);
double pi = 4.0 * atan(1.0);
std::complex<double> z(0.0, 2.0 * pi / n);
std::complex<double> omegaN = exp(z);
std::complex<double> omega(1.0, 0.0);
std::vector<std::complex<double>> y(n, 0.0);
for (int k = 0; k <= n / 2 - 1; k++)
{
y[k] = y0[k] + omega * y1[k];
y[(long long)k + n / 2] = y0[k] - omega * y1[k];
omega *= omegaN;
}
return y;
}
// FilteringNoisySignal.cpp : Defines the entry point for the application.
// Copyright (c) Monday, June 15, 2026 by James Pate Williams, Jr.
// Reference: "Numerical Computation 2: Methods, Software and Analysis"
// (c) 1997 by Christoph W. Ueberhuber pages 52-53.
#include "framework.h"
#include "Resource.h"
#include "FilteringNoisySignal.h"
#include "Transform.h"
#include <float.h>
#include <cmath>
#include <vector>
#define MAX_LOADSTRING 100
typedef struct tagPoint2d
{
double t, f;
} Point2d, * PPoint2d;
// Global Variables:
HINSTANCE hInst; // current instance
WCHAR szTitle[MAX_LOADSTRING]; // The title bar text
WCHAR szWindowClass[MAX_LOADSTRING]; // the main window class name
char thresholdText[128]; // threshold buffer
char noisePCText[128]; // noise % buffer
double threshold; // noise threshold
double noisePercent; // noise parameter
int Npts = 1024; // number of data points
std::vector<double> originalSignal; // original signal
std::vector<double> perturbedSignalReal; // perturbed signal real part
std::vector<double> perturbedSignalImag; // perturbed signal imag part
std::vector<double> recoveredSignalReal; // recovered signal after filtering
std::vector<double> recoveredSignalImag; // recovered signal after filtering
std::vector<Point2d> points; // plotting data
// Forward declarations of functions included in this code module:
ATOM MyRegisterClass(HINSTANCE hInstance);
BOOL InitInstance(HINSTANCE, int);
LRESULT CALLBACK WndProc(HWND, UINT, WPARAM, LPARAM);
INT_PTR CALLBACK About(HWND, UINT, WPARAM, LPARAM);
INT_PTR CALLBACK InputDialog(HWND, UINT, WPARAM, LPARAM);
INT_PTR CALLBACK DrawGraphDialog(HWND, UINT, WPARAM, LPARAM);
int APIENTRY wWinMain(_In_ HINSTANCE hInstance,
_In_opt_ HINSTANCE hPrevInstance,
_In_ LPWSTR lpCmdLine,
_In_ int nCmdShow)
{
UNREFERENCED_PARAMETER(hPrevInstance);
UNREFERENCED_PARAMETER(lpCmdLine);
// TODO: Place code here.
// Initialize global strings
LoadStringW(hInstance, IDS_APP_TITLE, szTitle, MAX_LOADSTRING);
LoadStringW(hInstance, IDC_FILTERINGNOISYSIGNAL, szWindowClass, MAX_LOADSTRING);
MyRegisterClass(hInstance);
// Perform application initialization:
if (!InitInstance (hInstance, nCmdShow))
{
return FALSE;
}
HACCEL hAccelTable = LoadAccelerators(hInstance, MAKEINTRESOURCE(IDC_FILTERINGNOISYSIGNAL));
MSG msg;
// Main message loop:
while (GetMessage(&msg, nullptr, 0, 0))
{
if (!TranslateAccelerator(msg.hwnd, hAccelTable, &msg))
{
TranslateMessage(&msg);
DispatchMessage(&msg);
}
}
return (int) msg.wParam;
}
//
// FUNCTION: MyRegisterClass()
//
// PURPOSE: Registers the window class.
//
ATOM MyRegisterClass(HINSTANCE hInstance)
{
WNDCLASSEXW wcex = { 0 };
wcex.cbSize = sizeof(WNDCLASSEX);
wcex.style = CS_HREDRAW | CS_VREDRAW;
wcex.lpfnWndProc = WndProc;
wcex.cbClsExtra = 0;
wcex.cbWndExtra = 0;
wcex.hInstance = hInstance;
wcex.hIcon = LoadIcon(hInstance, MAKEINTRESOURCE(IDI_FILTERINGNOISYSIGNAL));
wcex.hCursor = LoadCursor(nullptr, IDC_ARROW);
wcex.hbrBackground = (HBRUSH)(COLOR_WINDOW+1);
wcex.lpszMenuName = MAKEINTRESOURCEW(IDC_FILTERINGNOISYSIGNAL);
wcex.lpszClassName = szWindowClass;
wcex.hIconSm = LoadIcon(wcex.hInstance, MAKEINTRESOURCE(IDI_SMALL));
return RegisterClassExW(&wcex);
}
//
// FUNCTION: InitInstance(HINSTANCE, int)
//
// PURPOSE: Saves instance handle and creates main window
//
// COMMENTS:
//
// In this function, we save the instance handle in a global variable and
// create and display the main program window.
