Apply a digital filter (direct form II transposed): Difference between revisions

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Digital filters are used to apply a mathematical operation to a sampled signal. One of the common formulations is the "direct form II transposed" which can represent both infinite impulse response (IIR) and finite impulse response (FIR) filters, as well as being more numerically stable than other forms. ^[1]

Task

Filter a signal using an order 3 low-pass Butterworth filter. The coefficients for the filter are a=[1.00000000, -2.77555756e-16, 3.33333333e-01, -1.85037171e-17] and b = [0.16666667, 0.5, 0.5, 0.16666667]

The signal that needs filtering is the following vector: [-0.917843918645, 0.141984778794, 1.20536903482, 0.190286794412, -0.662370894973, -1.00700480494, -0.404707073677 ,0.800482325044, 0.743500089861, 1.01090520172, 0.741527555207, 0.277841675195, 0.400833448236, -0.2085993586, -0.172842103641, -0.134316096293, 0.0259303398477, 0.490105989562, 0.549391221511, 0.9047198589]

C

Given the number of values a coefficient or signal vector can have and the number of digits, this implementation reads data from a file and prints it to the console if no output file is specified or writes to the specified output file. Usage printed on incorrect invocation. <lang C>

include<stdlib.h>
include<string.h>
include<stdio.h>

define MAX_LEN 1000

typedef struct{ float* values; int size; }vector;

vector extractVector(char* str){ vector coeff; int i=0,count = 1; char* token;

while(str[i]!=00){ if(str[i++]==' ') count++; }

coeff.values = (float*)malloc(count*sizeof(float)); coeff.size = count;

token = strtok(str," ");

i = 0;

while(token!=NULL){ coeff.values[i++] = atof(token); token = strtok(NULL," "); }

return coeff; }

vector processSignalFile(char* fileName){ int i,j; float sum; char str[MAX_LEN]; vector coeff1,coeff2,signal,filteredSignal;

FILE* fp = fopen(fileName,"r");

fgets(str,MAX_LEN,fp); coeff1 = extractVector(str);

fgets(str,MAX_LEN,fp); coeff2 = extractVector(str);

fgets(str,MAX_LEN,fp); signal = extractVector(str);

       fclose(fp);

filteredSignal.values = (float*)calloc(signal.size,sizeof(float)); filteredSignal.size = signal.size;

for(i=0;i<signal.size;i++){ sum = 0;

for(j=0;j<coeff2.size;j++){ if(i-j>=0) sum += coeff2.values[j]*signal.values[i-j]; }

for(j=0;j<coeff1.size;j++){ if(i-j>=0) sum -= coeff1.values[j]*filteredSignal.values[i-j]; }

sum /= coeff1.values[0]; filteredSignal.values[i] = sum; }

return filteredSignal; }

void printVector(vector v, char* outputFile){ int i;

if(outputFile==NULL){ printf("["); for(i=0;i<v.size;i++) printf("%.12f, ",v.values[i]); printf("\b\b]"); }

else{ FILE* fp = fopen(outputFile,"w"); for(i=0;i<v.size-1;i++) fprintf(fp,"%.12f, ",v.values[i]); fprintf(fp,"%.12f",v.values[i]); fclose(fp); }

}

int main(int argC,char* argV[]) { char *str; if(argC<2||argC>3) printf("Usage : %s <name of signal data file and optional output file.>",argV[0]); else{ if(argC!=2){ str = (char*)malloc((strlen(argV[2]) + strlen(str) + 1)*sizeof(char)); strcpy(str,"written to "); } printf("Filtered signal %s",(argC==2)?"is:\n":strcat(str,argV[2])); printVector(processSignalFile(argV[1]),argV[2]); } return 0; } </lang> Input file, 3 lines containing first ( a ) and second ( b ) coefficient followed by the signal, all values should be separated by a single space:

1.00000000 -2.77555756e-16 3.33333333e-01 -1.85037171e-17
0.16666667 0.5 0.5 0.16666667
-0.917843918645 0.141984778794 1.20536903482 0.190286794412 -0.662370894973 -1.00700480494 -0.404707073677 0.800482325044 0.743500089861 1.01090520172 0.741527555207 0.277841675195 0.400833448236 -0.2085993586 -0.172842103641 -0.134316096293 0.0259303398477 0.490105989562 0.549391221511 0.9047198589

Invocation and output for writing to file :

C:\rosettaCode>filterSignal.exe signalData.txt signalOut1.txt
Filtered signal written to signalOut1.txt

Output file :

-0.152973994613, -0.435257852077, -0.136043429375, 0.697503268719, 0.656444668770, -0.435482472181, -1.089239478111, -0.537676513195, 0.517050027847, 1.052249789238, 0.961854279041, 0.695690035820, 0.424356281757, 0.196262255311, -0.027835110202, -0.211721926928, -0.174745559692, 0.069258414209, 0.385445863008, 0.651770770550

C++

This uses the C++11 method of initializing vectors. In g++, use the -std=c++0x compiler switch.

