Digital Signal Processing: Complex Numbers, Transforms, and Filters
Complex Numbers
Given
Polar Form
Systems
Sampler
Time
equals
taking samples every T seconds.
Frequency
equals
extensively
and frequency
Decimator
Time
This eliminates one of every M samples.
Frequency
The amplitude scale
and the frequency is multiplied (expanded) by M. The stage is divided by M.
The sampling frequency should be:
Insertaceros
Time
Insert L-1 zeros between samples
Frequency
Divide (compresses) the frequency by a factor L and the amplitude is unchanged. The stage is multiplied by L.
Retardation
Time
Delays
Read MoreProbability Distributions and Sampling Methods
Probability Density Function
A function used to compute probabilities for a continuous random variable. The area under the graph of a probability density function over an interval represents probability.
Uniform Probability Distribution
A continuous probability distribution for which the probability that the random variable will assume a value in any interval is the same for each interval of equal length.
Normal Probability Distribution
A continuous probability distribution. Its probability density function
Read MoreUnderstanding Numbers, Data, and Visualizations
Writing About Numbers
1. Use Miller’s ‘W’s’ to give context
- ‘The Ws’: what, when, where, who.
- ‘Relevance, simplicity, plausibility’
- Take care with jargon or technical language
- Interpret and/or provide analogies to explain numbers
2. Use the GEE method to write about patterns
- Generalise, Example, Exception
3. Prose, table or chart? Consider
- Extent and complexity of the information
- Audience
- Story: is the overall pattern or particular values?
- Attention: what is most important?
Describing Data
Understanding Mathematical Functions: Key Concepts and Definitions
RELATIONSHIP: A relationship exists between two sets if there is a link between them. These sets may be different or may occur within the same set.
ROLE: This is a relationship with two key features:
- Existence: For each element of the set of departure, there is another element in the set of arrival to which it is linked.
- Uniqueness: Each element of the set of departure is bound to a single element in the set of arrival.
SET OF DEPARTURE: The first set involved in the relationship.
SET OF ARRIVAL: The
Read MoreKey Math Concepts: Definitions and Theorems
A magnitude is anything that can be measured or counted.
Direct and Inverse Proportionality
Magnitudes directly proportional: If one magnitude is multiplied by a number, the other is divided by the same number automatically. For example, speed and time are inversely proportional; their product is constant.
Magnitudes inversely proportional: If one magnitude is multiplied or divided by a number, the other is divided or multiplied by that number, respectively.
Sequences
A sequence is an infinite set of
Read MoreAlgebraic Expressions, Equations, and Identities
Algebraic Expressions
An algebraic expression is a combination of numbers and letters connected by arithmetic operation signs. The letters are called variables.
Monomials
A monomial is an algebraic expression where the only operations affecting the variables are multiplication and natural exponentiation. Monomials with the same literal part are like terms.
Polynomials
A polynomial is an algebraic expression formed by the sum or difference of two or more monomials. The degree of a polynomial is the highest
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