Introduction to Digital Signal and System Analysis - Tutorsindia
Introduction to Digital Signal and System Analysis - Tutorsindia
Introduction to Digital Signal and System Analysis - Tutorsindia
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<strong>Introduction</strong> <strong>to</strong> <strong>Digital</strong> <strong>Signal</strong> <strong>and</strong> <strong>System</strong> <strong>Analysis</strong><br />
Time-domain <strong>Analysis</strong><br />
x<br />
1[ n]*<br />
x2[<br />
n]<br />
= x2[<br />
n]*<br />
x1[<br />
n]<br />
(3.20)<br />
Example 3.4: A filter’s difference equation is y[n]-0.5 y[n-1]=0.5 x[n], where x[n]: ...0 0 4 5 6 7 8 9 10 ...<br />
↑<br />
a) Find the impulse response of the filter <strong>and</strong> <strong>to</strong> calculate samples of response y[0], y[1], ... , y[4].<br />
b) Check y[n] can be found by the difference equation.<br />
Solution:<br />
a) From<br />
y[n]=0.5 y[n-1] + 0.5 x[n]<br />
we know<br />
h[n]=0.5 h[n-1]+ 0.5 d[n]<br />
Then, the impulse response can be evaluated<br />
h[0]= 0.5 ´ 1=0.5<br />
h[1]= 0.5 ´ 0.5 =0.25<br />
h[2]=0.5 ´ 0.25=0.125<br />
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