<lang cpp>#include <vector>

include <iostream>

using namespace std;

void Filter(const vector<float> &b, const vector<float> &a, const vector<float> &in, vector<float> &out) {

out.resize(0); out.resize(in.size());

for(int i=0; i < in.size(); i++) { float tmp = 0.; int j=0; out[i] = 0.f; for(j=0; j < b.size(); j++) { if(i - j < 0) continue; tmp += b[j] * in[i-j]; }

for(j=1; j < a.size(); j++) { if(i - j < 0) continue; tmp -= a[j]*out[i-j]; }

tmp /= a[0]; out[i] = tmp; } }

int main() { vector<float> sig = {-0.917843918645,0.141984778794,1.20536903482,0.190286794412,-0.662370894973,-1.00700480494,\ -0.404707073677,0.800482325044,0.743500089861,1.01090520172,0.741527555207,\ 0.277841675195,0.400833448236,-0.2085993586,-0.172842103641,-0.134316096293,\ 0.0259303398477,0.490105989562,0.549391221511,0.9047198589};

//Constants for a Butterworth filter (order 3, low pass) vector<float> a = {1.00000000, -2.77555756e-16, 3.33333333e-01, -1.85037171e-17}; vector<float> b = {0.16666667, 0.5, 0.5, 0.16666667};

vector<float> result; Filter(b, a, sig, result);

for(size_t i=0;i<result.size();i++) cout << result[i] << ","; cout << endl;

return 0; }</lang>

Output:

-0.152974,-0.435258,-0.136043,0.697503,0.656445,-0.435483,-1.08924,-0.537677,0.51705,1.05225,0.961854,0.69569,0.424356,0.196262,-0.0278351,-0.211722,-0.174746,0.0692584,0.385446,0.651771,

C#

Translation of: Java

<lang csharp>using System;

namespace ApplyDigitalFilter {

   class Program {
       private static double[] Filter(double[] a, double[] b, double[] signal) {
           double[] result = new double[signal.Length];
           for (int i = 0; i < signal.Length; ++i) {
               double tmp = 0.0;
               for (int j = 0; j < b.Length; ++j) {
                   if (i - j < 0) continue;
                   tmp += b[j] * signal[i - j];
               }
               for (int j = 1; j < a.Length; ++j) {
                   if (i - j < 0) continue;
                   tmp -= a[j] * result[i - j];
               }
               tmp /= a[0];
               result[i] = tmp;
           }
           return result;
       }

       static void Main(string[] args) {
           double[] a = new double[] { 1.00000000, -2.77555756e-16, 3.33333333e-01, -1.85037171e-17 };
           double[] b = new double[] { 0.16666667, 0.5, 0.5, 0.16666667 };

           double[] signal = new double[] {
               -0.917843918645, 0.141984778794, 1.20536903482, 0.190286794412,
               -0.662370894973, -1.00700480494, -0.404707073677, 0.800482325044,
               0.743500089861, 1.01090520172, 0.741527555207, 0.277841675195,
               0.400833448236, -0.2085993586, -0.172842103641, -0.134316096293,
               0.0259303398477, 0.490105989562, 0.549391221511, 0.9047198589
           };

           double[] result = Filter(a, b, signal);
           for (int i = 0; i < result.Length; ++i) {
               Console.Write("{0,11:F8}", result[i]);
               Console.Write((i + 1) % 5 != 0 ? ", " : "\n");
           }
       }
   }

}</lang>

Output:

-0.15297399, -0.43525783, -0.13604340,  0.69750333,  0.65644469
-0.43548245, -1.08923946, -0.53767655,  0.51704999,  1.05224975
 0.96185430,  0.69569009,  0.42435630,  0.19626223, -0.02783512
-0.21172192, -0.17474556,  0.06925841,  0.38544587,  0.65177084

D

Translation of: Kotlin

<lang D>import std.stdio;

alias T = real; alias AT = T[];

AT filter(const AT a, const AT b, const AT signal) {

   AT result = new T[signal.length];

   foreach (int i; 0..signal.length) {
       T tmp = 0.0;
       foreach (int j; 0..b.length) {
           if (i-j<0) continue;
           tmp += b[j] * signal[i-j];
       }
       foreach (int j; 1..a.length) {
           if (i-j<0) continue;
           tmp -= a[j] * result[i-j];
       }
       tmp /= a[0];
       result[i] = tmp;
   }

   return result;

