Bài giảng xử lý tín hiệu số signal and system in time domain ngô quốc cường

Xử lý tín hiệu số
Signal and System in Time Domain

Ngô Quốc Cường

Ngô Quốc Cường
sites.google.com/a/hcmute.edu.vn/ngoquoccuong


Signal and System in Time Domain
• Discrete time signals
• Discrete time systems
• LTI systems

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2.1 Discrete - time signals
• A discrete time signal x(n) is a function of an independent
variable that is integer.

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2.1 Discrete - time signals
• Alternative representation of discrete time signal:

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2.1 Discrete - time signals

• Alternative representation of discrete time signal:

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2.1.1 Some elementary signals

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2.1.1 Some elementary signals

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2.1.1 Some elementary signals

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2.1.1 Some elementary signals

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2.1.2 Classification of discrete time signal
• Energy signals and power signal
– The energy E of a signal x(n) is given:

– If E is finite, x(n) is call an energy signal.

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2.1.2 Classification of discrete time signal
• Energy signals and power signal
– The average power P of a signal x(n) is defined:

– If P is finite (and nonzero), x(n) is called a power signal.

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2.1.2 Classification of discrete time signal
• Energy signals and power signal
– Example: the average power of the unit step signal is:

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2.1.2 Classification of discrete time signal
• Periodic signals and aperiodic signals
– A signal x(n) is periodic with period N (N >0) if and only if

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2.1.2 Classification of discrete time signal
• Symmetric (even) and antisymmetric (odd) signals
– A real value signal x(n) is call symmetric if

– A signal is call antisymmetric if

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2.1.2 Classification of discrete time signal
• Symmetric (even) and antisymmetric (odd) signals

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2.1.2 Classification of discrete time signal
– The even signal component is formed by adding x(n) to x(n) and dividing by 2.

– Odd signal component

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2.1.3 Simple manipulations of signals
• Transformation of time
– A signal x(n) may be shifted by replacing n bay n-k.
• k is positive number: delay
• k is negative number: advance
– Folding: replace n by -n
– Time scaling: replace n by cn (c is an integer)

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2.1.3 Simple manipulations of signals
• Transformation of time
– Find x(n-3) and x(n+2) of x(n)

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2.1.3 Simple manipulations of signals
• Transformation of time
– Find x(-n) and x(-n+2) of x(n)

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2.1.3 Simple manipulations of signals
• Transformation of time
– Show the graphical representation of y(n) = x(2n), where
x(n) is

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2.1.3 Simple manipulations of signals
• Addition, multiplication, and scaling
– Amplitude scaling

– Sum

– Product

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Exercises

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Exercises
• x(n) is illustrated in the figure

• Sketch the following signals

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2.2 Discrete time systems
• Device or algorithm that performed some prescribed
operation on discrete time signal.

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2.2 Discrete time systems
• Determine the response of the following systems to the input
signal

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