public static FilterOrderSpec ConvertFrequencySpecToOrderSpec(FilterFrequencySpec freqSpec)
{
// Do sanity checks on the frequency spec
bool singleTransition = (freqSpec.BandType == BandType.LowPass || freqSpec.BandType == BandType.HighPass);
if (freqSpec.BandType == BandType.LowPass && freqSpec.PassFreqs.First >= freqSpec.StopFreqs.First)
throw new Exception("A low-pass filter must have its pass-band frequency less than its stop-band frequency.");
bool isError = false;
isError |= (freqSpec.StopFreqs.First < 0 && freqSpec.StopFreqs.First > Math.PI);
isError |= (freqSpec.StopFreqs.Second < 0 && freqSpec.StopFreqs.Second > Math.PI);
isError |= (freqSpec.StopFreqs.First < 0 && freqSpec.StopFreqs.First > Math.PI);
isError |= (freqSpec.StopFreqs.Second < 0 && freqSpec.StopFreqs.Second > Math.PI);
if (isError)
throw new Exception("Frequencies must be between 0 and PI inclusive");
//!! Make sure we did all checks
switch (freqSpec.FilterType)
{
case IirFilterType.Butterworth: return Butterworth(freqSpec);
case IirFilterType.ChebyshevType1: return ChebyshevType1(freqSpec);
case IirFilterType.ChebyshevType2: return ChebyshevType2(freqSpec);
default: Debug.Assert(false); throw new Exception();
}
}
/// <summary>
/// Gets the minimum filter order and corner frequency needed to meet the design specifications of a low-pass or high-pass filter.
/// All parameters are in the continuous (analog) domain. Based off of Matlab's buttord function.
/// </summary>
static FilterOrderSpec Butterworth(FilterFrequencySpec freqSpec)
{
Debug.Assert(freqSpec.FilterType == IirFilterType.Butterworth);
bool singleTransition = (freqSpec.BandType == BandType.LowPass || freqSpec.BandType == BandType.HighPass);
// Get stop frequency if filter were an analog prototype (low-pass with pass frequency at 1)
double prototypeStopFreq;
if (singleTransition)
prototypeStopFreq = FindPrototypeStopFreq(freqSpec.PassFreqs.First, freqSpec.StopFreqs.First);
else
prototypeStopFreq = FindPrototypeStopFreq(freqSpec.PassFreqs, freqSpec.StopFreqs);
// Find the minimum order needed to meet the spec
double stopRipplePart = Math.Pow(10, 0.1 * Math.Abs(freqSpec.StopRipple)) - 1;
double passRipplePart = Math.Pow(10, 0.1 * Math.Abs(freqSpec.PassRipple)) - 1;
int order = (int)Math.Ceiling(Math.Log10(stopRipplePart / passRipplePart) / (2 * Math.Log10(prototypeStopFreq)));
if (order == 0)
order = 1;
// Find the corner frequency which will give exactly stopRipple dB at the prototype stop frequency.
double prototypeCornerFreq = prototypeStopFreq / Math.Pow(stopRipplePart, 1 / (2 * Math.Abs(order)));
// Convert this frequency back to original analog filter type
Pair<double, double> cornerFreqs = new Pair<double, double>(0.0, 0.0);
switch (freqSpec.BandType)
{
case BandType.LowPass:
cornerFreqs.First = prototypeCornerFreq * freqSpec.PassFreqs.First;
break;
case BandType.HighPass:
cornerFreqs.First = freqSpec.PassFreqs.First / prototypeCornerFreq;
break;
case BandType.BandPass:
double passFreq1 = freqSpec.PassFreqs.First;
double passFreq2 = freqSpec.PassFreqs.Second;
double bandWidth = passFreq2 - passFreq1;
Func<double, double> transform = x => -x * bandWidth / 2 + Math.Sqrt(x * x / (4*bandWidth*bandWidth + passFreq1*passFreq2));
double firstCornerFreq = transform(prototypeCornerFreq);
double secondCornerFreq = transform(-prototypeCornerFreq);
cornerFreqs.First = Math.Max(firstCornerFreq, secondCornerFreq);
cornerFreqs.Second = Math.Min(firstCornerFreq, secondCornerFreq);
break;
case BandType.BandStop:
throw new NotSupportedException("Creating a band-stop Butterworth filter from a frequency spec is not supported");
default: Debug.Assert(false); throw new Exception();
}
// Create the filter order spec
return FilterOrderSpec.CreateButterworthSpec(cornerFreqs, order, freqSpec.BandType);
}
/// <summary>
/// Creates an infinite-impulse response filter based on corner frequencies of each band.
/// </summary>
public static IirFilter CreateIirFilter(FilterFrequencySpec freqSpec)
{
FilterOrderSpec orderSpec = OrderSelectors.ConvertFrequencySpecToOrderSpec(freqSpec);
return CreateIirFilter(orderSpec);
}
/// <summary>
/// Gets the minimum filter order and corner frequency needed to meet the design specifications of a low-pass or high-pass filter.
