Manual DFT and IDFT Implementation in MATLAB/Octave
Implementing DFT and IDFT Manually in MATLAB/Octave
This document provides the complete MATLAB/Octave code for generating a sinusoidal signal, calculating its Discrete Fourier Transform (DFT) manually, and then reconstructing the original signal using the Inverse Discrete Fourier Transform (IDFT).
1. Signal Setup and Initialization
We begin by clearing the workspace and defining the time vector and the sinusoidal signal. The code uses 1-based indexing typical of MATLAB/Octave.
clear all; clc; closeRead More
Data Structures and Algorithms C Implementation
Counting Nodes in a Singly Linked List
int count(struct node *p) {
int c = 0;
while(p) {
c++;
p = p->next;
}
return c;
}Postfix Expression Evaluation
Given values: A=2, B=10, C=4, D=1
i) AB–CD*
- Substitute: 2 10 – 4 1 *
- Step 1: 2 – 10 = –8
- Step 2: 4 * 1 = 4
- Final Result: –4
ii) ABC–*
- Substitute: 2 10 4 – *
- Step 1: 10 – 4 = 6
- Step 2: 2 * 6 = 12
- Final Result: 12
Graph Theory Definitions
- Bridge: An edge whose removal increases the number of connected components.
- Cyclic
Neural Network Architectures and Learning Concepts
Feedforward Neural Network (FNN)
A Feedforward Neural Network is the simplest type of artificial neural network in which information flows in only one direction, from the input layer to the output layer. There are no feedback connections or loops.
Basic Structure
- Consists of an input layer, one or more hidden layers, & an output layer.
- Data flows from input → hidden → output.
Single-layer Feedforward Network
Has an input layer & an output layer only. The output layer performs the main computation
Read MoreData Visualization Principles and Web Implementation
Visualization Fundamentals
The ability to analyze data, process it, extract value, visualize it, and communicate it is an extremely important skill, given the ubiquitous availability of data today. The primary goals of visualization include:
- Recording information.
- Analyzing data to support reasoning, such as confirming hypotheses (e.g., John Snow’s work during the London Cholera Outbreak in 1854).
- Communicating ideas to others.
Visualization functions effectively by addressing the fundamental limitations
Read MoreData Structures and Algorithms Concepts Explained
1. Algorithm Fundamentals
Definition and Characteristics of an Algorithm
An algorithm is a structured step-by-step procedure designed to solve a specific problem efficiently and correctly.
- Input Requirement: It may accept zero or more input values that provide necessary data for producing meaningful results.
- Output Requirement: It always produces at least one definite output representing the final answer of the computation.
- Finiteness Property: Every valid algorithm must complete execution after a limited
Sorting Algorithms, Inversion Counting & Complexity
Hybrid Merge-Insertion Sort
[2-1 Hybrid Merge-Insertion Sort]
Stops recursion when a subarray size ≤ k and uses insertion sort for that subarray; MERGE is unchanged.
Pseudocode
INSERTION_SORT(A, p, r)
for j = p+1 to r
key = A[j]
i = j - 1
while i >= p and A[i] > key
A[i+1] = A[i]
i = i - 1
A[i+1] = key
HYBRID_MERGE_SORT(A, p, r, k)
if r - p + 1 <= k
INSERTION_SORT(A, p, r)
else if p < r
q = floor((p + r) / 2)
HYBRID_MERGE_SORT(A, p, q, k)