![Discrete Time Signal
Discreet-Time signals are
represented mathematically as sequences of numbers
The sequence is denoted 𝑥[Discreet-Time signals are
represented mathematically as sequences of numbers
The sequence is denoted 𝑥[𝑛
], and it is written formally as
𝑥 = 𝑥 𝑛 ; −∞ < 𝑛 < ∞
where n is an integer number
In practice sequences arises from the periodic sam
pling of an analog signal
], and it is written formally as
𝑥 = 𝑥 𝑛 ; −∞ < 𝑛 < ∞
where n is an integer number
In practice sequences arises from the periodic sam
pling of an analog signal](https://image.slidesharecdn.com/digitalsignalprocessingbyyeasinnewaj-210413161300/85/Digital-signal-processing-by-YEASIN-NEWAJ-6-320.jpg)
![Convolution
Figure below shows the notation when convolution is used with linear systems. An
input signal, x[n], enters a linear system with an impulse response, h[n], resulting in
an output signal, y[n]. In equation form: x[n] t h[n] ' y[n]. Expressed in words, the input
signal convolved with the impulse response is equal to the output signal. Just as
addition is represented by the plus, +, and multiplication by the cross, ×, convolution
is represented by the star, t. It is unfortunate that most programming languages also
use the star to indicate multiplication. A star in a computer program means
multiplication, while a star in an equation means convolution.](https://image.slidesharecdn.com/digitalsignalprocessingbyyeasinnewaj-210413161300/85/Digital-signal-processing-by-YEASIN-NEWAJ-32-320.jpg)
Digital signal processing by YEASIN NEWAJ
- 1. Digital Signal Processing Signal and System (Digital)
- 2. Presenter Mohammad Yeasin Newaj Khan BSc. In EEE
- 3. Contents Signal • Digital Signal • Discrete Time Signal • Visual of Discrete Time Signal with Examples • Representation of Discrete Time Signal • Classification of Discrete Time Signal • Manipulation of Discrete Time Signal System • Block Diagram • Delay Elements • Recursive System • Static and Dynamic System • Convolution • Correlation
- 4. SIGNAL 01
- 5. Digital Signal A digital signal is a signal that is being used to represent data as a sequence of discrete values; at any given time it can only take on, at most, one of a finite number of values. What is Digital Signal?
- 6. Discrete Time Signal Discreet-Time signals are represented mathematically as sequences of numbers The sequence is denoted 𝑥[Discreet-Time signals are represented mathematically as sequences of numbers The sequence is denoted 𝑥[𝑛 ], and it is written formally as 𝑥 = 𝑥 𝑛 ; −∞ < 𝑛 < ∞ where n is an integer number In practice sequences arises from the periodic sam pling of an analog signal ], and it is written formally as 𝑥 = 𝑥 𝑛 ; −∞ < 𝑛 < ∞ where n is an integer number In practice sequences arises from the periodic sam pling of an analog signal
- 7. Visual Representation of Discrete Time Signal Example - 1
- 8. Visual Representation of Discrete Time Signal Example - 2
- 9. Types of Representation of Discrete Time Signal There are four types of representation in discrete time signal. These are:
- 10. Types of Representation of Discrete Time Signal
- 11. Classification of Discrete time signal
- 12. Classification Discrete time signals can be classified as follows: • Even and odd signals • Periodic and non-periodic signals • Deterministic and random signals • Energy signals and power signals • Multichannel and multidimensional signals
- 13. Periodic and Non-Periodic Signal
- 14. Periodic Signal A signal is considered to be periodic signal if it completes a pattern within a measurable time frame, called a period and repeats that pattern over identical subsequent periods. A period is defined as the amount of time (expressed in seconds) required to complete one full cycle. Sinusoidal wave, cosine wave, triangle wave and square wave are example of periodic signal. Periodic signals are more commonly identified by their frequency (f) rather than their period. The frequency of a signal is the inverse of the period. Mathematically, this means that: F=1/T The frequency of a signal tells us how many times the signal repeats itself during one second. Units of frequency are in cycles per second or Hertz (Hz). Therefore, a signal with a frequency of 100Hz goes through 100 cycles (Periods) in one second (the period of the signal is 0.01 seconds.
- 15. Aperiodic Signal ○ Aperiodic signal is a signal which does not repeat itself after a specific interval of time. ○ Example of aperiodic signal is signal created by microphone or telephone when one or two words are pronounced. Also, signal propagated by AM radio station or FM radio stations are all aperiodic signal. Aperiodic Signal
- 16. Symmetric and Asymmetric Signal
- 17. Symmetric and Asymmetric signal Signal is said to be even or symmetric if the time reversed signal is equal to the signal itself. Signal is an odd or anti-symmetric when the time reversed signal is equal to negation of signal. When signal does not satisfy the above two, it is non-Symmetric in nature.
- 18. Manupulation of Discrete time signal
- 19. Manipulation
- 20. Manipulation
- 21. SYSTEM 02
- 22. Block Diagram
- 23. What is a Block Diagram in a System? A block diagram is used to represent a control system in diagram form. In other words, the practical representation of a control system is its block diagram. Each element of the control system is represented with a block and the block is the symbolic representation of the transfer function of that element.
- 24. Delay Elements
- 25. Delay Elements
- 26. Recursive System
- 27. Recursive System
- 28. Static and Dynamic System
- 29. Static and Dynamic System • A static system is a system in which output at any instant of time depends on the input sample at the same time. In other words, the system in which output depends only on the present input at any constant of time then this is known as the static system. • A static system is a system in which output at any instant of time depends on the input sample at the same time as well at other times. In other words, the system in which output depends only on the past and/or the future input at any constant of time then this is known as the dynamic system. Dynamic system possesses memory.
- 30. Convolution
- 31. Convolution
- 32. Convolution Figure below shows the notation when convolution is used with linear systems. An input signal, x[n], enters a linear system with an impulse response, h[n], resulting in an output signal, y[n]. In equation form: x[n] t h[n] ' y[n]. Expressed in words, the input signal convolved with the impulse response is equal to the output signal. Just as addition is represented by the plus, +, and multiplication by the cross, ×, convolution is represented by the star, t. It is unfortunate that most programming languages also use the star to indicate multiplication. A star in a computer program means multiplication, while a star in an equation means convolution.
- 33. Correlation
- 34. Correlation
- 36. Autocorrelation
- 38. THANK YOU