3. Apply the Fast Fourier Transform (FFT) for Spectral Analysis of Signals in Both Time and Frequency Domains
The chapter explores spectral analysis and the application of the Fast Fourier Transform (FFT) in decomposing signals into their frequency components. Key concepts include the differences between time and frequency domains, the basics of Fourier Transform and Discrete Fourier Transform, and the advantages of using FFT in real-time signal processing. The applications extend to communication systems, audio and image compression, with considerations for signal length and spectral leakage.
Sections
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What we have learnt
- Spectral analysis helps in identifying dominant frequencies and noise in signals.
- The Fourier Transform converts a time-domain signal into its frequency-domain representation.
- Fast Fourier Transform drastically improves computation efficiency for signal processing.
Key Concepts
- -- Spectral Analysis
- Decomposing a signal to identify its frequency components, dominant frequencies, and noise.
- -- Fourier Transform
- A mathematical transformation that converts time-domain signals into frequency-domain representations.
- -- Fast Fourier Transform (FFT)
- An efficient algorithm for computing the Discrete Fourier Transform (DFT), reducing computational complexity.
- -- Discrete Fourier Transform (DFT)
- The sampled version of the Fourier Transform for digital signals, turning time samples into frequency components.
- -- Spectral Leakage
- The effect that occurs when a non-periodic signal is analyzed, which can be mitigated using windowing techniques.
Additional Learning Materials
Supplementary resources to enhance your learning experience.