public void SpectrumTest()
{
const double fd = 100;
const double dt = 1 / fd;
const double f0 = 10;
//const double eps = 1e-14;
//const double f = f0;
const int samples_count = 100;
//const double total_time = dt * samples_count;
//const double df = 1 / total_time;
var rc = new LowPassRC(f0, dt);
const double A1 = 1;
const double f1 = 3;
const double phi1 = 30 * ToRad;
var s1 = new SamplesDigitalSignal(dt, samples_count, t => A1 * Cos(2 * PI * f1 * t + phi1));
const double A2 = 8;
const double f2 = 10;
const double phi2 = 0 * ToRad;
var s2 = new SamplesDigitalSignal(dt, samples_count, t => A2 * Cos(2 * PI * f2 * t + phi2));
const double A3 = 4;
const double f3 = 15;
const double phi3 = 60 * ToRad;
var s3 = new SamplesDigitalSignal(dt, samples_count, t => A3 * Cos(2 * PI * f3 * t + phi3));
//var s = s1 + s2 + s3;
}
public void SignalProcessing()
{
const double fp = 0.1; // Гц // Граничная частота полосы пропускания
const double fs = 0.3; // Гц // Граничная частота полосы запирания
const double fd = 1; // Гц // Частота дискретизации
const double dt = 1 / fd; // 2с // Период дискретизации
const double Rp = 1; // Неравномерность в полосе пропускания (дБ)
const double Rs = 30; // Неравномерность в полосе пропускания (дБ)
var Gp = (-Rp).From_dB();
var Gs = (-Rs).From_dB();
var filter = new DSP.Filters.ButterworthLowPass(dt, fp, fs, Gp, Gs);
const int samples_count = 1024;
// Сигнал s0(t) = 1
var s_0 = new SamplesDigitalSignal(dt, Repeat(1d, samples_count));
// Гармонические сигналы разной частоты и амплитудой = √2
const double a0 = Consts.sqrt_2;
// Сигнал с частотой равной частоте пропускания (граничной частоте фильтра)
var s_fp = MathSamplesSignal.Cos(a0, fp, 0, dt, samples_count);
// Сигнал с частотой равной частоте заграждения
var s_fs = MathSamplesSignal.Cos(a0, fs, 0, dt, samples_count);
// Сигнал с частотой равной половине частоты дискретизации
var s_fd05 = MathSamplesSignal.Cos(a0, fd / 2, 0, dt, samples_count);
var y_0 = filter.ProcessIndividual(s_0);
var y_fp = filter.ProcessIndividual(s_fp);
var y_fs = filter.ProcessIndividual(s_fs);
var y_fd05 = filter.ProcessIndividual(s_fd05);
// Постоянный сигнал не должен измениться своей мощности
Assert.That.Value(y_0.Power).IsEqual(s_0.Power, 2.81e-3);
// На граничной частоте сигнал должен быть ослаблен на коэффициент Gp (на Gp^2 по мощности)
Assert.That.Value(y_fp.Power).IsEqual(s_0.Power * Gp * Gp, 3.2e-3);
// На частоте заграждения сигнал должен быть ослаблен на коэффициент Gs (на Gs^2 по мощности)
Assert.That.Value(y_fs.Power).IsEqual(s_fs.Power * Gs * Gs, 1.84e-4);
// На частоте в половину частоты дискретизации сигнал должен быть подавлен
Assert.That.Value(y_fd05.Power).IsEqual(0, 1.33e-4);
}
public void ProcessSignalAtCutOffFrequencyTestTest()
{
const double fd = 100;
const double dt = 1 / fd;
const double f0 = 10;
const double eps = 3e-3;
const double A0 = sqrt_2;
var x0 = new SamplesDigitalSignal(dt, 1024, t => A0 * Cos(2 * PI * f0 * t));
var x0_power = x0.Power;
Assert.AreEqual(1, x0_power, eps);
var rc = new LowPassRC(f0, dt);
var y0 = rc.Process(x0);
var y0_power = y0.Power;
Assert.AreEqual(x0_power / 2, y0_power, eps);
}
public void ProcessSignalAtHighFrequencyTestTest()
{
const double fd = 1000;
const double dt = 1 / fd;
const double f0 = 30;
