SignalUtils.FirImpulse Method

Overload List

#	Signature	Description
1	procedure FirImpulse(const H: TVec; W: TDoubleArray; FilterType: TFilterType; FS: Double);	Design a FIR filter with rectangular window.
2	procedure FirImpulse(const H: TVec; W: TDoubleArray; WindowParam: Double; FilterType: TFilterType; WindowType: TSignalWindowType; Gain: Double; FS: Double);	Windowed-sinc FIR impulse response of a preset length.

Overload 1: procedure FirImpulse(const H: TVec; W: TDoubleArray; FilterType: TFilterType; FS: Double);

Design a FIR filter with rectangular window.

#	Name	Type	Description
1	H	TVec
2	W	TDoubleArray
3	FilterType	TFilterType
4	FS	Double	scalar

Result: stored in self (calling object)

Remarks:

Compute a FIR impulse response filter (no window applied) and place the result in H. The transition regions are defined with the W array. There must be at least one (lowpass, highpass) and at most two (bandpass, bandstop) transition regions (2 or 4 elements). Filter type is defined with TFilterType. The length of the filter H.Length must be preset. Filters of even length (odd order), must have a stop band next to the nyquist (FS/2) frequency. 20*Log10(Ripple) is also the required attenuation of the stop band in decibel. FS is the sampling frequency.

Examples

uses MtxExpr, Math387, MtxVec, SignalUtils, MtxVecTee, MtxVecEdit;

procedure TForm1.Button1Click(Sender: TObject);
var FS: double;
n: integer;
H, Response, X: Vector;
begin
    FS := 2;  //sampling frequency
    n := 41;  // filter length

    //lowpass design with cutoff frequency
    FIRImpulse(H.Size(n), [0.5], ftLowpass,FS);
    FrequencyResponse(H,nil,Response,8);
    X := Ramp(Response.Length, mvDouble, 0, 1/Response.Length);
    DrawIt(X,Response,'Lowpass with cutoff at 0.5');

    //lowpass design with transition band
    FIRImpulse(H.Size(n), [0.3,0.5], ftLowpass,FS);
    FrequencyResponse(H,nil,Response,8);
    DrawIt(X,Response,'Lowpass with transition band: 0.3-0.5');

    //Highpass design with cutoff frequency
    FIRImpulse(H.Size(n), [0.5], ftHighpass,FS);
    FrequencyResponse(H,nil,Response,8);
    DrawIt(X,Response,'Highpass with cutoff at 0.5');

    //Highpass design with transition band
    FIRImpulse(H.Size(n), [0.3,0.5], ftHighpass,FS);
    FrequencyResponse(H,nil,Response,8);
    DrawIt(X,Response,'Highpass with transition band: 0.3-0.5');

    //Bandpass design with transition bands
    FIRImpulse(H.Size(n), [0.3,0.4,0.5,0.6], ftBandpass,FS);
    FrequencyResponse(H,nil,Response,8);
    DrawIt(X,Response,'Bandpass with transitoin band: 0.3-0.4, 0.5-0.6');

    //Bandstop design with transition bands
    FIRImpulse(H.Size(n), [0.3,0.4,0.5,0.6], ftBandstop,FS);
    FrequencyResponse(H,nil,Response,8);
    DrawIt(X,Response,'Bandstop with transition bands: 0.3-0.4, 0.5-0.6');

    //Hilbert III
    FIRImpulse(H.Size(n), [0], ftHilbertIII,FS);
    FrequencyResponse(H,nil,Response,8);
    DrawIt(X,Response);

    //Hilbert IV
    Inc(n);  //n must be even
    FIRImpulse(H.Size(n), [0], ftHilbertIV,FS);
    FrequencyResponse(H,nil,Response,8);
    DrawIt(X,Response);

    //Differentiator III
    Dec(n); // n must be odd
    FIRImpulse(H.Size(n), [0], ftDifferentiatorIII,FS);
    FrequencyResponse(H,nil,Response,8);
    DrawIt(X,Response);

    //Differentiator IV
    Inc(n);  //n must be even
    FIRImpulse(H.Size(n), [0], ftDifferentiatorIV,FS);
    FrequencyResponse(H,nil,Response,8);
    DrawIt(X,Response);
end;

Overload 2: procedure FirImpulse(const H: TVec; W: TDoubleArray; WindowParam: Double; FilterType: TFilterType; WindowType: TSignalWindowType; Gain: Double; FS: Double);

Windowed-sinc FIR impulse response of a preset length.

#	Name	Type	Description
1	H	TVec
2	W	TDoubleArray
3	WindowParam	Double	scalar
4	FilterType	TFilterType
5	WindowType	TSignalWindowType
6	Gain	Double	scalar
7	FS	Double	scalar

Result: stored in self (calling object)

Remarks:

Fills H (length preset by the caller) with the linear-phase windowed-sinc FIR taps for the given FilterType, then multiplies by the chosen window and by Gain. The ideal kernel about the centre alpha=(N-1)/2 is, e.g. for a lowpass with normalised cutoff omega_c = (W[0]+W[1])/ FS,

h[n] = (sinbig(pi omega_c (n-alpha)big))/(pi (n-alpha)), h[alpha] = omega_c

with highpass, bandpass and bandstop using the matching spectral complements, and the Hilbert/differentiator types using their odd-symmetric kernels. WindowType selects the taper (WindowParam carries its parameter, e.g. the Kaiser beta); wtRectangular leaves the raw sinc. H.FloatPrecision sets the working precision. Domain: H.Length must be at least 4 (an exception is raised otherwise); W must supply 1-2 band edges for lowpass/highpass and 2-4 for bandpass/bandstop; integrator types are rejected. FS is the sampling frequency (default 2, so cutoffs are in cycles per Nyquist). Finite input yields finite taps.