ENTC 4337

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ENTC 4337

• Sine Generation

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Z-Transform Table
Impulse d(n) 1
Unit Step u(n)
Ramp nu(n)
Exponential an
Sinusoidal sin(wnT)
cos(wnT)
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Digital Oscillator Design
Impulse Response h(n)sin(wnt)
Impulse x(n)1,0,0,...,0
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Design a digital filter that generates an 800 Hz
sine wave in response to an impulse. Sampling
frequency is 10,000 Hz. Test the filter by
observing the first 10 output samples. Hint
Use the Z-transform table and convert H(z) to a
difference equation.
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n x(n) x(n-1) y(n) y(n-1) y(n-2)
0 1 0 0 0 0
1 0 1 0.4818 0 0
2 0 0 0.8443 0.4818 0
3 0 0 0.9980 0.8443 0.4818
4 0 0 0.9048 0.9980 0.8443
5 0 0 0.5878 0.9048 0.9980
6 0 0 0.1253 0.5878 0.9048
7 0 0 -0.3681 0.1253 0.5878
8 0 0 -0.7705 -0.3681 0.1253
9 0 0 -0.9823 -0.7705 -0.3681
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Types of Sequences
Impulse
function x,nimpseq(n0,n1,n2) Generates
x(n)delta(n-n0) n1ltnltn2 ---------------------
---------------- x,nimpseq(n0,n1,n2) nn1n
2 x(n-n0)0
gtgtx,nimpseq(0,-3,9) gtgtstem(n,x)
grid gtgtaxis(0 10 0 2)
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Sinusoidal Sequence
n09 hsin(0.503n) stem(n,h),grid
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Convolution
x,nimpseq(0,-3,9) hsin(0.503n)
yconv(x,h) y Columns 1 through 7
0 0 0 -0.9981 -0.8447
-0.4821 0 Columns 8 through 14
0.4821 0.8447 0.9981 0.9042 0.5864
0.1233 -0.3704 Columns 15 through 21
-0.7723 -0.9829 0 0 0
0 0 Columns 22 through 25
0 0 0 0
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yHAND0,0.4821,0.8443,0.9980,0.9048,0.5878,0.1253
,-0.3681,-0.7705,-0.9823
yMATLAB0,0.4821,0.8447,0.9981,0.9042,0.5864,0.12
33,-0.3704,-0.7723,-0.9829
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Design a digital filter that generates an 1000 Hz
sine wave in response to an impulse. Sampling
frequency is 10,000 Hz. Test the filter by
observing the first 10 output samples. Hint
Use the Z-transform table and convert H(z) to a
difference equation.
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MATLAB Implementation
gtgt x,nimpseq(0,-3,25) gtgt hsin(0.628n) gtgt
yconv(x,h) gtgt t-61length(y)-7 gtgt
stem(t,y),grid
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Note that 1 period is 10 samples and that 10 X
.0001 seconds is 1 ms, or a frequency of 1 kHz.