/// All parameters are in the continuous (analog) domain. Based off of Matlab's cheb2ord function.
/// </summary>
static FilterOrderSpec ChebyshevType2(FilterFrequencySpec freqSpec)
{
Debug.Assert(freqSpec.FilterType == IirFilterType.ChebyshevType2);
bool singleTransition = (freqSpec.BandType == BandType.LowPass || freqSpec.BandType == BandType.HighPass);
// Get stop frequency if filter were an analog prototype (low-pass with pass frequency at 1)
double prototypeStopFreq;
if (singleTransition)
prototypeStopFreq = FindPrototypeStopFreq(freqSpec.PassFreqs.First, freqSpec.StopFreqs.First);
else
prototypeStopFreq = FindPrototypeStopFreq(freqSpec.PassFreqs, freqSpec.StopFreqs);
//Find the minimum order needed to meet the spec
double stopRipplePart = Math.Pow(10, 0.1 * Math.Abs(freqSpec.StopRipple)) - 1;
double passRipplePart = Math.Pow(10, 0.1 * Math.Abs(freqSpec.PassRipple)) - 1;
int order = (int)Math.Ceiling(SpecialMath.acosh(Math.Sqrt(stopRipplePart / passRipplePart)) / SpecialMath.acosh(prototypeStopFreq));
//Find the corner frequency which will give exactly stopRipple dB at the prototype stop frequency.
double prototypeCornerFreq = 1/Math.Cosh(SpecialMath.acosh(Math.Sqrt(stopRipplePart / passRipplePart) / order));
// Convert this frequency back to original analog filter type
Pair<double, double> cornerFreqs = new Pair<double, double>(0.0, 0.0);
switch (freqSpec.BandType)
{
case BandType.LowPass:
cornerFreqs.First = freqSpec.PassFreqs.First / prototypeCornerFreq;
break;
case BandType.HighPass:
cornerFreqs.First = freqSpec.PassFreqs.First * prototypeCornerFreq;
break;
case BandType.BandPass:
double x = prototypeCornerFreq;
double passFreq1 = freqSpec.PassFreqs.First;
double passFreq2 = freqSpec.PassFreqs.Second;
double bandWidth = passFreq2 - passFreq1;
cornerFreqs.First = (-bandWidth) / (2 * x) + Math.Sqrt(bandWidth*bandWidth / (4 * x * x) + passFreq1 * passFreq2);
cornerFreqs.Second = passFreq1 * passFreq2 / cornerFreqs.First;
break;
case BandType.BandStop:
throw new NotSupportedException("Creating a band-stop Chebyshev Type II filter from a frequency spec is not supported");
default: Debug.Assert(false); throw new Exception();
}
// Create the filter order spec
return FilterOrderSpec.CreateChebyshevType2Spec(cornerFreqs, order, freqSpec.StopRipple, freqSpec.BandType);
}
/// <summary>
/// Gets the minimum filter order and corner frequency needed to meet the design specifications of a low-pass or high-pass filter.
/// All parameters are in the continuous (analog) domain. Based off of Matlab's cheb1ord function.
/// </summary>
static FilterOrderSpec ChebyshevType1(FilterFrequencySpec freqSpec)
{
Debug.Assert(freqSpec.FilterType == IirFilterType.ChebyshevType1);
bool singleTransition = (freqSpec.BandType == BandType.LowPass || freqSpec.BandType == BandType.HighPass);
// Get stop frequency if filter were an analog prototype (low-pass with pass frequency at 1)
double prototypeStopFreq;
if (singleTransition)
prototypeStopFreq = FindPrototypeStopFreq(freqSpec.PassFreqs.First, freqSpec.StopFreqs.First);
else
prototypeStopFreq = FindPrototypeStopFreq(freqSpec.PassFreqs, freqSpec.StopFreqs);
//Find the minimum order needed to meet the spec
double stopRipplePart = Math.Pow(10, 0.1 * Math.Abs(freqSpec.StopRipple)) - 1;
double passRipplePart = Math.Pow(10, 0.1 * Math.Abs(freqSpec.PassRipple)) - 1;
int order = (int)Math.Ceiling(SpecialMath.acosh(Math.Sqrt(stopRipplePart / passRipplePart)) / SpecialMath.acosh(prototypeStopFreq));
// Convert this frequency back to original analog filter type
Pair<double, double> cornerFreqs = new Pair<double, double>(0.0, 0.0);
// Natural frequencies are just the passband frequencies
cornerFreqs.First = freqSpec.PassFreqs.First;
cornerFreqs.Second = freqSpec.PassFreqs.Second;
// Create the filter order spec
return FilterOrderSpec.CreateChebyshevType1Spec(cornerFreqs, order, freqSpec.PassRipple, freqSpec.BandType);
}
