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C++ > Mathematics Code Examples

Program to Compute DFT Coefficients Directly

/* Program to Compute DFT Coefficients Directly This is a C++ Program to compute the coefficients of the DFT (Discrete Fourier Transform) directly. In mathematics, the discrete Fourier transform (DFT) converts a finite list of equally spaced samples of a function into the list of coefficients of a finite combination of complex sinusoids, ordered by their frequencies, that has those same sample values. It can be said to convert the sampled function from its original domain (often time or position along a line) to the frequency domain. */ #include<iostream> #include<math.h> using namespace std; #define PI 3.14159265 class DFT_Coefficient { public: double real, img; DFT_Coefficient() { real = 0.0; img = 0.0; } }; int main(int argc, char **argv) { int N = 10; cout << "Calculation DFT Coefficients\n"; cout << "Enter the coefficient of simple linear function:\n"; cout << "ax + by = c\n"; double a, b, c; cin >> a >> b >> c; double function[N]; for (int j = 0; j < N; j++) { function[j] = (((a * (double) j) + (b * (double) j)) - c); //System.out.print( " "+function[j] + " "); } cout << "Enter the max K value: "; int k; cin >> k; double cosine[N]; double sine[N]; for (int j = 0; j < N; j++) { cosine[j] = cos((2 * j * k * PI) / N); sine[j] = sin((2 * j * k * PI) / N); } DFT_Coefficient dft_val; cout << "The coefficients are: "; for (int j = 0; j < N; j++) { dft_val.real += function[j] * cosine[j]; dft_val.img += function[j] * sine[j]; } cout << "(" << dft_val.real << ") - " << "(" << dft_val.img << " j)"; }

Transform range. Applies an operation sequentially to the elements of one (1) or two (2) ranges and stores the result in the range that begins at result. The transform() function in C++ sequentially applies an operation to the elements of an array(s) and then stores the result in another output array. The transform function is used in two forms: Unary operation: The operation is applied to each element in the input range, and the result is stored in the output array. The transform() function takes the pointer to the starting and ending position of a single input array and to the starting position of the output array.

Compute sine. Returns the sine of an angle of x radians. sin() function is a library function of cmath header, it is used to find the sine of the given number (angle), it accepts a number (x) and returns the sine of angle x radians. Additional overloads are provided in this header (<cmath>) for the integral types: These overloads effectively cast x to a double before calculations (defined for T being any integral type). This function is also overloaded in <complex> and <valarray> (see complex sin and valarray sin).

As the name already suggests, these operators help in assigning values to variables. These operators help us in allocating a particular value to the operands. The main simple assignment operator is '='. We have to be sure that both the left and right sides of the operator must have the same data type. We have different levels of operators. Assignment operators are used to assign the value, variable and function to another variable. Assignment operators in C are some of the C Programming Operator, which are useful to assign the values to the declared variables. Let's discuss the various types of the assignment operators such as =, +=, -=, /=, *= and %=. The following table lists the assignment operators supported by the C language:

In the C++ Programming Language, the #define directive allows the definition of macros within your source code. These macro definitions allow constant values to be declared for use throughout your code. Macro definitions are not variables and cannot be changed by your program code like variables. You generally use this syntax when creating constants that represent numbers, strings or expressions. The syntax for creating a constant using #define in the C++ is: #define token value

Compute cosine. Returns the cosine of an angle of x radians. cos() function is a library function of cmath header, it is used to find the cosine of the given number (angle), it accepts a number (x) and returns the cosine of angle x radians. In trigonometry, the cos function of a right-angled triangle is defined as the length of the adjacent side over the longest side, i.e., the hypotenuse. The cos function in C++ works precisely like the cosine function in trigonometry. The return value of the cos function is the cosine of an angle given in radian. Function returns cosine of x radians.

The main purpose of C++ programming is to add object orientation to the C programming language and classes are the central feature of C++ that supports object-oriented programming and are often called user-defined types. A class is used to specify the form of an object and it combines data representation and methods for manipulating that data into one neat package. The data and functions within a class are called members of the class.

In computer programming, loops are used to repeat a block of code. For example, when you are displaying number from 1 to 100 you may want set the value of a variable to 1 and display it 100 times, increasing its value by 1 on each loop iteration. When you know exactly how many times you want to loop through a block of code, use the for loop instead of a while loop. A for loop is a repetition control structure that allows you to efficiently write a loop that needs to execute a specific number of times.

#include is a way of including a standard or user-defined file in the program and is mostly written at the beginning of any C/C++ program. This directive is read by the preprocessor and orders it to insert the content of a user-defined or system header file into the following program. These files are mainly imported from an outside source into the current program. The process of importing such files that might be system-defined or user-defined is known as File Inclusion. This type of preprocessor directive tells the compiler to include a file in the source code program.

Consider a situation, when we have two persons with the same name, jhon, in the same class. Whenever we need to differentiate them definitely we would have to use some additional information along with their name, like either the area, if they live in different area or their mother's or father's name, etc. Same situation can arise in your C++ applications. For example, you might be writing some code that has a function called xyz() and there is another library available which is also having same function xyz(). Now the compiler has no way of knowing which version of xyz() function you are referring to within your code.

The cin object is used to accept input from the standard input device i.e. keyboard. It is defined in the iostream header file. C++ cin statement is the instance of the class istream and is used to read input from the standard input device which is usually a keyboard. The extraction operator(>>) is used along with the object cin for reading inputs. The extraction operator extracts the data from the object cin which is entered using the keyboard. The "c" in cin refers to "character" and "in" means "input". Hence cin means "character input". The cin object is used along with the extraction operator >> in order to receive a stream of characters.

Arithmetic Operator is used to performing mathematical operations such as addition, subtraction, multiplication, division, modulus, etc., on the given operands. For example: 6 + 3 = 9, 5 - 3 = 2, 3 * 4 = 12, etc. are the examples of arithmetic operators. Let's discuss the different types of Arithmetic Operators in the C programming. Plus Operator is a simple Plus (+) Operator used to add two given operands. We can use Plus Operator with different data types such as integer, float, long, double, enumerated and string type data to add the given operand. The minus operator is denoted by the minus (-) symbol. It is used to return the subtraction of the first number from the second number. The data type of the given number can be different types, such as int, float, double, long double, etc., in the programing language.

In C++, constructor is a special method which is invoked automatically at the time of object creation. It is used to initialize the data members of new object generally. The constructor in C++ has the same name as class or structure. Constructors are special class functions which performs initialization of every object. The Compiler calls the Constructor whenever an object is created. Constructors initialize values to object members after storage is allocated to the object. Whereas, Destructor on the other hand is used to destroy the class object. • Default Constructor: A constructor which has no argument is known as default constructor. It is invoked at the time of creating object.

A program shall contain a global function named main, which is the designated start of the program in hosted environment. main() function is the entry point of any C++ program. It is the point at which execution of program is started. When a C++ program is executed, the execution control goes directly to the main() function. Every C++ program have a main() function.