lecture03: Discrete Fourier Transforms
This lecture considers real signals (which are almost all
discrete) and the Discrete Fourier Transform (DFT), and its
properties.
Topics covered
- Discrete signals
- Moore's Law
- Gates's law
- Real signals
- Discrete time
- Quantization: discrete-value
- Approximation
- Sampling
- Aliasing
- Another example of aliasing
- Aliasing: time domain view
%
- Aliasing analysis (ii)
- Aliasing: frequency domain view
- Delta train
- Aliasing: frequency representation
- Nyquist sampling theorem
- Example
- Example: Sample at 17.5 MHz
- Example: Sample at 15 MHz
- Example: Sample at 11.25 MHz
- Example: Sample at 7.5 MHz
- Bandlimiting
- Some more sampling theory
- Shannon theorem
- Shannon interpolation
- Digital to Analogue converter
- Quantization: discrete-value
- Dynamic range
- Dynamic range: examples
- Dynamic range of the human senses
- Death of Dynamic Range
- Introduced noise
- Quantization noise notes
- Clipping
- Example
- Example: extreme audio
- Discrete transformation
- Discrete Fourier Transformation
- Inverse DFT
- Examples (i)
- Examples (i) IDFT
- Examples (ii)
- Examples (iii)
- DFT basis
- DFT transform matrix
- Examples (i)
- Frequency resolution
- Getting units right
- Matlab
- Matlab example
- Symmetry
- Matlab example 2
- Properties of the DFT
- Duality and the DFT
- Properties of the DFT
- Leakage example
- Properties of the DFT: Leakage
- DFT properties: padding
- Padding (packing) example (ii)
- Padding (packing) example
- DFT properties: similarity
- Similarity example (ii)
- Similarity application
- Similarity application: upsampling
- Upsampling example
- Upsampling tricks
- Upsampling applications: audio