The Discrete Fourier Transform (DFT) is a version of the Fourier Transform specifically designed for finite, discrete data sets—like a sequence of numbers you might get from sampling a signal (e.g., audio recordings, stock prices, or sensor readings). Unlike the continuous Fourier Transform, which works with infinite, continuous functions, the DFT takes a fixed number of points and converts them from the time domain (or whatever your sample domain is) into the frequency domain, revealing the frequency components present in that sequence.
Definition
How It Works
Key Properties
Why It’s Useful?
The DFT is practical because real-world data is discrete—computers don’t handle continuous signals natively. It’s used in:
- Audio Processing: To identify tones or filter noise.
- Image Compression: In JPEG, it helps isolate spatial frequencies.
- Market Analysis: To find cycles in time series data.
Fast Fourier Transform (FFT)