}

void main() {

   AT a = [1.00000000, -2.77555756e-16, 3.33333333e-01, -1.85037171e-17];
   AT b = [0.16666667, 0.5, 0.5, 0.16666667];

   AT signal = [
       -0.917843918645, 0.141984778794, 1.20536903482, 0.190286794412,
       -0.662370894973, -1.00700480494, -0.404707073677, 0.800482325044,
       0.743500089861, 1.01090520172, 0.741527555207, 0.277841675195,
       0.400833448236, -0.2085993586, -0.172842103641, -0.134316096293,
       0.0259303398477, 0.490105989562, 0.549391221511, 0.9047198589
   ];

   AT result = filter(a,b,signal);
   foreach (i; 0..result.length) {
       writef("% .8f", result[i]);
       if ((i+1)%5 != 0) {
           write(", ");
       } else {
           writeln;
       }
   }

}</lang>

Output:

-0.15297399, -0.43525783, -0.13604340,  0.69750333,  0.65644469
-0.43548245, -1.08923946, -0.53767655,  0.51704999,  1.05224975
 0.96185430,  0.69569009,  0.42435630,  0.19626223, -0.02783512
-0.21172192, -0.17474556,  0.06925840,  0.38544587,  0.65177084

Go

<lang go>package main

import "fmt"

type filter struct {

   b, a []float64

}

func (f filter) filter(in []float64) []float64 {

   out := make([]float64, len(in))
   s := 1. / f.a[0]
   for i := range in {
       tmp := 0.
       b := f.b
       if i+1 < len(b) {
           b = b[:i+1]
       }
       for j, bj := range b {
           tmp += bj * in[i-j]
       }
       a := f.a[1:]
       if i < len(a) {
           a = a[:i]
       }
       for j, aj := range a {
           tmp -= aj * out[i-j-1]
       }
       out[i] = tmp * s
   }
   return out

}

//Constants for a Butterworth filter (order 3, low pass) var bwf = filter{

   a: []float64{1.00000000, -2.77555756e-16, 3.33333333e-01, -1.85037171e-17},
   b: []float64{0.16666667, 0.5, 0.5, 0.16666667},

}

var sig = []float64{

   -0.917843918645, 0.141984778794, 1.20536903482, 0.190286794412,
   -0.662370894973, -1.00700480494, -0.404707073677, 0.800482325044,
   0.743500089861, 1.01090520172, 0.741527555207, 0.277841675195,
   0.400833448236, -0.2085993586, -0.172842103641, -0.134316096293,
   0.0259303398477, 0.490105989562, 0.549391221511, 0.9047198589,

}

func main() {

   for _, v := range bwf.filter(sig) {
       fmt.Printf("%9.6f\n", v)
   }

}</lang>

Output:

Java

Translation of: Kotlin

<lang Java>public class DigitalFilter {

   private static double[] filter(double[] a, double[] b, double[] signal) {
       double[] result = new double[signal.length];
       for (int i = 0; i < signal.length; ++i) {
           double tmp = 0.0;
           for (int j = 0; j < b.length; ++j) {
               if (i - j < 0) continue;
               tmp += b[j] * signal[i - j];
           }
           for (int j = 1; j < a.length; ++j) {
               if (i - j < 0) continue;
               tmp -= a[j] * result[i - j];
           }
           tmp /= a[0];
           result[i] = tmp;
       }
       return result;
   }

   public static void main(String[] args) {
       double[] a = new double[]{1.00000000, -2.77555756e-16, 3.33333333e-01, -1.85037171e-17};
       double[] b = new double[]{0.16666667, 0.5, 0.5, 0.16666667};

       double[] signal = new double[]{
           -0.917843918645, 0.141984778794, 1.20536903482, 0.190286794412,
           -0.662370894973, -1.00700480494, -0.404707073677, 0.800482325044,
           0.743500089861, 1.01090520172, 0.741527555207, 0.277841675195,
           0.400833448236, -0.2085993586, -0.172842103641, -0.134316096293,
           0.0259303398477, 0.490105989562, 0.549391221511, 0.9047198589
       };

       double[] result = filter(a, b, signal);
       for (int i = 0; i < result.length; ++i) {
           System.out.printf("% .8f", result[i]);
           System.out.print((i + 1) % 5 != 0 ? ", " : "\n");
       }
   }

}</lang>

Output:

-0.15297399, -0.43525783, -0.13604340,  0.69750333,  0.65644469
-0.43548245, -1.08923946, -0.53767655,  0.51704999,  1.05224975
 0.96185430,  0.69569009,  0.42435630,  0.19626223, -0.02783512
-0.21172192, -0.17474556,  0.06925841,  0.38544587,  0.65177084

