FFT Intordection

1. Introduction to Fast Fourier
Transform (FFT)
Unlocking the Power of Frequency
Domain
Presented by: [Your Name] | [Date]

2. What is FFT?
• • FFT stands for Fast Fourier Transform.
• • It’s an optimized method to compute the
Discrete Fourier Transform (DFT).
• • Converts signals from time domain to
frequency domain quickly.

3. Why Use FFT?
• • Reduces computation from O(N²) to O(N log
N).
• • Suitable for real-time applications.
• • Forms the backbone of digital signal
processing (DSP).

4. Understanding the DFT
• • DFT computes frequency components of a
signal.
• • Formula: X(k) = Σ x(n)·e^(-j2πkn/N)
• • Used for analyzing signal behavior in the
frequency domain.

5. FFT Algorithm Basics
• • Divides a large DFT into smaller ones (divide
and conquer).
• • Common version: Cooley-Tukey algorithm.
• • Handles data sizes that are powers of 2
efficiently.

6. Applications: Audio Processing
• • Visualize and edit sound frequencies (e.g.,
EQ tools).
• • Remove noise by filtering unwanted
frequency bands.
• • Core to audio compression formats like MP3.

7. Applications: Image Analysis
• • Frequency filtering for blurring or
sharpening.
• • JPEG compression uses frequency transform
(DCT variant).
• • Detect patterns and textures in images.

8. Other Real-World Uses
• • Telecommunications: OFDM in 5G/4G.
• • Medical imaging: MRI and CT scan data
processing.
• • Radar & Seismology: Signal detection and
interpretation.

9. Conclusion
• • FFT is a fast and efficient way to analyze
signals.
• • Crucial in countless real-world technologies.
• • Knowing FFT opens the door to advanced
DSP tasks.