Revisions to How to implement a discrete transfer function into an arduino?

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edited Apr 1, 2020 at 1:22

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I am here asking how does one transfer a difference equation into a MCU? I have never done it personally and looking into this topic I was never able to find a good answer. Its usually used with Matlab but never a MCU.

I have a continuous transfer function:

$$LPF_A = \frac{1}{6.416\cdot 10^{-11}s^2+1.133\cdot 10^{-5}s+1}$$

Its a 2nd Order Butterworth filter with a \$F_c = 20\text{kHz}\$.

Using the Tustin method I have the discrete equation:

$$LPF_D=\frac{0.1441z^2+0.2881z+0.1441}{z^2-0.6777z+0.254}$$ With a sample of \$T_s = \$ 8e-6 seconds, in scientific E notation.

The difference equation:

\$Y\$ = Output

\$U\$ = Input

$$Y_i =0.1441U_{i}+0.2281U_{i-1}+0.1441U_{i-2}+0.6777Y_{i-1}-0.254Y_{i-2}$$

I know I have to make my ADC output = \$U_i\$ and initialize \$U_{i-1}\$, \$U_{i-2}\$, \$Y_{i-1}\$, \$Y_{i-2} = 0\$, But after that no idea.

I have no idea what to do with this after. I have always used Matlab's embedded ways of doing it but never have transferred a difference equation into a MCU before. Any help would be appreciated.

Edit: Here's the code based on what I think

  unsigned short x;
intdouble Y_i[10];Y_i[10] = {0,0,0,0,0,0,0,0,0,0};
intdouble U_i[10];U_i[10] = {0,0,0,0,0,0,0,0,0,0};
intdouble Y_i_1 = 0;
intdouble Y_i_2 = 0;
intdouble U_i_1 = 0;
intdouble U_i_2 = 0;

void setup() {
  
  ADMUX |= 0xC0;
  ADCSRA |= 0x8F;
  ADCSRA |= 0x40;
  Serial.begin(9600);
  
}

ISR(ADC_vect) {
 x = ADCL << 2;
 x |= ADCH;
 ADCSRA |= 0x40;
}

void loop() {
  //Yi = 0.1441Ui + 0.2281Ui-1 + 0.1441Ui-2 + 0.6777Yi-1 - 0.254Yi-2 
 
  for (int i = 1; i < 3;4; i++){

    if (i == 1) {
       Y_i[i] = 0.1441*x144*x + 0.2281*U_i_1 + 0.1441*U_i_2 + 0.6777*Y_i_1 - 0.254*Y_i_2;
       U_i[i] = x;
    }
    else if (i == 2) {
      Y_i[i] = 0.1441*x144*x + 0.2281*U_i[i-1] + 0.1441*U_i[i-2] + 0.6777*Y_i[i-1] - 0.254*Y_i[i-2];
      U_i[i] = x;
    } else {
      Y_i[i] = 0.1441*x144*x + 0.2281*U_i[i-1] + 0.1441*U_i[i-2] + 0.6777*Y_i[i-1] - 0.254*Y_i[i-2];
      U_i[i] = x;
    }
    
  }
  
}

What happens after the iteration is done? It resets? thats it?

I am here asking how does one transfer a difference equation into a MCU? I have never done it personally and looking into this topic I was never able to find a good answer. Its usually used with Matlab but never a MCU.

I have a continuous transfer function:

$$LPF_A = \frac{1}{6.416\cdot 10^{-11}s^2+1.133\cdot 10^{-5}s+1}$$

Its a 2nd Order Butterworth filter with a \$F_c = 20\text{kHz}\$.

Using the Tustin method I have the discrete equation:

$$LPF_D=\frac{0.1441z^2+0.2881z+0.1441}{z^2-0.6777z+0.254}$$ With a sample of \$T_s = \$ 8e-6 seconds, in scientific E notation.

