Chapter 3

Chapter 3 Digital Signals

Discrete离散 Time Series序列

Analog	Digital
x ( t )	x [ n ] = x ( nT_s )
t : Continuous Time, Second	n: Index of Sample Instance, Integer Scalar

T_s : Sampling Interval or Sampling Period

Shifting时移: y [ n ] = x [ n - 2 ]

Downsampling压缩: y [ n ] = x [ 3n ]

Upsampling延拓: y [ n ] = x [ n / 3 ]，n=0,3,6,9,...

= 0 otherwise

Flipping反转: y [ n ] = x [ - n ]

Functions

Unit Impulse单位脉冲

x [ n ] = x [0] d [ n ] + x [1] d [ n-1] + x [2] d [ n-2] + ?/font>

------------------------------------------------------------------------------

Unit Step单位阶跃

u [ n ] = d [ n ] + d [ n -1] + d [ n -2] + ?/font>

d [ n ] = u [ n ] ?u [ n -1]

------------------------------------------------------------------------------

Exponential指数

x [ n ] = A e ^(bn)

b > 0, Grows

b < 0, Decays

------------------------------------------------------------------------------

Complex Exponential复指数

x [ n ] = A e^{(
jbn
)}

e^{(
j
b
n
)} = cos(bn) + j sin( bn )

------------------------------------------------------------------------------

Sinusoid正弦

x [ n ] = A sin( nW + q )

Periodic only when

(T /T_s ) is Rational

q : Phase Shift

W : Digital Frequency

Digital Image

Gray Scale Image灰度图像

Total Number of Bits =

(# Rows)x(# Columns)x(# Bits per Pixel像素)

Gray Scale Matrix