//
BOOL InitInstance(HINSTANCE hInstance, int nCmdShow)
{
hInst = hInstance; // Store instance handle in our global variable
HWND hWnd = CreateWindowW(szWindowClass, szTitle, WS_OVERLAPPEDWINDOW,
CW_USEDEFAULT, 0, CW_USEDEFAULT, 0, nullptr, nullptr, hInstance, nullptr);
if (!hWnd)
{
return FALSE;
}
ShowWindow(hWnd, nCmdShow);
UpdateWindow(hWnd);
return TRUE;
}
static double f(double t)
{
double pi = 4.0 * atan(1.0);
double arg = 2.0 * pi * t;
return 2.0 * sin(arg / 500.0) + cos(arg / 200.0) -
0.5 * sin(arg / 50.0);
}
//
// FUNCTION: WndProc(HWND, UINT, WPARAM, LPARAM)
//
// PURPOSE: Processes messages for the main window.
//
// WM_COMMAND - process the application menu
// WM_PAINT - Paint the main window
// WM_DESTROY - post a quit message and return
//
//
LRESULT CALLBACK WndProc(HWND hWnd, UINT message, WPARAM wParam, LPARAM lParam)
{
switch (message)
{
case WM_COMMAND:
{
int wmId = LOWORD(wParam);
// Parse the menu selections:
switch (wmId)
{
case IDM_ABOUT:
DialogBox(hInst, MAKEINTRESOURCE(IDD_ABOUTBOX), hWnd, About);
break;
case IDM_INPUT:
DialogBox(hInst, MAKEINTRESOURCE(IDD_INPUT_DIALOG), hWnd, InputDialog);
break;
case IDM_EXIT:
DestroyWindow(hWnd);
break;
default:
return DefWindowProc(hWnd, message, wParam, lParam);
}
}
break;
case WM_PAINT:
{
PAINTSTRUCT ps;
HDC hdc = BeginPaint(hWnd, &ps);
// TODO: Add any drawing code that uses hdc here...
EndPaint(hWnd, &ps);
}
break;
case WM_DESTROY:
PostQuitMessage(0);
break;
default:
return DefWindowProc(hWnd, message, wParam, lParam);
}
return 0;
}
// Message handler for about box.
INT_PTR CALLBACK About(HWND hDlg, UINT message, WPARAM wParam, LPARAM lParam)
{
UNREFERENCED_PARAMETER(lParam);
switch (message)
{
case WM_INITDIALOG:
return (INT_PTR)TRUE;
case WM_COMMAND:
if (LOWORD(wParam) == IDOK || LOWORD(wParam) == IDCANCEL)
{
EndDialog(hDlg, LOWORD(wParam));
return (INT_PTR)TRUE;
}
break;
}
return (INT_PTR)FALSE;
}
static void AddWhiteNoise(
int n, unsigned int seed)
{
double signalMin = DBL_MAX;
double signalMax = DBL_MIN;
std::vector<double> noise(n, 0.0);
perturbedSignalReal.resize(n, 0.0);
srand(seed);
for (int i = 0; i < n; i++)
{
if (originalSignal[i] < signalMin)
signalMin = originalSignal[i];
if (originalSignal[i] > signalMax)
signalMax = originalSignal[i];
}
for (int i = 0; i < n; i++)
noise[i] = (signalMax - signalMin) * rand() /
RAND_MAX + signalMin;
for (int i = 0; i < n; i++)
{
double newSignal = originalSignal[i] +
noisePercent * noise[i];
if (newSignal < signalMin)
newSignal = signalMin;
if (newSignal > signalMax)
newSignal = signalMax;
perturbedSignalReal[i] = newSignal;
}
}
static void Filter(
double threshold, int n, unsigned int seed, HWND hDlg)
{
double pi = 4.0 * atan(1.0);
double step = 2.0 * pi * 200.0 / n, t = 0;
points.clear();
for (int i = 0; i < n; i++)
{
double ft = f(t);
Point2d pt = { t, ft };
points.push_back(pt);