The difference equation:

\$Y\$ = Output

\$U\$ = Input

$$Y_i =0.1441U_{i}+0.2281U_{i-1}+0.1441U_{i-2}+0.6777Y_{i-1}-0.254Y_{i-2}$$

I know I have to make my ADC output = \$U_i\$ and initialize \$U_{i-1}\$, \$U_{i-2}\$, \$Y_{i-1}\$, \$Y_{i-2} = 0\$, But after that no idea.

I have no idea what to do with this after. I have always used Matlab's embedded ways of doing it but never have transferred a difference equation into a MCU before. Any help would be appreciated.

Edit: Here's the code based on what I think

unsigned short x;
int Y_i[10];
int U_i[10];
int Y_i_1 = 0;
int Y_i_2 = 0;
int U_i_1 = 0;
int U_i_2 = 0;

void setup() {
  
  ADMUX |= 0xC0;
  ADCSRA |= 0x8F;
  ADCSRA |= 0x40;
  Serial.begin(9600);
  
}

ISR(ADC_vect) {
 x = ADCL << 2;
 x |= ADCH;
 ADCSRA |= 0x40;
}

void loop() {
  //Yi = 0.1441Ui + 0.2281Ui-1 + 0.1441Ui-2 + 0.6777Yi-1 - 0.254Yi-2 
 
  for (int i = 1; i < 3; i++){

    if (i == 1){
      Y_i[i] = 0.1441*x + 0.2281*U_i_1 + 0.1441*U_i_2 + 0.6777*Y_i_1 - 0.254*Y_i_2;
      U_i[i] = x;
    }
    else if (i == 2){
      Y_i[i] = 0.1441*x + 0.2281*U_i[i-1] + 0.1441*U_i[i-2] + 0.6777*Y_i[i-1] - 0.254*Y_i[i-2];
      U_i[i] = x;
    } else {
      Y_i[i] = 0.1441*x + 0.2281*U_i[i-1] + 0.1441*U_i[i-2] + 0.6777*Y_i[i-1] - 0.254*Y_i[i-2];
      U_i[i] = x;
    }
    
  }

}

I am here asking how does one transfer a difference equation into a MCU? I have never done it personally and looking into this topic I was never able to find a good answer. Its usually used with Matlab but never a MCU.

I have a continuous transfer function:

$$LPF_A = \frac{1}{6.416\cdot 10^{-11}s^2+1.133\cdot 10^{-5}s+1}$$

Its a 2nd Order Butterworth filter with a \$F_c = 20\text{kHz}\$.

Using the Tustin method I have the discrete equation:

$$LPF_D=\frac{0.1441z^2+0.2881z+0.1441}{z^2-0.6777z+0.254}$$ With a sample of \$T_s = \$ 8e-6 seconds, in scientific E notation.

The difference equation:

\$Y\$ = Output

\$U\$ = Input

$$Y_i =0.1441U_{i}+0.2281U_{i-1}+0.1441U_{i-2}+0.6777Y_{i-1}-0.254Y_{i-2}$$

I know I have to make my ADC output = \$U_i\$ and initialize \$U_{i-1}\$, \$U_{i-2}\$, \$Y_{i-1}\$, \$Y_{i-2} = 0\$, But after that no idea.

I have no idea what to do with this after. I have always used Matlab's embedded ways of doing it but never have transferred a difference equation into a MCU before. Any help would be appreciated.

Edit: Here's the code based on what I think

  unsigned short x;
double Y_i[10] = {0,0,0,0,0,0,0,0,0,0};
double U_i[10] = {0,0,0,0,0,0,0,0,0,0};
double Y_i_1 = 0;
double Y_i_2 = 0;
double U_i_1 = 0;
double U_i_2 = 0;

void setup() {
  
  ADMUX |= 0xC0;
  ADCSRA |= 0x8F;
  ADCSRA |= 0x40;
  Serial.begin(9600);
}

ISR(ADC_vect) {
 x = ADCL << 2;
 x |= ADCH;
 ADCSRA |= 0x40;
}

void loop() {
  //Yi = 0.1441Ui + 0.2281Ui-1 + 0.1441Ui-2 + 0.6777Yi-1 - 0.254Yi-2 
  for (int i = 1; i < 4; i++){