Julia

Translation of: zkl

<lang julia>function DF2TFilter(a::Vector, b::Vector, sig::Vector)

   rst = zeros(sig)
   for i in eachindex(sig)
       tmp =  sum(b[j] * sig[i-j+1] for j in 1:min(i, length(b)))
       tmp -= sum(a[j] * rst[i-j+1] for j in 1:min(i, length(a)))
       rst[i] = tmp / a[1]
   end
   return rst

end

acoef = [1.00000000, -2.77555756e-16, 3.33333333e-01, -1.85037171e-17] bcoef = [0.16666667, 0.5, 0.5, 0.16666667] signal = [-0.917843918645, 0.141984778794, 1.20536903482, 0.190286794412,

         -0.662370894973, -1.00700480494, -0.404707073677,  0.800482325044,
          0.743500089861,  1.01090520172,  0.741527555207,  0.277841675195,
          0.400833448236, -0.2085993586,  -0.172842103641, -0.134316096293,
          0.0259303398477, 0.490105989562, 0.549391221511,  0.9047198589]

@show DF2TFilter(acoef, bcoef, signal)</lang>

Output:

DF2TFilter(acoef, bcoef, signal) = [-0.152974, -0.435258, -0.136043, 0.697503, 0.656445, -0.435482, -1.08924, -0.537677, 0.51705, 1.05225, 0.961854, 0.69569, 0.424356, 0.196262, -0.0278351, -0.211722, -0.174746, 0.0692584, 0.385446, 0.651771]

Kotlin

Translation of: C++

<lang scala>// version 1.1.3

fun filter(a: DoubleArray, b: DoubleArray, signal: DoubleArray): DoubleArray {

   val result = DoubleArray(signal.size)
   for (i in 0 until signal.size) {
       var tmp = 0.0
       for (j in 0 until b.size) {
           if (i - j < 0) continue
           tmp += b[j] * signal[i - j]
       }
       for (j in 1 until a.size) {
           if (i - j < 0) continue
           tmp -= a[j] * result[i - j]
       }
       tmp /= a[0]
       result[i] = tmp
   }
   return result

}

fun main(args: Array<String>) {

   val a = doubleArrayOf(1.00000000, -2.77555756e-16, 3.33333333e-01, -1.85037171e-17)
   val b = doubleArrayOf(0.16666667, 0.5, 0.5, 0.16666667)

   val signal = doubleArrayOf(
       -0.917843918645, 0.141984778794, 1.20536903482, 0.190286794412,
       -0.662370894973, -1.00700480494, -0.404707073677, 0.800482325044,
       0.743500089861, 1.01090520172, 0.741527555207, 0.277841675195,
       0.400833448236, -0.2085993586, -0.172842103641, -0.134316096293,
       0.0259303398477, 0.490105989562, 0.549391221511, 0.9047198589
   )

   val result = filter(a, b, signal)
   for (i in 0 until result.size) {
       print("% .8f".format(result[i]))
       print(if ((i + 1) % 5 != 0) ", " else "\n")
   }

}</lang>

Output:

-0.15297399, -0.43525783, -0.13604340,  0.69750333,  0.65644469
-0.43548245, -1.08923946, -0.53767655,  0.51704999,  1.05224975
 0.96185430,  0.69569009,  0.42435630,  0.19626223, -0.02783512
-0.21172192, -0.17474556,  0.06925841,  0.38544587,  0.65177084

MATLAB

MATLAB is commonly used for filter design and implementation. To implement this filter, and display the original signal and the filtered result: <lang MATLAB> signal = [-0.917843918645, 0.141984778794, 1.20536903482, 0.190286794412, -0.662370894973, -1.00700480494, -0.404707073677 ,0.800482325044, 0.743500089861, 1.01090520172, 0.741527555207, 0.277841675195, 0.400833448236, -0.2085993586, -0.172842103641, -0.134316096293, 0.0259303398477, 0.490105989562, 0.549391221511, 0.9047198589]; a = [1.00000000, -2.77555756e-16, 3.33333333e-01, -1.85037171e-17]; b = [0.16666667, 0.5, 0.5, 0.16666667];

out = filter(b,a,signal)

figure subplot(1,2,1) stem(0:19, signal) xlabel('n') title('Original Signal')

subplot(1,2,2) stem(0:19, out) xlabel('n') title('Filtered Signal') </lang>

Output:

out =

  Columns 1 through 10

   -0.1530   -0.4353   -0.1360    0.6975    0.6564   -0.4355   -1.0892   -0.5377    0.5170    1.0522