t += step;
}
DialogBox(hInst, MAKEINTRESOURCE(IDD_DRAW_GRAPH_DIALOG), hDlg,
DrawGraphDialog);
originalSignal.resize(n, 0.0);
for (int i = 0; i < n; i++)
originalSignal[i] = points[i].f;
AddWhiteNoise(n, seed);
points.clear();
t = 0;
for (int i = 0; i < n; i++)
{
double ft = perturbedSignalReal[i];
Point2d pt = { t, ft };
points.push_back(pt);
t += step;
}
DialogBox(hInst, MAKEINTRESOURCE(IDD_DRAW_GRAPH_DIALOG), hDlg,
DrawGraphDialog);
perturbedSignalImag.resize(n, 0.0);
recoveredSignalReal.resize(n, 0.0);
recoveredSignalImag.resize(n, 0.0);
Transform::FFT(+1, static_cast<int>(log2(n)),
perturbedSignalReal, perturbedSignalImag);
for (int i = 0; i < n; i++)
{
double magnitude2 =
perturbedSignalReal[i] *
perturbedSignalReal[i] +
perturbedSignalImag[i] *
perturbedSignalImag[i];
if (magnitude2 > threshold)
{
recoveredSignalReal[i] = perturbedSignalReal[i];
recoveredSignalImag[i] = perturbedSignalImag[i];
}
}
Transform::FFT(+1, static_cast<int>(log2(n)),
recoveredSignalReal, recoveredSignalImag);
points.clear();
t = 6 * step;
for (int i = 6; i < n - 6; i++)
{
double ft = recoveredSignalReal[i];
Point2d pt = { t, ft };
points.push_back(pt);
t += step;
}
DialogBox(hInst, MAKEINTRESOURCE(IDD_DRAW_GRAPH_DIALOG), hDlg,
DrawGraphDialog);
}
INT_PTR CALLBACK InputDialog(HWND hDlg, UINT message, WPARAM wParam, LPARAM lParam)
{
UNREFERENCED_PARAMETER(lParam);
switch (message)
{
case WM_INITDIALOG:
SetDlgItemText(hDlg, IDC_EDIT_THRESHOLD, L"1.0e-2");
SetDlgItemText(hDlg, IDC_EDIT_NOISE, L"0.25");
SetDlgItemText(hDlg, IDC_EDIT_N, L"1024");
return (INT_PTR)TRUE;
case WM_COMMAND:
if (LOWORD(wParam) == IDC_BUTTON_DRAW)
{
GetDlgItemTextA(hDlg, IDC_EDIT_THRESHOLD, thresholdText, 128);
threshold = atof(thresholdText);
GetDlgItemTextA(hDlg, IDC_EDIT_NOISE, noisePCText, 128);
noisePercent = atof(noisePCText);
Npts = GetDlgItemInt(hDlg, IDC_EDIT_N, FALSE, FALSE);
if (LOWORD(wParam) == IDC_BUTTON_DRAW)
{
Filter(threshold, Npts, 1, hDlg);
return (INT_PTR)TRUE;
}
}
if (LOWORD(wParam) == IDCANCEL)
{
EndDialog(hDlg, LOWORD(wParam));
return (INT_PTR)TRUE;
}
break;
}
return (INT_PTR)FALSE;
}
static void FindMinMax(
double& tMin, double& tMax,
double& fMin, double& fMax)
{
// uses global 2D double points structure
tMin = fMin = DBL_MAX;
tMax = fMax = DBL_MIN;
for (size_t i = 0; i < points.size(); i++)
{
Point2d pt = points[i];
double t = pt.t;
double f = pt.f;
if (t < tMin)
tMin = t;
if (t > tMax)
tMax = t;
if (f < fMin)
fMin = f;
if (f > fMax)
fMax = f;
}
}
static void DrawFormattedText(HDC hdc, char text[], RECT rect)
{
// Draw the text with formatting options
DrawTextA(hdc, text, -1, &rect, DT_SINGLELINE | DT_NOCLIP);
}
INT_PTR CALLBACK DrawGraphDialog(
HWND hDlg, UINT message, WPARAM wParam, LPARAM lParam)
{
UNREFERENCED_PARAMETER(lParam);
WCHAR line[256] = { };
switch (message)
{
case WM_INITDIALOG:
SetWindowText(hDlg, L"Graph Dialog");