    if (i == 1) {
       Y_i[i] = 0.144*x + 0.2281*U_i_1 + 0.1441*U_i_2 + 0.6777*Y_i_1 - 0.254*Y_i_2;
       U_i[i] = x;
    } else if (i == 2) {
      Y_i[i] = 0.144*x + 0.2281*U_i[i-1] + 0.1441*U_i[i-2] + 0.6777*Y_i[i-1] - 0.254*Y_i[i-2];
      U_i[i] = x;
    } else {
      Y_i[i] = 0.144*x + 0.2281*U_i[i-1] + 0.1441*U_i[i-2] + 0.6777*Y_i[i-1] - 0.254*Y_i[i-2];
      U_i[i] = x;
    }
    
  }
  
}

What happens after the iteration is done? It resets? thats it?

added 1057 characters in body

Source Link

edited Mar 31, 2020 at 22:22

Leoc

1.4k
1
11
25

I am here asking how does one transfer a difference equation into a MCU? I have never done it personally and looking into this topic I was never able to find a good answer. Its usually used with Matlab but never a MCU.

I have a continuous transfer function:

$$LPF_A = \frac{1}{6.416\cdot 10^{-11}s^2+1.133\cdot 10^{-5}s+1}$$

Its a 2nd Order Butterworth filter with a \$F_c = 20\text{kHz}\$.

Using the Tustin method I have the discrete equation:

$$LPF_D=\frac{0.1441z^2+0.2881z+0.1441}{z^2-0.6777z+0.254}$$ With a sample of \$T_s = \$ 8e-6 seconds, in scientific E notation.

The difference equation:

\$Y\$ = Output

\$U\$ = Input

$$Y_i =0.1441U_{i}+0.2281U_{i-1}+0.1441U_{i-2}+0.6777Y_{i-1}-0.254Y_{i-2}$$

I know I have to make my ADC output = \$U_i\$ and initialize \$U_{i-1}\$, \$U_{i-2}\$, \$Y_{i-1}\$, \$Y_{i-2} = 0\$, But after that no idea.

I have no idea what to do with this after. I have always used Matlab's embedded ways of doing it but never have transferred a difference equation into a MCU before. Any help would be appreciated.

Edit: Here's the code based on what I think

unsigned short x;
int Y_i[10];
int U_i[10];
int Y_i_1 = 0;
int Y_i_2 = 0;
int U_i_1 = 0;
int U_i_2 = 0;

void setup() {
  
  ADMUX |= 0xC0;
  ADCSRA |= 0x8F;
  ADCSRA |= 0x40;
  Serial.begin(9600);
  
}

ISR(ADC_vect) {
 x = ADCL << 2;
 x |= ADCH;
 ADCSRA |= 0x40;
}

void loop() {
  //Yi = 0.1441Ui + 0.2281Ui-1 + 0.1441Ui-2 + 0.6777Yi-1 - 0.254Yi-2 

  for (int i = 1; i < 3; i++){

    if (i == 1){
      Y_i[i] = 0.1441*x + 0.2281*U_i_1 + 0.1441*U_i_2 + 0.6777*Y_i_1 - 0.254*Y_i_2;
      U_i[i] = x;
    }
    else if (i == 2){
      Y_i[i] = 0.1441*x + 0.2281*U_i[i-1] + 0.1441*U_i[i-2] + 0.6777*Y_i[i-1] - 0.254*Y_i[i-2];
      U_i[i] = x;
    } else {
      Y_i[i] = 0.1441*x + 0.2281*U_i[i-1] + 0.1441*U_i[i-2] + 0.6777*Y_i[i-1] - 0.254*Y_i[i-2];
      U_i[i] = x;
    }
    
  }

}

I am here asking how does one transfer a difference equation into a MCU? I have never done it personally and looking into this topic I was never able to find a good answer. Its usually used with Matlab but never a MCU.

