Outline. Arrays. Function Arguments. Arrays. Adding Two Arrays /* */ /* This program adds 2 arrays */ ELEC 330 1

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1 ELEC Arrays ELEC 06 Computer Applications for Electrical Engineers Dr. Ron Hayne Outline Arrays Statistical Measurements Functions Revisited 06_C6 Arrays One-dimensional array List of values Arranged in either a row or a column Offsets (Subscripts) distinguish between elements in the array Identifier holds address of first element Offsets always start at 0 Definition and Initialization Declaration double x[4]; Initialization double x[4] = 1., -.4, 0.8, 6.1; int t[100] = 0; char v[] = 'a', 'e', 'i', 'o', 'u'; The size of the array must be specified by a constant in brackets, or by an initialization list Loops double g[1]; for (int k=0; k<=0; k++) g[k] = k*0.5; 06_C6 3 06_C6 4 Adding Two Arrays /* */ /* This program adds arrays */ int x[]=1,3,6,4,6; int y[]=,4,1,5,0; for (int k=0; k<=4; k++) y[k] = x[k] + y[k]; cout << y[k] << endl; system("pause"); return 0; /* */ 06_C6 5 Function Arguments Passing array information to a function Two parameters usually used Specific array Number of elements in the array Always call by reference Address of the array 06_C6 6

2 ELEC 330 Data Files Reading data into arrays double time[10], motion[10]; ifstream sensor3("sensor3.dat");... if(!sensor3.fail()) for (int k=0; k<=9; k++) sensor3 >> time[k] >> motion[k]; /* Program chapter6_ */ /* */ /* This program reads values from a data file and */ /* calls a function to determine the maximum value */ /* with a function. */ #include <fstream> // Define constants and declare function prototypes. double maxval(double x[], int n); // open file ifstream sensor1; // Declare object stream sensor1.open("sensor1.dat"); if(sensor1.fail()) cout << "Error opening input file\n"; 06_C6 7 06_C6 8 else // Read a data value from the file. int N, npts(0); sensor1 >> N; double time, y[n]; while (npts <= (N-1)) sensor1 >> time >> y[npts]; cout << y[npts] <<endl; npts++; //read in num pts from file // declare array y //read data into y in a loop //print y values to screen // Increment npts. // Find and print the maximum value. cout << "Maximum value: " << maxval(y,npts) << endl; //call function maxval() // Close file and exit program. sensor1.close(); system("pause"); return 0; /* */ /* This function returns the maximum */ /* value in the array x with n elements. */ double maxval(double x[], int n) // Declare local objects. double max_x; // Determine maximum value in the array. max_x = x[0]; for (int k=1; k<=n-1; k++) if (x[k] > max_x) max_x = x[k]; // Return maximum value. / return max_x; /* */ 06_C6 9 06_C6 10 Statistical Measurements Maximum Minimum Mean (average) Median (middle) Variance Average squared deviation from the mean Standard Deviation Square root of the variance 06_C6 11 Mean double mean(double x[], int n) double sum(0); sum += x[k]; return sum/n; 06_C6 1

3 ELEC Variance Random Numbers double variance(double x[], int n) double sum(0), mu; mu = mean(x,n); sum += (x[k] - mu)*(x[k] - mu); return sum/(n-1); 06_C6 13 The following relation exists between the limits (a, b) of a sequence of uniform random numbers And the theoretical mean (µ) and variance (σ ). ( b a) ( a + b) σ = µ = 1 Solving for a and b yields 1σ a = µ and b = µ a 06_C6 14 HW Problem 6-0 /* Problem chapter6_0 */ /* */ /* This program generates two sequences of 500 points. Each */ /* sequence should have a theoretical mean of 4, but one sequence */ /* should have a variance of 0.5 and the other a variance of. */ /* The computed means and variances are printed. */ #include <cstdlib> #include <cmath> const double MEAN = 4.0; const double VAR1 = 0.5; const double VAR =.0; const int MAX_POINTS = 500; HW 6-0 continued //Define function prototypes double rand_float(double, double); double variance(double x[], int); double mean(double x[], int); /* Define variables and function prototypes. */ int index = 0; double first_sequence[max_points], second_sequence[max_points]; double a1, b1, a, b, mean1, mean, var1, var; /* Find the limits (a1, b1, a, b) on the random number generator. */ a1 = b1 = a = b = 06_C _C6 16 HW 6-0 continued /* Generate random numbers in the sample. */ for (index=0; index<max_points; index++) first_sequence[index] = second_sequence[index] = /* Calculate sample means and variances. */ var1 = var = mean1 = mean = /* Print results. */ cout << "Sequence 1: Mean: " << mean1 << " Variance: " << var1 << endl; cout << "Sequence : Mean: " << mean << " Variance: " << var << endl; cout << "Theoretically: Mean: " << MEAN << " Variance 1: " << VAR1 << " Variance : " << VAR << endl; system ( pause ); return (0); /* */ // Add the three functions here. 1. rand_float();. variance(); 3. and mean(); 06_C6 17 Function Overloading Function name can have more than one definition Each function definition has a unique function signature Each function call looks for a function prototype with a matching function signature double maxval(double x[], int n); int maxval(int x[], int n); char maxval(char x[], int n); 06_C6 18

