# Apply a digital filter (direct form II transposed)

Apply a digital filter (direct form II transposed)
You are encouraged to solve this task according to the task description, using any language you may know.

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]

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.

` /*Abhishek Ghosh, 25th October 2017*/ #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;} `

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.

`#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;}`
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,`

## D

Translation of: Kotlin
`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;        }    }}`
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

`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)    }}`
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
```

## Java

Translation of: 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");        }    }}`
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
`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 rstend 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)`
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++
`// 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")    }}`
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:

` 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) figuresubplot(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') `
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

`/* 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,retDo i=1 To ret~items  Say format(i,2) format(ret[i],2,12)  EndExit ::Routine filterUse Arg a,b,s,retDo 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]  EndReturn ::OPTIONS digits 24      /* Numeric Digits 24, everywhere */ `
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
`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 *;`
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,
)```

## Python

`#!/bin/pythonfrom __future__ import print_functionfrom scipy import signalimport 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()`
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
`/*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                               /*process each of the vector elements. */     #=0                                         /*temp variable used in calculations.  */         do j=1  for words(@b); if i-j >= 0  then #= #  +  word(@b, j)  *  word(@s, i-j+1)         end   /*j*/                             /* [↑]  process all the B coefficients.*/          do k=1  for words(@a);   _=i - k + 1;   if i-k >= 0  then #=# - word(@a, k) * \$._         end   /*k*/                             /* [↑]  process all the A coefficients.*/     \$.i= # / word(@a ,1);        call tell      /*only display using half the dec digs.*/     end               /*i*/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`
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
`/* REXX */Numeric Digits 24acoef = '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-1Do i=1 By 1 While bcoef>'';  Parse Var bcoef b.i . ',' bcoef;   End; b.0=i-1Do i=1 By 1 While signal>''; Parse Var signal s.i . ',' signal; End; s.0=i-1 ret.=0Do 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`
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
`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!();}`
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
`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 "]"`
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
]
```

## zkl

Translation of: C++
`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}`
`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);`
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]