I have a continuous transfer function:

$$LPF_A = \frac{1}{6.416\cdot 10^{-11}s^2+1.133\cdot 10^{-5}s+1}$$

Its a 2nd Order Butterworth filter with a \$F_c = 20\text{kHz}\$.

Using the Tustin method I have the discrete equation:

$$LPF_D=\frac{0.1441z^2+0.2881z+0.1441}{z^2-0.6777z+0.254}$$ With a sample of \$T_s = \$ 8e-6 seconds, in scientific E notation.

The difference equation:

\$Y\$ = Output

\$U\$ = Input

$$Y_i =0.1441U_{i}+0.2281U_{i-1}+0.1441U_{i-2}+0.6777Y_{i-1}-0.254Y_{i-2}$$

I know I have to make my ADC output = \$U_i\$ and initialize \$U_{i-1}\$, \$U_{i-2}\$, \$Y_{i-1}\$, \$Y_{i-2} = 0\$, But after that no idea.

I have no idea what to do with this after. I have always used Matlab's embedded ways of doing it but never have transferred a difference equation into a MCU before. Any help would be appreciated.

I am here asking how does one transfer a difference equation into a MCU? I have never done it personally and looking into this topic I was never able to find a good answer. Its usually used with Matlab but never a MCU.

I have a continuous transfer function:

$$LPF_A = \frac{1}{6.416\cdot 10^{-11}s^2+1.133\cdot 10^{-5}s+1}$$

Its a 2nd Order Butterworth filter with a \$F_c = 20\text{kHz}\$.

Using the Tustin method I have the discrete equation:

$$LPF_D=\frac{0.1441z^2+0.2881z+0.1441}{z^2-0.6777z+0.254}$$ With a sample of \$T_s = \$ 8e-6 seconds, in scientific E notation.

The difference equation:

\$Y\$ = Output

\$U\$ = Input

$$Y_i =0.1441U_{i}+0.2281U_{i-1}+0.1441U_{i-2}+0.6777Y_{i-1}-0.254Y_{i-2}$$

I know I have to make my ADC output = \$U_i\$ and initialize \$U_{i-1}\$, \$U_{i-2}\$, \$Y_{i-1}\$, \$Y_{i-2} = 0\$, But after that no idea.

I have no idea what to do with this after. I have always used Matlab's embedded ways of doing it but never have transferred a difference equation into a MCU before. Any help would be appreciated.

Edit: Here's the code based on what I think

unsigned short x;
int Y_i[10];
int U_i[10];
int Y_i_1 = 0;
int Y_i_2 = 0;
int U_i_1 = 0;
int U_i_2 = 0;

void setup() {
  
  ADMUX |= 0xC0;
  ADCSRA |= 0x8F;
  ADCSRA |= 0x40;
  Serial.begin(9600);
  
}

ISR(ADC_vect) {
 x = ADCL << 2;
 x |= ADCH;
 ADCSRA |= 0x40;
}

void loop() {
  //Yi = 0.1441Ui + 0.2281Ui-1 + 0.1441Ui-2 + 0.6777Yi-1 - 0.254Yi-2 

  for (int i = 1; i < 3; i++){

    if (i == 1){
      Y_i[i] = 0.1441*x + 0.2281*U_i_1 + 0.1441*U_i_2 + 0.6777*Y_i_1 - 0.254*Y_i_2;
      U_i[i] = x;
    }
    else if (i == 2){
      Y_i[i] = 0.1441*x + 0.2281*U_i[i-1] + 0.1441*U_i[i-2] + 0.6777*Y_i[i-1] - 0.254*Y_i[i-2];
      U_i[i] = x;
    } else {
      Y_i[i] = 0.1441*x + 0.2281*U_i[i-1] + 0.1441*U_i[i-2] + 0.6777*Y_i[i-1] - 0.254*Y_i[i-2];
      U_i[i] = x;
    }
    
  }

}

edited body

Source Link

edited Mar 31, 2020 at 18:46

Leoc

1.4k
1
11
25

I am here asking how does one transfer a difference equation into a MCU? I have never done it personally and looking into this topic I was never able to find a good answer. Its usually used with Matlab but never a MCU.