4 ELEC Function Templates Sorting Algorithms Generic algorithm for a function that is not tied to a specific data type template <class Data_type> Data_type minval(data_type x[], int n) Data_type minx;... Sorting Arranging in ascending (descending) order Not one "best" algorithm Depends on characteristics of data Selection Sort Find smallest value from current position to end Swap smallest with current position Move to next position 06_C _C6 0 //Chap6_selection_sort.cpp #include <cstdlib> void sort(double x[], int n) // Selection sort int m; // marker double hold; void sort(double x[], int n); void display(double x[], int n); const int N = 6; double data[n] = 5.0, 3.0, 1.0, 8.0, 1.0, 9.0; cout << "Initial data" << endl; display(data, N); sort(data, N); cout << "Sorted data" << endl; display(data, N); for (int k=0; k<=n-; k++) m = k; // Find smallest value for (int j=k+1; j<=n-1; j++) if (x[j] < x[m]) m = j; hold = x[m]; // Swap smallest with current x[m] = x[k]; x[k] = hold; cout << "After k=" << k << endl; display(x, n); void display(double x[], int n) cout << x[k] << ' '; cout << endl; Speech Signal Analysis Problem Statement Compute the following statistical measurements for a speech utterance: average power, average magnitude, and number of zero crossings. Input/Output Description Average power Average magnitude Zero.dat Zero crossings 06_C6 3 06_C6 4

5 ELEC Hand Example test.dat Average power = Average magnitude =.7 Number of zero crossings = Algorithm Development main read speech signal from data file and determine number of points, n compute statistical measurements using functions ave_power(x, n) set sum to zero for k: add x[k] to sum return sum/n 06_C6 5 06_C6 6 Algorithm Development ave_mag(x, n) set sum to zero for k: add x[k] to sum return sum/n crossings(x, n) set count to zero for k: if x[k] * x[k+1] < 0, increment count return count /* This program computes a set of statistical */ /* measurements from a speech signal. */ #include <cstdlib> #include <fstream> #include <string> #include <cmath> // Declare function prototypes and define constants. double ave_power(double x[], int n); double ave_magn(double x[], int n); int crossings(double x[], int n); const int MAXIMUM = 500; 06_C6 7 // Declare objects. int npts=0; double speech[maximum]; string filename; ifstream file_1; // Prompt user for file name and open file. cout << "Enter filename "; cin >> filename; file_1.open(filename.c_str()); if( file_1.fail() ) cout << "error opening file " << filename << endl; return 1; // Read information from a data file. while (npts <= MAXIMUM-1 && file_1 >> speech[npts]) npts++; // Compute and print statistics. cout << "Statistics \n"; cout << "\taverage power: " << ave_power(speech,npts) << endl; cout << "\taverage magnitude: " << ave_magn(speech,npts) << endl; cout << "\tzero crossings: " << crossings(speech,npts) << endl; // Close file and exit program. file_1.close(); system("pause"); return 0;

6 ELEC /* This function returns the average power */ /* of an array x with n elements. */ /* This function returns the average magnitude */ /* of an array x with n values. */ double ave_power(double x[], int n) double sum=0; // Determine average power. sum += x[k]*x[k]; double ave_magn(double x[], int n) double sum=0; // Determine average magnitude. sum += abs(x[k]); // Return average power. return sum/n; // Return average magnitude. return sum/n; /* This function returns a count of the number */ /* of zero crossings in an array x with n values. */ Testing int crossings(double x[], int n) int count=0; // Determine number of zero crossings. for (int k=0; k<=n-; k++) if (x[k]*x[k+1] < 0) count++; // Return number of zero crossings. return count; 06_C6 34 Testing Summary Arrays Statistical Measurements Functions Revisited Selection Sort End of Chapter Summary C++ Statements Style Notes Debugging Notes 06_C _C6 36