const double delta_f = 10;
const double eps = 2.31e-5;
var x0 = new SamplesDigitalSignal(dt, 1024, t => 1 * Cos(2 * PI * fd / 2 * t));
var x0_power = x0.Power;
Assert.AreEqual(1, x0_power, eps);
var rlc = new BandStopRLC(f0, delta_f, dt);
var y0 = rlc.Process(x0);
var y0_power = y0.Power;
Assert.AreEqual(x0_power, y0_power, eps, $"delta:{Abs(x0_power - y0_power):e2}");
}
public void ProcessSignalAtZerroFrequencyTestTest()
{
const double fd = 1000;
const double dt = 1 / fd;
const double f0 = 30;
const double Df = 10;
const double eps = 0.86e-3;
var x0 = new SamplesDigitalSignal(dt, 1024, t => 1 * Cos(2 * PI * 0 * t));
var x0_power = x0.Power;
Assert.AreEqual(1, x0_power, eps);
var rlc = new BandPassRLC(f0, Df, dt);
var y0 = rlc.Process(x0);
var y0_power = y0.Power;
Assert.AreEqual(0, y0_power, eps, $"delta:{Abs(0 - y0_power)}");
}
public void ProcessSignalAtCentralFrequencyTestTest()
{
const double fd = 1000;
const double dt = 1 / fd;
const double f0 = 30;
const double delta_f = 10;
const double eps = 0.048;
const double A0 = Consts.sqrt_2;
var x0 = new SamplesDigitalSignal(dt, 1024, t => A0 * Cos(2 * PI * f0 * t));
var x0_power = x0.Power;
Assert.AreEqual(1, x0_power, eps);
var rlc = new BandStopRLC(f0, delta_f, dt);
var y0 = rlc.Process(x0);
var y0_power = y0.Power;
Assert.AreEqual(0, y0_power, eps, $"delta:{Abs(0 - y0_power)}");
}
public void SpectrumPassTest()
{
const double fd = 1000;
const double dt = 1 / fd;
const double f0 = 30;
const double Df = 10;
var rlc = new BandPassRLC(f0, Df, dt);
const int samples_count = 1000;
var s0 = new SamplesDigitalSignal(dt, Enumerable.Repeat(1, samples_count));
var s1 = new SamplesDigitalSignal(dt, samples_count, t => 1 * Cos(2 * PI * (f0 - Df / 2) * t));
var s2 = new SamplesDigitalSignal(dt, samples_count, t => 1 * Cos(2 * PI * f0 * t));
var s3 = new SamplesDigitalSignal(dt, samples_count, t => 1 * Cos(2 * PI * (f0 + Df / 2) * t));
var s = s0 + s1 + s2 + s3;
s.FourierTransform().ToAbsArg(out var abs_S, out var arg_S);
var abs_S_25 = abs_S[25];
var abs_S_30 = abs_S[30];
var abs_S_35 = abs_S[35];
var arg_S_25 = arg_S[25];
var arg_S_30 = arg_S[30];
var arg_S_35 = arg_S[35];
var y = rlc.ProcessIndividual(s);
y.FourierTransform().ToAbsArg(out var abs_Y, out var arg_Y);
Assert.That.Value(abs_Y[0]).IsEqual(0, 1.68e-3);
var abs_Y_25 = abs_Y[25];
var abs_Y_30 = abs_Y[30];
var abs_Y_35 = abs_Y[35];
var H_25 = rlc.GetTransmissionCoefficient(f0 - Df / 2, dt);
var H_30 = rlc.GetTransmissionCoefficient(f0, dt);
var H_35 = rlc.GetTransmissionCoefficient(f0 + Df / 2, dt);
var H_25_abs = H_25.Abs;
var H_30_abs = H_30.Abs;
var H_35_abs = H_35.Abs;
var K25 = abs_Y_25 / abs_S_25;
var K30 = abs_Y_30 / abs_S_30;
var K35 = abs_Y_35 / abs_S_35;
Assert.That.Value(K25).IsEqual(H_25_abs, 0.042);
Assert.That.Value(K30).IsEqual(H_30_abs, 0.062);
Assert.That.Value(K35).IsEqual(H_35_abs, 0.045);
var arg_Y_25 = arg_Y[25];
var arg_Y_30 = arg_Y[30];
var arg_Y_35 = arg_Y[35];
var H_25_arg = H_25.Arg;
var H_30_arg = H_30.Arg;
var H_35_arg = H_35.Arg;
var Arg25 = arg_S_25 - arg_Y_25;
var Arg30 = arg_S_30 - arg_Y_30;
var Arg35 = arg_S_35 - arg_Y_35;
Assert.That.Value(Arg25).IsEqual(H_25_arg, 1.82e-2);
Assert.That.Value(Arg30).IsEqual(H_30_arg, 1.71e-2);
Assert.That.Value(Arg35).IsEqual(H_35_arg, 1.66e-2);
}