I have a continuous transfer function:

$$LPF_A = \frac{1}{6.416\cdot 10^{-11}s^2+1.133\cdot 10^{-5}s+1}$$

Its a 2nd Order Butterworth filter with a \$F_c = 20\text{kHz}\$.

Using the Tustin method I have the discrete equation:

$$LPF_D=\frac{0.1441z^2+0.2881z+0.1441}{z^2-0.6777z+0.254}$$ With a sample of \$T_s = \$ 8e-6 seconds, in scientific E notation.

The difference equation:

\$Y\$ = outputOutput

\$U\$ = Input

$$Y_i =0.1441U_{i}+0.2281U_{i-1}+0.1441U_{i-2}+0.6777Y_{i-1}-0.254Y_{i-2}$$

I know I have to make my ADC output = \$U_i\$ and initialize \$U_{i-1}\$, \$U_{i-2}\$, \$Y_{i-1}\$, \$Y_{i-2} = 0\$, But after that no idea.

I have no idea what to do with this after. I have always used Matlab's embedded ways of doing it but never have transferred a difference equation into a MCU before. Any help would be appreciated.

I am here asking how does one transfer a difference equation into a MCU? I have never done it personally and looking into this topic I was never able to find a good answer. Its usually used with Matlab but never a MCU.

I have a continuous transfer function:

$$LPF_A = \frac{1}{6.416\cdot 10^{-11}s^2+1.133\cdot 10^{-5}s+1}$$

Its a 2nd Order Butterworth filter with a \$F_c = 20\text{kHz}\$.

Using the Tustin method I have the discrete equation:

$$LPF_D=\frac{0.1441z^2+0.2881z+0.1441}{z^2-0.6777z+0.254}$$ With a sample of \$T_s = \$ 8e-6 seconds, in scientific E notation.

The difference equation:

\$Y\$ = output

\$U\$ = Input

$$Y_i =0.1441U_{i}+0.2281U_{i-1}+0.1441U_{i-2}+0.6777Y_{i-1}-0.254Y_{i-2}$$

I know I have to make my ADC output = \$U_i\$ and initialize \$U_{i-1}\$, \$U_{i-2}\$, \$Y_{i-1}\$, \$Y_{i-2} = 0\$, But after that no idea.

I have no idea what to do with this after. I have always used Matlab's embedded ways of doing it but never have transferred a difference equation into a MCU before. Any help would be appreciated.

I am here asking how does one transfer a difference equation into a MCU? I have never done it personally and looking into this topic I was never able to find a good answer. Its usually used with Matlab but never a MCU.

I have a continuous transfer function:

$$LPF_A = \frac{1}{6.416\cdot 10^{-11}s^2+1.133\cdot 10^{-5}s+1}$$

Its a 2nd Order Butterworth filter with a \$F_c = 20\text{kHz}\$.

Using the Tustin method I have the discrete equation:

$$LPF_D=\frac{0.1441z^2+0.2881z+0.1441}{z^2-0.6777z+0.254}$$ With a sample of \$T_s = \$ 8e-6 seconds, in scientific E notation.

The difference equation:

\$Y\$ = Output

\$U\$ = Input

$$Y_i =0.1441U_{i}+0.2281U_{i-1}+0.1441U_{i-2}+0.6777Y_{i-1}-0.254Y_{i-2}$$

I know I have to make my ADC output = \$U_i\$ and initialize \$U_{i-1}\$, \$U_{i-2}\$, \$Y_{i-1}\$, \$Y_{i-2} = 0\$, But after that no idea.

I have no idea what to do with this after. I have always used Matlab's embedded ways of doing it but never have transferred a difference equation into a MCU before. Any help would be appreciated.