lecture08: Windows and the STFT
This lecture considers window functions, and the Short-Time
Fourier Transform (STFT), which uses window functions to localize
frequency analysis by the FT.
Topics covered
- Leakage
- Leakage example
- What causes leakage
- Alternative view
- Periodic signal view
- Yet another view
- Windows
- Impact of Windows
- Windows
- Basis for Comparison
- Rectangular Window
- Triangular Window
- Welch Window
- Hanning Window
- Hamming Window
- Blackman Window
- Blackman-Harris Window (3 term)
- Gaussian Window
- Windowing
- Tunable tradeoffs
- Kaiser Window
- Tunable tradeoffs
- Uncertainty principle
- Regularity and decay
- Rectangular Window
- Triangular Window
- Welch Window
- Hanning Window
- Hamming Window
- Blackman Window
- Regularity and decay and duality
- Compactness
- Meaning
- Windows summary
- Sensitivity vs resolution
- Transient signals
- EM Frequency Band Allocations
- Amplitude Modulation (AM)
- Frequency Modulation (FM)
- Envelope and phase
- A Chirp
- An Example Chirp
- A Chirp
- Instantaneous frequency
- Windows, windows everywhere
- STFT of a Chirp
- Short Time Fourier Transform
- Discrete time STFT
- Example spectrogram
- Cutting up the time-frequency space
- Uncertainty
- Resolution
- Cutting up the time-frequency space
- Spectrogram of a Chirp
- Windows
- Limitations of the STFT
- The answer: wavelets