  Columns 11 through 20

    0.9619    0.6957    0.4244    0.1963   -0.0278   -0.2117   -0.1747    0.0693    0.3854    0.6518

ooRexx

<lang oorexx>/* REXX */ a=.array~of(1.00000000, -2.77555756e-16, 3.33333333e-01, -1.85037171e-17) b=.array~of(0.16666667, 0.5, 0.5, 0.16666667) s=.array~of(-0.917843918645, 0.141984778794, 1.20536903482, 0.190286794412,,

           -0.662370894973, -1.00700480494, -0.404707073677 ,0.800482325044,,
            0.743500089861, 1.01090520172, 0.741527555207, 0.277841675195,,
            0.400833448236, -0.2085993586, -0.172842103641, -0.134316096293,,
            0.0259303398477, 0.490105989562, 0.549391221511, 0.9047198589)

ret=.array~new(s~items)~~fill(0) /* create array and fill with zeroes */

Call filter a,b,s,ret Do i=1 To ret~items

 Say format(i,2) format(ret[i],2,12)
 End

Exit

Routine filter

Use Arg a,b,s,ret Do i=1 To s~items

 temp=0
 Do j=1 To b~items
   if i-j>=0 Then
     temp=temp+b[j]*s[i-j+1]
   End
 Do j=1 To a~items
   if i-j>=0 Then Do
     u=i-j+1
     temp=temp-a[j]*ret[u]
     End
   End
 ret[i]=temp/a[1]
 End

Return

OPTIONS digits 24 /* Numeric Digits 24, everywhere */

</lang>

output:

 1 -0.152973989500
 2 -0.435257829050
 3 -0.136043396988
 4  0.697503326548
 5  0.656444692469
 6 -0.435482453256
 7 -1.089239461153
 8 -0.537676549563
 9  0.517049992313
10  1.052249747155
11  0.961854300374
12  0.695690094010
13  0.424356295096
14  0.196262231822
15 -0.027835124463
16 -0.211721915450
17 -0.174745562223
18  0.069258408901
19  0.385445874307
20  0.651770838819

Perl 6

Works with: Rakudo version 2016.11

Translation of: zkl

<lang perl6>sub TDF-II-filter ( @signal, @a, @b ) {

   my @out = 0 xx @signal;
   for ^@signal -> $i {
       my $this;
       $this += @b[$_] * @signal[$i-$_] if $i-$_ >= 0 for ^@b;
       $this -= @a[$_] *    @out[$i-$_] if $i-$_ >= 0 for ^@a;
       @out[$i] = $this / @a[0];
   }
   @out

}

my @signal = [

   -0.917843918645,  0.141984778794, 1.20536903482,   0.190286794412,
   -0.662370894973, -1.00700480494, -0.404707073677,  0.800482325044,
    0.743500089861,  1.01090520172,  0.741527555207,  0.277841675195,
    0.400833448236, -0.2085993586,  -0.172842103641, -0.134316096293,
    0.0259303398477, 0.490105989562, 0.549391221511,  0.9047198589

]; my @a = [ 1.00000000, -2.77555756e-16, 3.33333333e-01, -1.85037171e-17 ]; my @b = [ 0.16666667, 0.5, 0.5, 0.16666667 ];

say TDF-II-filter(@signal, @a, @b)».fmt("% 0.8f")

   Z~ flat (', ' xx 4, ",\n") xx *;</lang>

Output:

(-0.15297399,  -0.43525783,  -0.13604340,   0.69750333,   0.65644469,
 -0.43548245,  -1.08923946,  -0.53767655,   0.51704999,   1.05224975,
  0.96185430,   0.69569009,   0.42435630,   0.19626223,  -0.02783512,
 -0.21172192,  -0.17474556,   0.06925841,   0.38544587,   0.65177084,
)

Phix

Translation of: Julia

Note however that the a[j]* starts from index 2, unlike Julia/C/Perl6/Rust/Sidef/zkl, but the same as C++/C#/D/Java/Kotlin - and it does not seem to make any difference... <lang Phix>function direct_form_II_transposed_filter(sequence a, b, signal)

   sequence result = repeat(0,length(signal))
   for i=1 to length(in) do
       atom tmp = 0
       for j=1 to min(i,length(b)) do tmp += b[j]*signal[i-j+1] end for
       for j=2 to min(i,length(a)) do tmp -= a[j]*result[i-j+1] end for
       result[i] = tmp/a[1]
   end for
   return result

end function

constant acoef = {1.00000000, -2.77555756e-16, 3.33333333e-01, -1.85037171e-17},

        bcoef = {0.16666667, 0.5, 0.5, 0.16666667}
        signal = {-0.917843918645,0.141984778794,1.20536903482,0.190286794412,-0.662370894973,
                  -1.00700480494,-0.404707073677,0.800482325044,0.743500089861,1.01090520172,
                   0.741527555207,0.277841675195,0.400833448236,-0.2085993586,-0.172842103641,
                  -0.134316096293,0.0259303398477,0.490105989562,0.549391221511,0.9047198589},

pp(direct_form_II_transposed_filter(acoef, bcoef, signal),{pp_FltFmt,"%9.6f",pp_Maxlen,110})</lang>

