lecture01: Introduction
Note that not everything said in the lectures is included
in the notes provided. You must listen, and take notes. These spaces
in your handout notes are provided to allow you to take notes in
lectures. You may be examined on material that is discussed in
lectures, even if it does not appear explicitly in your notes!
Topics covered
- Outline
- Some reference books
- On-line materials
- Motivation
- Motivation for transformation
- Application areas
- Applications: signal processing
- Integral transforms
- Linear operators
- Examples of integral transforms
- An example: the Fourier transform
- An example: Beats
- Example: ECG
- Sound and Waves
- Pitch
- Equal temperment scale
- Harmonics
- Harmonics of A (440 Hz)
%
- Chords
- Musical Scale
- Tone/Timbre of instrument
- Application: Pitch Estimation
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- Fourier Transform examples
- Example spectrogram
- Application: Changing pitch
- Application: Compression
- Application: Acoustic fingerprints
- Application: Transcription
- Some 2D integral transforms
- An example: Radon transform
- Other integral transforms
- Relationships between transforms
- Basis functions
- Linear algebra example
- Examples of integral transforms
- Properties of basis functions
- Transform properties
- Inversion
- Transform complexity
- Key transform property
- What will we miss?
- Complex numbers
- Simple signals
- Delta ``function'' $\delta(t)$
- Some useful functions: sinc
- Signal characteristics
- Even signals
- Odd signals
- Hermitian signals
- Periodic signals
- Frequency terminology
- Simple transformations