In this assignment we will learn more about frequency response by writing a C++
ID: 2990156 • Letter: I
Question
In this assignment we will learn more about frequency response by writing a C++ function. Your function
should have the following prototype:
std::vector<double> calculate_mag_response(double start_freq, double end_freq,
int N, std::vector<double> num, std::vector<double> den)
The function should return a vector size
N
of magnitude responses in decibels of the transfer function
dened by numerator and denominator vectors num and den.
I will test your function with a driver program call it say main.cpp, similar to the following. To adequately
test, you should drive this with more transfer functions.
#include <vector>
#include <iostream>
#include <cstdlib>
#include <ifstream>
using namespace std;
int main(int argc,char *argv[])
{
vector<double> myNum, myDen, results;
ifstream outfile;
int N;
outfile.open("datafile.txt");
myNum.push_back(1.0);
myNum.push_back(1.0); //create a smple zero at s=-1
myDen.push_back(1.0);
myDen.push_back(3.0);
myDen.push_back(2.0); //create two poles at s=-1,-2
results=calculate_mag_response(.1,1000,100,myNum,myDen); //Call the student function
if (N=results.size()!= 100)
{
cout << "Your function did not provide correct number of data points. Please fix" << endl;
exit(0);
}
for (int i=0;i<N;i++)
outfile << i << " " << results[i] << endl; //Write this garbage to a file
return(0);
}
Explanation / Answer
#include <vector>
#include <iostream>
#include <cstdlib>
#include <fstream>
#include <math.h>
using namespace std;
std::vector<double> calculate_mag_response(double start_freq, double end_freq, int N, std::vector<double> num, std::vector<double> den)
{
int count=0;
//------------------FOR FREQUENCY ARRAY -------------------//
double freq_step =(end_freq-start_freq)/(N-1); // calculate step size for N; Formula is (end_freq-start_freq)/(N-1)
std::vector<double> freq;
std::vector<double> result;
freq.push_back(start_freq); //insert start_freq into frequency vector
for(int i=1;i<N;i++)
freq.push_back(start_freq+i*freq_step); //insert frequency with increment with step size
//--------------------------------------------------------//
//-----------FOR REAL AND IMAGINARY COEFFICIENT ----------//
std::vector<double> den_re;
std::vector<double> den_img;
std::vector<double> num_re;
std::vector<double> num_img;
double omega=0;
//-------------------Denominator-------------------------------------
while(!den.empty()) // Seperate Imaginary and Real Coefficent From the Denominator
{
if(count%2==0) // for every polynomial when s=jw then even power of s coefficents are real
{
if(count%4==0) // For Real coefficient s^0 have +ve sign, s^2 -ve sign
den_re.push_back(den.back());
if(count%4==2)
den_re.push_back(-den.back());
den.pop_back();
}
else // for every polynomial when s=jw then odd power of s coefficents are real
{
if(count%4==1) // For Real coefficient s^1 have +ve sign, s^3 -ve sign
den_img.push_back(den.back());
if(count%4==3)
den_img.push_back(-den.back());
den.pop_back();
}
count++;
}
count=0;
//-------------------Numerator-------------------------------------
while(!num.empty())
{
if(count%2==0)
{
if(count%4==0)
num_re.push_back(num.back());
if(count%4==2)
num_re.push_back(-num.back());
num.pop_back();
}
else
{
if(count%4==1)
num_img.push_back(num.back());
if(count%4==3)
num_img.push_back(-num.back());
num.pop_back();
}
count++;
}
//--------------------------------------------------------//
for(int i=0;i<freq.size();i++)
{
//-----------------------CALCULATION FOR DENOMINATOR MAGNITUDE COEFFICIENT-------------------------
double sum_re=0;
double sum_img=0;
double sum_den;
double sum_num;
double num_den;
for(int j=0;j<den_re.size();j++)
{
double comp1=den_re[j]*pow(freq[i],(2*j)); //coefficient * power of Frequency term for Real
sum_re+=comp1;
}
sum_re=pow(sum_re,2); // Final Real Term Square
for(int j=0;j<den_img.size();j++)
{
double comp1=den_img[j]*pow(freq[i],(2*j+1)); //coefficient * power of Frequency term for Imaginary
sum_img+=comp1;
}
sum_img=pow(sum_img,2); // Final Imaginary Term Square
sum_den=sqrt(sum_re+sum_img);
//-----------------------CALCULATION FOR NUMERATOR COEFFICIENT-------------------------
sum_re=0;
sum_img=0;
for(int j=0;j<num_re.size();j++)
{
double comp1=num_re[j]*pow(freq[i],(2*j));
sum_re+=comp1;
}
sum_re=pow(sum_re,2);
for(int j=0;j<num_img.size();j++)
{
double comp1=num_img[j]*pow(freq[i],(2*j+1));
sum_img+=comp1;
}
sum_img=pow(sum_img,2);
sum_num=sqrt(sum_re+sum_img);
num_den=sum_num/sum_den; // Numerator Magnitude with Frquency divide Numerator Magnitude with Frquency
result.push_back(num_den);
//cout<<"Num : "<<sum_num<<" Den : "<<sum_den<<" Mag : "<<result[i]<<endl;
}
return result;
}
int main(int argc,char *argv[])
{
vector<double> myNum, myDen, results;
ofstream outfile; // ifstream outfile; This is Wrong By Professor
int N;
outfile.open("datafile.txt");
myNum.push_back(1.0);
myNum.push_back(1.0); //create a smple zero at s=-1
myDen.push_back(1.0);
myDen.push_back(3.0);
myDen.push_back(2.0); //create two poles at s=-1,-2
results=calculate_mag_response(.1,1000,100,myNum,myDen); //Call the student function
if (N=results.size()!= 100)
{
cout << "Your function did not provide correct number of data points. Please fix" << endl;
exit(0);
}
for (int i=0;i<results.size();i++)
outfile << i << " " << results[i] << endl; //Write this garbage to a file
return(0);
}