Output:

{-0.152974,-0.435258,-0.136043, 0.697503, 0.656445,-0.435482,-1.089239,-0.537677, 0.517050, 1.052250,
  0.961854, 0.695690, 0.424356, 0.196262,-0.027835,-0.211722,-0.174746, 0.069258, 0.385446, 0.651771}

Python

<lang python>#!/bin/python from __future__ import print_function from scipy import signal import matplotlib.pyplot as plt

if __name__=="__main__": sig = [-0.917843918645,0.141984778794,1.20536903482,0.190286794412,-0.662370894973,-1.00700480494, -0.404707073677,0.800482325044,0.743500089861,1.01090520172,0.741527555207, 0.277841675195,0.400833448236,-0.2085993586,-0.172842103641,-0.134316096293, 0.0259303398477,0.490105989562,0.549391221511,0.9047198589]

#Create an order 3 lowpass butterworth filter #Generated using b, a = signal.butter(3, 0.5) a = [1.00000000, -2.77555756e-16, 3.33333333e-01, -1.85037171e-17] b = [0.16666667, 0.5, 0.5, 0.16666667]

#Apply the filter to signal filt = signal.lfilter(b, a, sig) print (filt)

plt.plot(sig, 'b') plt.plot(filt, 'r--') plt.show()</lang>

Output:

[-0.15297399 -0.43525783 -0.1360434   0.69750333  0.65644469 -0.43548245
 -1.08923946 -0.53767655  0.51704999  1.05224975  0.9618543   0.69569009
  0.4243563   0.19626223 -0.02783512 -0.21172192 -0.17474556  0.06925841
  0.38544587  0.65177084]

REXX

version 1

Translation of: Julia

<lang REXX>/*REXX pgm filters a signal with a order3 lowpass Butterworth, direct form II transposed*/ numeric digits 24 /*use 20 decimal digs*/ @a= '1 -2.77555756e-16 3.33333333e-1 -1.85037171e-17' /*filter coefficients*/ @b= 0.16666667 0.5 0.5 0.16666667 /* " " */ @s= '-0.917843918645 0.141984778794 1.20536903482 0.190286794412 -0.662370894973' ,

   '-1.00700480494  -0.404707073677   0.800482325044   0.743500089861   1.01090520172 ' ,
   ' 0.741527555207  0.277841675195   0.400833448236  -0.2085993586    -0.172842103641' ,
   '-0.134316096293  0.0259303398477  0.490105989562   0.549391221511   0.9047198589  '

$.=0; N= words(@s); w= length(n) /* [↑] signal vector*/

    do i=1  for N;                #=0           /*process each of the vector elements. */
      do j=1  for words(@b); if i-j >= 0  then #= # + word(@b, j) * word(@s, i-j+1);  end
      do k=1  for words(@a); _= i -k +1;  if i-k >= 0  then #= # - word(@a, k) * $._; end
    $.i= # / word(@a ,1);         call tell
    end   /*i*/                                 /* [↑]  only show using ½ the dec. digs*/

exit /*stick a fork in it, we're all done. */ /*──────────────────────────────────────────────────────────────────────────────────────*/ tell: numeric digits digits()%2; say right(i, w) " " left(, $.i>=0)$.i /1; return</lang>

output:

 1   -0.1529739895
 2   -0.43525782905
 3   -0.136043396988
 4    0.697503326548
 5    0.656444692469
 6   -0.435482453256
 7   -1.08923946115
 8   -0.537676549563
 9    0.517049992313
10    1.05224974716
11    0.961854300374
12    0.69569009401
13    0.424356295096
14    0.196262231822
15   -0.0278351244634
16   -0.21172191545
17   -0.174745562223
18    0.0692584089012
19    0.385445874307
20    0.651770838819

version 2

Translation of: Julia

<lang REXX>/* REXX */ Numeric Digits 24 acoef = '1.00000000, -2.77555756e-16, 3.33333333e-01, -1.85037171e-17' bcoef = '0.16666667, 0.5, 0.5, 0.16666667' signal = '-0.917843918645, 0.141984778794, 1.20536903482, 0.190286794412,',

        '-0.662370894973, -1.00700480494, -0.404707073677 ,0.800482325044,',
        ' 0.743500089861, 1.01090520172, 0.741527555207, 0.277841675195,',
        ' 0.400833448236, -0.2085993586, -0.172842103641, -0.134316096293,',
        ' 0.0259303398477, 0.490105989562, 0.549391221511, 0.9047198589'