return (INT_PTR)TRUE;
case WM_COMMAND:
if (LOWORD(wParam) == IDOK || LOWORD(wParam) == IDCANCEL)
{
EndDialog(hDlg, LOWORD(wParam));
return (INT_PTR)TRUE;
}
break;
case WM_PAINT:
double h = 0;
double tMax = 0, tMin = 0, fMax = 0, fMin = 0;
FindMinMax(tMin, tMax, fMin, fMax);
float tSpan = (float)(tMax - tMin);
float fSpan = (float)(fMax - fMin);
RECT rect = { };
GetClientRect(hDlg, &rect);
float width = (float)(rect.right - rect.left + 1);
float height = (float)(rect.bottom - rect.top - 32 + 1);
float st0 = 2.0f * width / 16.0f;
float st1 = 14.0f * width / 16.0f;
float sf0 = 2.0f * height / 16.0f;
float sf1 = 14.0f * height / 16.0f;
float deltaT = tSpan / 8.0f;
float deltaF = fSpan / 8.0f;
float tSlope = (st1 - st0) / tSpan;
float tInter = (float)(st0 - tSlope * tMin);
float fSlope = (sf0 - sf1) / fSpan;
float fInter = (float)(sf0 - fSlope * fMax);
float pt = 0, pf = 0, st = 0, sf = 0;
PAINTSTRUCT ps;
POINT wPt = { };
HDC hdc = BeginPaint(hDlg, &ps);
int i = 0;
float t = (float)tMin;
float f = (float)fMax;
pt = t;
pf = f;
st = tSlope * pt + tInter;
sf = fSlope * pf + fInter;
MoveToEx(hdc, (int)st, (int)sf0, &wPt);
char buffer[128] = { };
while (i <= 8)
{
st = tSlope * t + tInter;
wPt.x = wPt.y = 0;
MoveToEx(hdc, (int)st, (int)sf0, &wPt);
LineTo(hdc, (int)st, (int)sf1);
sprintf_s(buffer, "%5.4f", t);
SIZE size = { };
GetTextExtentPoint32A(
hdc,
buffer,
(int)strlen(buffer),
&size);
RECT textRect = { };
textRect.left = (long)(st - size.cx / 2.0f);
textRect.right = (long)(st + size.cx / 2.0f);
textRect.top = (long)sf1;
textRect.bottom = (long)(sf1 + size.cy / 2.0f);
DrawFormattedText(hdc, buffer, textRect);
t += deltaT;
i++;
}
i = 0;
f = (float)fMin;
while (i <= 8)
{
sf = fSlope * f + fInter;
wPt.x = wPt.y = 0;
MoveToEx(hdc, (int)st0, (int)sf, &wPt);
LineTo(hdc, (int)st, (int)sf);
if (i != 0)
{
sprintf_s(buffer, "%+5.3lf", f);
SIZE size = { };
GetTextExtentPoint32A(
hdc,
buffer,
(int)strlen(buffer),
&size);
RECT textRect = { };
textRect.left = (long)(st0 - size.cx - size.cx / 5.0f);
textRect.right = (long)(st0 - size.cx / 2.0f);
textRect.top = (long)(sf - size.cy / 2.0f);
textRect.bottom = (long)(sf + size.cy / 2.0f);
DrawFormattedText(hdc, buffer, textRect);
}
f += deltaF;
i++;
}
HGDIOBJ bPenNew = NULL;
HGDIOBJ hPenOld = NULL;
bPenNew = CreatePen(PS_SOLID, 2, RGB(0, 0, 255));
hPenOld = SelectObject(hdc, bPenNew);
pt = (float)points[0].t;
pf = (float)points[0].f;
st = tSlope * pt + tInter;
sf = fSlope * pf + fInter;
wPt.x = wPt.y = 0;
MoveToEx(hdc, (int)st, (int)sf, &wPt);
for (size_t j = 1; j < points.size(); j++)
{
pt = (float)points[j].t;
pf = (float)points[j].f;
st = tSlope * pt + tInter;
sf = fSlope * pf + fInter;
LineTo(hdc, (int)st, (int)sf);
}
SelectObject(hdc, hPenOld);
DeleteObject(bPenNew);
return (INT_PTR)FALSE;
}
return (INT_PTR)FALSE;
}
//Microsoft Visual C++ generated resource script.
