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1. Definition of the System in Digital Signal Processing.

2. Different features of the system.

3. How the features affect the processed signal.

2. Search online how the assigned feature is for the system.

require memory, and hence they are dynamic systems.

input signals to produce one or more output signals. The idea of systems and their analysis is

pervasive not only in engineering and the physical sciences, but also in other disciplines. For

example, we are familiar with the non-engineering ideas of a biological system, a social system and

an economic system. Implicit in all de fi nitions of systems is the idea that the inputs (e.g., force,

voltage, body temperature, industrial capacity) can be measured and that the system acts on those

inputs to produce outputs (e.g., displacement, current, blood pressure, GDP) in a manner that can

be modeled and quanti fi ed. In digital signal processing, a discrete-time system is a formula, an

algorithm, a mathematical operation or a piece of code that transforms an input sequence into

an output sequence.

x 1 [ n ] excitation produce y 1 [ n ] response and x 2 [ n ] produce y 2 [ n ] response. According

to additivity property of superposition theorem, if both x 1 [ n ] and x 2 [ n ] are applied

simultaneously, then

x 1 [ n ] + x 2 [ n ] = y 1 [ n ] + y 2 [ n ]

Let a 1 x 1 [ n ] and a 2 x 2 [ n ] be the inputs. According the homogeneity (scaling) property,

when these signals are separately applied,

a 1 x 1 [ n ] = a 1 y 1 [ n ]

a 2 x 2 [ n ] = a 2 y 2 [ n ]

If a 1 x 1 [ n ] + a 2 x 2 [ n ] are simultaneously applied, the output is obtained by applying

superposition theorem as,

a 1 x 1 [ n ] + a 2 x 2 [ n ] = a 1 y 1 [ n ] + a 2 y 2 [ n ]

In the above equation, a 1 x 1 [ n ] + a 2 x 2 [ n ] is called the weighted sum of input, and

a 1 y 1 [ n ] + a 2 y 2 [ n ] is called the weighted sum of the output.

2. y [ n − 1 ] = x [ n ]

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x1[n] + x2[n] = y1[n] + y2[n]

令 a1x1[n] 和 a2x2[n] 為輸入。根據均質性（縮放）性質，在分別應用這些信號時，有：

a1x1[n] = a1y1[n]

a2x2[n] = a2y2[n]

如果同時應用 a1x1[n] + a2x2[n]，則輸出可通過應用超複合定理獲得：

a1x1[n] + a2x2[n] = a1y1[n] + a2y2[n]

在上述方程中，a1x1[n] + a2x2[n] 被稱為輸入的加權和，a1y1[n] + a2y2[n] 被稱為輸出的加權和。

數或屬性不隨時間或任何其他自變數而變化或改變。靜態系統的特徵是平衡、穩定、不存在運動或變化。

y[n]=(x[3n]) 也代表一個非靜態系統。在這個系統中，輸出 y[n] 取決於輸入 x[3n]，表示輸出信號的取樣點是輸入信號每隔三個時間點的取樣。因此，系統的輸出不僅取決於當前的輸入，還取決於時間的總體結構，這顯示出非靜態性質。

y[n]=sin(x[n]) 有機會代表一個靜態系統。雖然因為輸出 y[n] 是根據當前時間點 n 的輸入值 x[n] 的正弦函數，不過因為他某段時間內波形是固定的，所以有機會。