Do i=1 By 1 While acoef>; Parse Var acoef a.i . ',' acoef; End; a.0=i-1 Do i=1 By 1 While bcoef>; Parse Var bcoef b.i . ',' bcoef; End; b.0=i-1 Do i=1 By 1 While signal>; Parse Var signal s.i . ',' signal; End; s.0=i-1

ret.=0 Do i=1 To s.0

 temp=0.0
 Do j=1 To b.0
   if i-j>=0 Then Do
     u=i-j+1
     temp=temp+b.j*s.u
     End
   End
 Do j=1 To a.0
   if i-j>=0 Then Do
     u=i-j+1
     temp=temp-a.j*ret.u
     End
   End
 ret.i=temp/a.1
 Say format(i,2) format(ret.i,2,12)
 End</lang>

output:

 1 -0.152973989500
 2 -0.435257829050
 3 -0.136043396988
 4  0.697503326548
 5  0.656444692469
 6 -0.435482453256
 7 -1.089239461153
 8 -0.537676549563
 9  0.517049992313
10  1.052249747155
11  0.961854300374
12  0.695690094010
13  0.424356295096
14  0.196262231822
15 -0.027835124463
16 -0.211721915450
17 -0.174745562223
18  0.069258408901
19  0.385445874307
20  0.651770838819

Rust

Translation of: Java

<lang Rust>use std::cmp::Ordering;

struct IIRFilter<'f>(&'f [f32], &'f [f32]);

impl<'f> IIRFilter<'f> {

   pub fn with_coefficients(a: &'f [f32], b: &'f [f32]) -> IIRFilter<'f> {
       IIRFilter(a, b)
   }

   // Performs the calculation as an iterator chain.
   pub fn apply<I: Iterator<Item = &'f f32> + 'f>(
       &self,
       samples: I,
   ) -> impl Iterator<Item = f32> + 'f {
       // Name some things for readability
       let a_coeff = self.0;
       let b_coeff = self.1;

       let mut prev_results = Vec::<f32>::new();
       let mut prev_samples = Vec::<f32>::new();

       // The actual calculation, done one number at a time
       samples.enumerate() // (i, sample[i])
           .map(move |(i, sample)| { // for each sample, apply this function
               prev_samples.push(*sample);
               prev_results.push(0f32); // the initial version of the previous result

               let sum_b: f32 = b_coeff.iter() // for each coefficient in b
                   .enumerate() // (j, b_coeff[j])
                   .map(|(j, c)| { // calculate the weight of the coefficient
                       if i >= j {
                           (*c) * prev_samples[i-j]
                       } else {
                           0f32
                       }
                   })
                   .sum(); // add them all together

               let sum_a: f32 = a_coeff.iter() // for each coefficient in a
                   .enumerate() // (j, a_coeff[j])
                   .map(|(j, c)| { // calculate the weight of the coefficient
                       if i >= j {
                           (*c) * prev_results[i-j]
                       } else {
                           0f32
                       }
                   })
                   .sum(); // add them all together

               // perform the final calculation
               let result = (sum_b - sum_a) / a_coeff[0];

               // update the previous result for the next iteration
               prev_results[i] = result;

               // return the current result in this iteration
               result
           }
       )
   }

}

fn main() {

   let a: &[f32] = &[1.00000000, -2.77555756e-16, 3.33333333e-01, -1.85037171e-17];
   let b: &[f32] = &[0.16666667, 0.5, 0.5, 0.16666667];

   let samples: Vec<f32> = vec![
       -0.917843918645,
       0.141984778794,
       1.20536903482,
       0.190286794412,
       -0.662370894973,
       -1.00700480494,
       -0.404707073677,
       0.800482325044,
       0.743500089861,
       1.01090520172,
       0.741527555207,
       0.277841675195,
       0.400833448236,
       -0.2085993586,
       -0.172842103641,
       -0.134316096293,
       0.0259303398477,
       0.490105989562,
       0.549391221511,
       0.9047198589,
   ];

   for (i, result) in IIRFilter::with_coefficients(a, b)
       .apply(samples.iter())
       .enumerate()
   {
       print!("{:.8}", result);
       if (i + 1) % 5 != 0 {
           print!(", ");
       } else {
           println!();
       }
   }
   println!();

}</lang>

output:

-0.15297399, -0.43525785, -0.13604343, 0.69750333, 0.65644467
-0.43548250, -1.08923948, -0.53767651, 0.51705003, 1.05224979
0.96185434, 0.69568992, 0.42435625, 0.19626230, -0.02783510
-0.21172196, -0.17474557, 0.06925842, 0.38544586, 0.65177077