//
#include "resource.h"
#define APSTUDIO_READONLY_SYMBOLS
/////////////////////////////////////////////////////////////////////////////
//
// Generated from the TEXTINCLUDE resource.
//
#ifndef APSTUDIO_INVOKED
#include "targetver.h"
#endif
#define APSTUDIO_HIDDEN_SYMBOLS
#include "windows.h"
#undef APSTUDIO_HIDDEN_SYMBOLS
/////////////////////////////////////////////////////////////////////////////
#undef APSTUDIO_READONLY_SYMBOLS
#if !defined(AFX_RESOURCE_DLL) || defined(AFX_TARG_ENU)
LANGUAGE 9, 1
/////////////////////////////////////////////////////////////////////////////
//
// Icon
//
// Icon with lowest ID value placed first to ensure application icon
// remains consistent on all systems.
IDI_FILTERINGNOISYSIGNAL ICON "FilteringNoisySignal.ico"
IDI_SMALL ICON "small.ico"
/////////////////////////////////////////////////////////////////////////////
//
// Menu
//
IDC_FILTERINGNOISYSIGNAL MENU
BEGIN
POPUP "&Start"
BEGIN
MENUITEM "&Input", IDM_INPUT
MENUITEM SEPARATOR
MENUITEM "E&xit", IDM_EXIT
END
POPUP "&Help"
BEGIN
MENUITEM "&About ...", IDM_ABOUT
END
END
/////////////////////////////////////////////////////////////////////////////
//
// Accelerator
//
IDC_FILTERINGNOISYSIGNAL ACCELERATORS
BEGIN
"?", IDM_ABOUT, ASCII, ALT
"/", IDM_ABOUT, ASCII, ALT
END
/////////////////////////////////////////////////////////////////////////////
//
// Dialog
//
IDD_ABOUTBOX DIALOGEX 0, 0, 170, 62
STYLE DS_SETFONT | DS_MODALFRAME | DS_FIXEDSYS | WS_POPUP | WS_CAPTION | WS_SYSMENU
CAPTION "About FilteringNoisySignal"
FONT 8, "MS Shell Dlg"
BEGIN
ICON IDI_FILTERINGNOISYSIGNAL,IDC_STATIC,14,14,21,20
LTEXT "FilteringNoisySignal, Version 1.0",IDC_STATIC,42,14,114,8,SS_NOPREFIX
LTEXT "Copyright (c) 2026",IDC_STATIC,42,26,114,8
DEFPUSHBUTTON "OK",IDOK,113,41,50,14,WS_GROUP
END
IDD_INPUT_DIALOG DIALOGEX 0, 0, 310, 120
STYLE DS_SETFONT | WS_POPUP | WS_VISIBLE | WS_CAPTION | WS_SYSMENU
CAPTION "Input Dialog"
FONT 10, "Courier New", 700
BEGIN
LTEXT "Threshold", IDC_STATIC, 10, 0, 40, 12
EDITTEXT IDC_EDIT_THRESHOLD, 55, 0, 40, 14, ES_AUTOHSCROLL
LTEXT "Noise %", IDC_STATIC, 10, 15, 40, 12
EDITTEXT IDC_EDIT_NOISE, 55, 15, 40, 14, ES_AUTOHSCROLL
LTEXT "N", IDC_STATIC, 10, 30, 40, 12
EDITTEXT IDC_EDIT_N, 55, 30, 40, 14, ES_AUTOHSCROLL
PUSHBUTTON "Draw", IDC_BUTTON_DRAW, 10, 75, 50, 16
PUSHBUTTON "Cancel", IDCANCEL, 180, 75, 50, 16
END
IDD_DRAW_GRAPH_DIALOG DIALOGEX 0, 0, 410, 310
STYLE DS_SETFONT | WS_POPUP | WS_VISIBLE | WS_CAPTION | WS_SYSMENU
CAPTION "Draw Graph Dialog"
FONT 10, "Courier New", 700
BEGIN
END
/////////////////////////////////////////////////////////////////////////////
//
// DESIGNINFO
//
#ifdef APSTUDIO_INVOKED
GUIDELINES DESIGNINFO
BEGIN
IDD_ABOUTBOX, DIALOG
BEGIN
LEFTMARGIN, 7
RIGHTMARGIN, 163
TOPMARGIN, 7
BOTTOMMARGIN, 55
END
END
#endif // APSTUDIO_INVOKED
#ifdef APSTUDIO_INVOKED
/////////////////////////////////////////////////////////////////////////////
//
// TEXTINCLUDE
//
1 TEXTINCLUDE
BEGIN
"resource.h\0"
END
2 TEXTINCLUDE
BEGIN
"#ifndef APSTUDIO_INVOKED\r\n"
"#include ""targetver.h""\r\n"
"#endif\r\n"
"#define APSTUDIO_HIDDEN_SYMBOLS\r\n"
"#include ""windows.h""\r\n"
"#undef APSTUDIO_HIDDEN_SYMBOLS\r\n"
"\0"
END
3 TEXTINCLUDE
BEGIN
"\r\n"
"\0"
END
#endif // APSTUDIO_INVOKED
/////////////////////////////////////////////////////////////////////////////
//
// String Table
//
STRINGTABLE
BEGIN
IDC_FILTERINGNOISYSIGNAL "FILTERINGNOISYSIGNAL"
IDS_APP_TITLE "FilteringNoisySignal"
END
#endif
/////////////////////////////////////////////////////////////////////////////
#ifndef APSTUDIO_INVOKED
/////////////////////////////////////////////////////////////////////////////
//
// Generated from the TEXTINCLUDE resource.
