LTI System, Basic Types of Digital signals, Basic Operations, Causality, Stability
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This document discusses digital signal processing concepts including: 1) Basic types of digital signals such as unit impulse sequences and unit step sequences. 2) Linear time-invariant (LTI) systems and their properties including causality and stability. LTI systems can be represented using impulse responses. 3) Convolution, which is used to analyze LTI systems in the time domain by representing the output as a sum of delayed and scaled impulse responses of the input.
![x[n] via i
mpulse functions](https://image.slidesharecdn.com/5-210202100341/85/LTI-System-Basic-Types-of-Digital-signals-Basic-Operations-Causality-Stability-8-320.jpg)
![x[n1,n2] via impulse
functions](https://image.slidesharecdn.com/5-210202100341/85/LTI-System-Basic-Types-of-Digital-signals-Basic-Operations-Causality-Stability-10-320.jpg)
![T
w o ways
As the representation of the output as a
sum of delayed and scaled impulse
responses.
As a computational formula for
computing y[n] (“y at time n”) from the
entire sequences x and h.
Form x[k]h[n-k] for -∞<k<+∞ for a fixed n
Sum over all k to produce y[n]](https://image.slidesharecdn.com/5-210202100341/85/LTI-System-Basic-Types-of-Digital-signals-Basic-Operations-Causality-Stability-21-320.jpg)
![x[k]h[nk]
k
Convolution in the time domain: y[n]
y[n] = 2 –3 3 3 –6 0 1 0 0](https://image.slidesharecdn.com/5-210202100341/85/LTI-System-Basic-Types-of-Digital-signals-Basic-Operations-Causality-Stability-24-320.jpg)
![First-Order
Example
Consider the difference equation
y[n] =ay[n−1] +x[n]
We can represent this system by the
following block diagram:](https://image.slidesharecdn.com/5-210202100341/85/LTI-System-Basic-Types-of-Digital-signals-Basic-Operations-Causality-Stability-36-320.jpg)
LTI System, Basic Types of Digital signals, Basic Operations, Causality, Stability
- 1. -Basic Types of Digital signals -Basic Operations -LTI System -Causality -Stability
- 2. Basic Types of Digital Signals
- 3. 2-D Unit impulse Se quence
- 5. 2-D Unit Step Sequence
- 6. Basic Types of Digital Signals
- 8. x[n] via i mpulse functions
- 13. Linear
- 15. Linear Time -Invariant System
- 16. Linear Time -Invariant System
- 20. LTI System
- 21. T w o ways As the representation of the output as a sum of delayed and scaled impulse responses. As a computational formula for computing y[n] (“y at time n”) from the entire sequences x and h. Form x[k]h[n-k] for -∞<k<+∞ for a fixed n Sum over all k to produce y[n]
- 22. 2-DLinear Shift Invariant (LSI) System
- 23. 2-DLinear Shift Invariant (LSI) System
- 24. x[k]h[nk] k Convolution in the time domain: y[n] y[n] = 2 –3 3 3 –6 0 1 0 0
- 25. Example-Convolution of Two Re c tangles
- 27. Example-Convolution Of Two Sequences
- 29. Stability
- 30. Causality
- 31. Causality & Stability- Ex ample
- 32. Pr operties of Convo luti on
- 33. Properties ofConvolut ion 2- D
- 34. Difference Equation For all computationally realizable LTI systems, the input and output satisfy a difference equation of the form This leads to the recurrence formula which can be used to compute the “present” output from the present and M past values of theinput and N past values of the output
- 35. Linear Constant-Coefficient Diff Equations (LCCD) = Autoregressive Moving AverageARMA
- 36. First-Order Example Consider the difference equation y[n] =ay[n−1] +x[n] We can represent this system by the following block diagram:
- 37. Linear Constant-Coefficient Diff Equations (LCCD)