Sidef

Translation of: Perl 6

<lang ruby>func TDF_II_filter(signal, a, b) {

   var out = [0]*signal.len
   for i in ^signal {
       var this = 0
       for j in ^b { i-j >= 0 && (this += b[j]*signal[i-j]) }
       for j in ^a { i-j >= 0 && (this -= a[j]*   out[i-j]) }
       out[i] = this/a[0]
   }
   return out

}

var signal = [

   -0.917843918645,  0.141984778794, 1.20536903482,   0.190286794412,
   -0.662370894973, -1.00700480494, -0.404707073677,  0.800482325044,
    0.743500089861,  1.01090520172,  0.741527555207,  0.277841675195,
    0.400833448236, -0.2085993586,  -0.172842103641, -0.134316096293,
    0.0259303398477, 0.490105989562, 0.549391221511,  0.9047198589

]

var a = [1.00000000, -2.77555756e-16, 3.33333333e-01, -1.85037171e-17] var b = [0.16666667, 0.5, 0.5, 0.16666667 ] var f = TDF_II_filter(signal, a, b)

say "[" say f.map { "% 0.8f" % _ }.slices(5).map{.join(', ')}.join(",\n") say "]"</lang>

Output:

[
-0.15297399, -0.43525783, -0.13604340,  0.69750333,  0.65644469,
-0.43548245, -1.08923946, -0.53767655,  0.51704999,  1.05224975,
 0.96185430,  0.69569009,  0.42435630,  0.19626223, -0.02783512,
-0.21172192, -0.17474556,  0.06925841,  0.38544587,  0.65177084
]

Yabasic

Translation of: D

<lang Yabasic>sub filter(a(), b(), signal(), result())

   local i, j, tmp

   for i = 0 to arraysize(signal(), 1)
       tmp = 0
       for j = 0 to arraysize(b(), 1)
           if (i-j<0) continue
           tmp = tmp + b(j) * signal(i-j)
       next
       for j = 0 to arraysize(a(), 1)
           if (i-j<0) continue
           tmp = tmp - a(j) * result(i-j)
       next
       tmp = tmp / a(0)
       result(i) = tmp
   next

end sub

dim a(4), b(4), signal(20), result(20)

// a() data 1, -2.77555756e-16, 3.33333333e-01, -1.85037171e-17 // b() data 0.16666667, 0.5, 0.5, 0.16666667 // signal() data -0.917843918645, 0.141984778794, 1.20536903482, 0.190286794412 data -0.662370894973, -1.00700480494, -0.404707073677, 0.800482325044 data 0.743500089861, 1.01090520172, 0.741527555207, 0.277841675195 data 0.400833448236, -0.2085993586, -0.172842103641, -0.134316096293 data 0.0259303398477, 0.490105989562, 0.549391221511, 0.9047198589

for i = 0 to 3 : read a(i) : next for i = 0 to 3 : read b(i) : next for i = 0 to 19 : read signal(i) : next

filter(a(),b(),signal(),result())

for i = 0 to 19

   print result(i) using "%11.8f";
   if mod(i+1, 5) <> 0 then
       print ", ";
   else
       print
   end if

next</lang>

zkl

Translation of: C++

<lang zkl>fcn direct_form_II_transposed_filter(b,a,signal){

  out:=List.createLong(signal.len(),0.0);  // vector of zeros
  foreach i in (signal.len()){
     tmp:=0.0;
     foreach j in (b.len()){ if(i-j >=0) tmp += b[j]*signal[i-j] }
     foreach j in (a.len()){ if(i-j >=0) tmp -= a[j]*out[i-j]    }
     out[i] = tmp/a[0];
  }
  out

}</lang> <lang zkl>signal:=T(-0.917843918645, 0.141984778794, 1.20536903482, 0.190286794412, -0.662370894973,-1.00700480494, -0.404707073677, 0.800482325044, 0.743500089861, 1.01090520172, 0.741527555207, 0.277841675195, 0.400833448236,-0.2085993586, -0.172842103641,-0.134316096293, 0.0259303398477,0.490105989562, 0.549391221511, 0.9047198589 ); a:=T(1.0, -2.77555756e-16, 3.33333333e-01, -1.85037171e-17 ); b:=T(0.16666667, 0.5, 0.5, 0.16666667 ); result:=direct_form_II_transposed_filter(b,a,signal); println(result);</lang>

Output:

L(-0.152974,-0.435258,-0.136043,  0.697503, 0.656445,-0.435482,
  -1.08924, -0.537677, 0.51705,   1.05225,  0.961854, 0.69569,
   0.424356, 0.196262,-0.0278351,-0.211722,-0.174746, 0.0692584,
   0.385446, 0.651771)

References

↑ [1]

[1] [1]

[1]