Provides infinite impulse response (IIR) filters More...

Static Public Member Functions
static double [][]	Butterworth (double fc, double fs, int poles, bool isHP)
	Returns the normalized recursion coefficents of a Butterworth filter More...

static double [][]	Chebyshev (double fc, double fs, double ripple, int poles, bool isHP)
	Returns the normalized recursion coefficents of a Type-I Chebyshev filter design More...

static double [][]	CombineStages (double[][] ZCoef1, double[][] ZCoef2, bool parallel)
	Combines the recursion coefficients of cascade or parallel stages into a single system More...

static double [][]	DC_Removal ()
	Returns the recursion coefficients of a DC removal filter More...

static double []	Filter (double[] A, double[][] ZCoef)
	Recursive operation used to filter data using the specified recursion coefficients More...

static double [][]	Narrow_BP (double fcenter, double bw, double fs)
	Returns the recursion coefficients of a two-pole narrow band pass filter More...

static double [][]	Narrow_BR (double fcenter, double bw, double fs)
	Returns the recursion coefficients of a two-pole narrow band stop filter More...

static double [][]	SinglePole_HP (double fc, double fs)
	Returns the recursion coefficients of a single pole high pass filter More...

static double [][]	SinglePole_LP (double fc, double fs)
	Returns the recursion coefficients of a single pole low pass filter More...

Detailed Description

Provides infinite impulse response (IIR) filters

Member Function Documentation

◆ Butterworth()

static double [][] dsp.IIR.Butterworth	(	double	fc,
		double	fs,
		int	poles,
		bool	isHP
	)

static

Returns the normalized recursion coefficents of a Butterworth filter

Butterworth filter is a filter with zero ripple (maximmaly flat)

Parameters

fc	cut-off frequency measured at an amplitude of 0.707 (-3dB), given in Hertz
fs	sampling rate (Hz)
poles	number of poles must be an even number from two till eight (2..8)
isHP	low pass (false), high pass (true)

◆ Chebyshev()

static double [][] dsp.IIR.Chebyshev	(	double	fc,
		double	fs,
		double	ripple,
		int	poles,
		bool	isHP
	)

static

Returns the normalized recursion coefficents of a Type-I Chebyshev filter design

When the filter type is low-pass the returned coefficients have unity gain at DC.
When the filter type is high-pass the coefficients have unity gain at the maximum frequency (0.5).

Parameters

fc	cut-off frequency measured at an amplitude of 0.707 (-3dB), given in Hertz
fs	sampling rate (Hz)
ripple	the percent ripple in the pass-band (max 30)
poles	number of poles must be an even number from two till eight (2..8)
isHP	low pass (false), high pass (true)

Example

double[][] lp = IIR.Chebyshev(20, 200, 0.5, 4, false);
Console.WriteLine(NArray.ToString(lp[0]));
Console.WriteLine(NArray.ToString(lp[1]));

0.00278075686761849 0.011123027470474 0.016684541205711 0.011123027470474 0.00278075686761849

0 2.76403050470442 -3.12285267835854 1.66455302410543 -0.350222960333201

◆ CombineStages()

static double [][] dsp.IIR.CombineStages	(	double	ZCoef1[][],
		double	ZCoef2[][],
		bool	parallel
	)

static

Combines the recursion coefficients of cascade or parallel stages into a single system

Parameters

ZCoef1	recursion coefficients
ZCoef2	recursion coefficients
parallel	cascade (false) or parallel (true) combination

Example
The example bellow combines the recursion coefficients of a two stage single pole low pass filter into a single system having two poles.

double[][] lp = IIR.SinglePole_LP(5, 200);
double[][] lp2 = IIR.CombineStages(lp, lp, false);
Console.WriteLine(NArray.ToString(lp2[0], ", "));
Console.WriteLine(NArray.ToString(lp2[1], ", "));

0.0211306927421788 0 0

0 1.70927199830647 -0.730402691048646

◆ DC_Removal()

static double [][] dsp.IIR.DC_Removal ( )

static

Returns the recursion coefficients of a DC removal filter

◆ Filter()

static double [] dsp.IIR.Filter	(	double []	A,
		double	ZCoef[][]
	)

static

Recursive operation used to filter data using the specified recursion coefficients

ZCoef[0] holds the a coefficients, while ZCoef[1] holds the b coefficients.

