Podcast
Questions and Answers
Which of the following statements is true regarding orthogonal vectors?
Which of the following statements is true regarding orthogonal vectors?
In the context of vector spaces, what does linear independence imply for orthogonal vectors?
In the context of vector spaces, what does linear independence imply for orthogonal vectors?
What geometric property distinguishes orthogonal vectors from non-orthogonal vectors?
What geometric property distinguishes orthogonal vectors from non-orthogonal vectors?
Which of the following is NOT a characteristic of orthogonal vectors?
Which of the following is NOT a characteristic of orthogonal vectors?
Signup and view all the answers
If two vectors are orthogonal, what can be said about their dot product?
If two vectors are orthogonal, what can be said about their dot product?
Signup and view all the answers
Which statement about orthogonal vectors and their span is true?
Which statement about orthogonal vectors and their span is true?
Signup and view all the answers
In a three-dimensional space, how many orthogonal vectors are needed to span the space?
In a three-dimensional space, how many orthogonal vectors are needed to span the space?
Signup and view all the answers
Why are orthogonal vectors used in various applications of machine learning?
Why are orthogonal vectors used in various applications of machine learning?
Signup and view all the answers
What is the primary focus of the course BME 596?
What is the primary focus of the course BME 596?
Signup and view all the answers
Who is the instructor for the course BME 596?
Who is the instructor for the course BME 596?
Signup and view all the answers
Which department offers the course BME 596?
Which department offers the course BME 596?
Signup and view all the answers
What type of learning does the course BME 596 incorporate?
What type of learning does the course BME 596 incorporate?
Signup and view all the answers
Which faculty is associated with the course BME 596?
Which faculty is associated with the course BME 596?
Signup and view all the answers
What might be a probable topic discussed in BME 596?
What might be a probable topic discussed in BME 596?
Signup and view all the answers
How is the course BME 596 classified at Yarmouk University?
How is the course BME 596 classified at Yarmouk University?
Signup and view all the answers
In which area is the instructor Dr. Bahaa W.Al-Sheikh specialized?
In which area is the instructor Dr. Bahaa W.Al-Sheikh specialized?
Signup and view all the answers
Study Notes
Signal Processing for Machine and Deep Learning (BME 596)
- Course offered at Yarmouk University
- Instructor: Dr. Bahaa W. Al-Sheikh
- Department of Biomedical Systems & Medical Informatics Engineering
- Hijjawi Faculty for Engineering Technology
Basic Definitions (Digital) Signal Processing
- Digital: The word "digital" originates from the Latin word "digitus" (finger). Computers represent information as lists or sequences of numbers.
- Signal: A signal is a function of one or more variables, carrying information about a phenomenon.
- Processing: Algorithms manipulate digital signals to extract information.
Basic Notation
- Discrete Signals: A discrete signal can be real or complex-valued. It's a function from the set of integers (ℤ) to either the set of complex numbers (ℂ) or the set of real numbers (ℝ). Used for discrete time. Examples include discrete-time waves.
- Continuous Signals: A continuous signal is a function from the set of real numbers (ℝ) to either the set of complex numbers (ℂ) or the set of real numbers (ℝ). Used for continuous time. Examples include temperature over time.
- Example (Discrete): x[n] = Average Dow-Jones index in year n
- Example (Continuous): x(t) = temperature at time t
Quantizing Discrete Signals to Digital Signals
- Shown visually through examples: 8-bit, 3-bit, 2-bit, and 1-bit quantization.
- Demonstrates how discrete signals become digital through quantization levels.
Quantizing Images
- Visual examples shown of digital image quantization at 8-bit, 7-bit, 6-bit, 5-bit, 4-bit, 3-bit, 2-bit, and 1-bit.
Quantizing Audio
- Visual examples of 24-bit, 8-bit, and 3-bit audio quantization.
Basic Notation (Continued)
- Delta Sequence: δ[n] = 1 if n = 0, 0 if n ≠ 0
- Exponential Decay: x[n] = anu[n], a ∈ ℂ, |a| < 1
- Complex Exponential: x[n] = ej(won+φ), j = √-1, wo = frequency, φ = phase
Sampling a Continuous Function to Get a Discrete Function
- If sampling occurs every T seconds, the value of the nth number in the sequence x[n] = xa(nT)
- Sampling Period (T): The time interval between samples.
- Sampling Frequency (1/T): The number of samples per unit time.
Sampling
- Nyquist-Shannon Sampling Theorem: A continuous signal can be completely determined from its samples if no frequencies higher than B hertz exist in the signal; sampling frequency is at least twice this frequency.
- Aliasing: Distortion that occurs when a lower sampling-rate is used and frequencies higher than the Nyquist rate are not eliminated.
Aliasing in Images
- Visual examples of aliasing in images and anti-aliasing filters.
Energy and Power
- Energy: Ex = ∑n=-∞∞ |x[n]|2.
- Power: Px = limN→∞ 1/(2N+1) ∑n=-NN |x[n]|2
Signal Processing and Geometry
- Finite-Length Signals: A finite-length discrete-time signal of length N is equivalent to a length-N vector.
- Notation: x = [x0, x1, ..., xN-1]T or x[n], n = 0, ..., N − 1
Geometry in ℂN
- Zero Vector (0): All other vectors are defined relative to zero.
- Inner Product: (x, y) = ∑k=0N-1 xkyk*
- Orthogonal (x ⊥ y): (x, y) = 0
Norm
- Norm (||x||): ||x|| = √(∑k=0N-1 |xk|2) = (x, x)1/2. This is also called the 2-norm or l2-norm.
- Norm in two dimensions: Relationship between norm, inner product, and the angle between two vectors.
Cauchy-Schwarz Inequality
- Theorem: |(x, y)| ≤ ||x||2||y||2
Basis
- Basis: A collection of M signals in a class, where any other signal in the class can be represented as a weighted sum of those M signals.
Why Change Basis?
- To compress data by having more small or zero coefficients.
- For classification, different classes have different coefficient patterns (e.g., Fourier).
Standard Basis
- Standard/Canonical Basis: The collection of shifted delta functions. c[m] = x[m] , x[n] = ∑m=0M-1c[m]δ[n – m]
How to Check If Signals Form a Basis?
- Linear Independence: A set of N signals, y(0)[n], ..., y(N-1)[n], is linearly independent if ∑m=0N-1 βmy(m)[n] = 0 implies that βm = 0 for all m=0, ..., N-1
Orthogonal Bases
- Orthogonal Bases: A basis is orthonormal if all basis vectors are mutually orthogonal ((y(k)[n], y(l)[n]) = 0 for k≠l) and have a norm of 1 (||y(k)[n]|| = 1 for all k).
- Example of Basis (orthogonal): Show example and how to make vectors norm one.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