//
/////////////////////////////////////////////////////////////////////////////
#endif // not APSTUDIO_INVOKED
//{{NO_DEPENDENCIES}}
// Microsoft Visual C++ generated include file.
// Used by FilteringNoisySignal.rc
#define IDS_APP_TITLE 103
#define IDR_MAINFRAME 128
#define IDD_FILTERINGNOISYSIGNAL_DIALOG 102
#define IDD_ABOUTBOX 103
#define IDM_ABOUT 104
#define IDM_EXIT 105
#define IDI_FILTERINGNOISYSIGNAL 107
#define IDI_SMALL 108
#define IDC_FILTERINGNOISYSIGNAL 109
#define IDC_MYICON 2
#ifndef IDC_STATIC
#define IDC_STATIC -1
#endif
// Next default values for new objects
//
#ifdef APSTUDIO_INVOKED
#ifndef APSTUDIO_READONLY_SYMBOLS
#define _APS_NO_MFC 130
#define _APS_NEXT_RESOURCE_VALUE 129
#define _APS_NEXT_COMMAND_VALUE 32771
#define _APS_NEXT_CONTROL_VALUE 1000
#define _APS_NEXT_SYMED_VALUE 110
#endif
#endif
#define IDD_INPUT_DIALOG 1000
#define IDC_EDIT_THRESHOLD 1010
#define IDC_EDIT_NOISE 1020
#define IDC_EDIT_N 1030
#define IDC_BUTTON_DRAW 1040
#define IDD_DRAW_GRAPH_DIALOG 2000
#define IDM_INPUT 32771
Author: jamespatewilliamsjr
My whole legal name is James Pate Williams, Jr. I was born in LaGrange, Georgia approximately 70 years ago. I barely graduated from LaGrange High School with low marks in June 1971. Later in June 1979, I graduated from LaGrange College with a Bachelor of Arts in Chemistry with a little over a 3 out 4 Grade Point Average (GPA). In the Spring Quarter of 1978, I taught myself how to program a Texas Instruments desktop programmable calculator and in the Summer Quarter of 1978 I taught myself Dayton BASIC (Beginner's All-purpose Symbolic Instruction Code) on LaGrange College's Data General Eclipse minicomputer. I took courses in BASIC in the Fall Quarter of 1978 and FORTRAN IV (Formula Translator IV) in the Winter Quarter of 1979. Professor Kenneth Cooper, a genius poly-scientist taught me a course in the Intel 8085 microprocessor architecture and assembly and machine language. We would hand assemble our programs and insert the resulting machine code into our crude wooden box computer which was designed and built by Professor Cooper. From 1990 to 1994 I earned a Bachelor of Science in Computer Science from LaGrange College. I had a 4 out of 4 GPA in the period 1990 to 1994. I took courses in C, COBOL, and Pascal during my BS work. After graduating from LaGrange College a second time in May 1994, I taught myself C++. In December 1995, I started using the Internet and taught myself client-server programming. I created a website in 1997 which had C and C# implementations of algorithms from the "Handbook of Applied Cryptography" by Alfred J. Menezes, et. al., and some other cryptography and number theory textbooks and treatises.
View all posts by jamespatewilliamsjr
Numerical Explorations 