Notes:
If custom coefficients are used assign a zero value to b0 coefficient (Zcoef[1][0] = 0), since ZCoef[0] and ZCoef[1] arrays must have an equal size (N).
If the same filter is to be used to more than one signal, run the function that return the coefficients just once, and apply the filter function per signal.

Parameters

A	real array
ZCoef	recursion coefficients

Returns: $\displaystyle y[n]=a_0{x}[n]+a_1{x}[n-1]+...+b_1{y}[n-1]+b_2{y}[n-2]+...$

Example
The following example shows how to filter a real signal (A) using a single pole low pass filter.

double[] A = new double[] { 3, 7, -2, 1, -5, 3, 9, 4 };
double[][] cf = IIR.SinglePole_LP(2, 6);
double[] res = IIR.Filter(A, cf);
res = NArray.Round(res, 2);
Console.WriteLine(NArray.ToString(res));

2.63 6.46 -0.96 0.76 -4.29 2.1 8.15 4.51

◆ Narrow_BP()

static double [][] dsp.IIR.Narrow_BP	(	double	fcenter,
		double	bw,
		double	fs
	)

static

Returns the recursion coefficients of a two-pole narrow band pass filter

Parameters

fcenter	center frequency (Hz)
bw	bandwidth measured at -3dB, given in Hertz
fs	sampling rate (Hz)

Example

double[][] bp = IIR.Narrow_BP(25,2, 200);
Console.WriteLine(NArray.ToString(bp[0]));
Console.WriteLine(NArray.ToString(bp[1]));

0.0284636038969323 0.00217279220613561 -0.0306363961030678

0 1.3717871555019 -0.9409

◆ Narrow_BR()

static double [][] dsp.IIR.Narrow_BR	(	double	fcenter,
		double	bw,
		double	fs
	)

static

Returns the recursion coefficients of a two-pole narrow band stop filter

Parameters

fcenter	center frequency (Hz)
bw	bandwidth measured at -3dB, given in Hertz
fs	sampling rate (Hz)

Example

double[][] bp = IIR.Narrow_BP(25,2, 200);
Console.WriteLine(NArray.ToString(bp[0]));
Console.WriteLine(NArray.ToString(bp[1]));

0.0284636038969323 0.00217279220613561 -0.0306363961030678

0 1.3717871555019 -0.9409

◆ SinglePole_HP()

static double [][] dsp.IIR.SinglePole_HP	(	double	fc,
		double	fs
	)

static

Returns the recursion coefficients of a single pole high pass filter

Parameters

fc	cut-off frequency measured at -3dB, given in Hertz
fs	sampling rate (Hz)

Example

double[][] hp = IIR.SinglePole_HP(5, 200);
Console.WriteLine(NArray.ToString(hp[0]));
Console.WriteLine(NArray.ToString(hp[1]));

0.927317999576617 -0.927317999576617

0 0.854635999153233

◆ SinglePole_LP()

static double [][] dsp.IIR.SinglePole_LP	(	double	fc,
		double	fs
	)

static

Returns the recursion coefficients of a single pole low pass filter

Parameters

fc	cut-off frequency measured at -3dB, given in Hertz
fs	sampling rate (Hz)

Example

double[][] lp = IIR.SinglePole_LP(5, 200);
Console.WriteLine(NArray.ToString(lp[0]));
Console.WriteLine(NArray.ToString(lp[1]));

0.145364000846767 0

0 0.854635999153233

Static Public Member Functions

Detailed Description

Member Function Documentation

◆ Butterworth()

◆ Chebyshev()

◆ CombineStages()

◆ DC_Removal()

◆ Filter()

◆ Narrow_BP()

◆ Narrow_BR()

◆ SinglePole_HP()

◆ SinglePole_LP()