Introduction to Digital Signal and System Analysis - Tutorsindia

Introduction to Digital Signal and System Analysis
Basic Types of Digital Signals
where A, β are constants and n the sample number.
--
Complex signals z
A digital signal x[n] can be complex, a simple example is
x[ n]
= cos( nW)
+ j sin( nW)
where j = −1
, and the signal has real and imaginary parts. Note that according to Euler formula
exp
( jnΩ) = cos( nΩ) + j sin( nΩ)
, t, there are relationships:
1
cos( nW)
= {exp( jn W)
+ exp( − jn W)}
2
1
sin( nW)
= {exp( jn W)
− exp( − jn W)}
2 j
(2.6)
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