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ENTC 4337 Sine Generation

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Z-Transform Table Impulse n) 1 Unit Stepu(n) Rampnu(n) Exponentialanan Sinusoidal sin( nT) cos( nT)

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Digital Oscillator Design ? Impulse x(n)={1,0,0,...,0} Impulse Response h(n)=sin( nt)

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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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nx(n)x(n-1)y(n)y(n-1)y(n-2)

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Types of Sequences Impulse function [x,n]=impseq(n0,n1,n2) %Generates x(n)=delta(n-n0); n1<=n<=n2 % %[x,n]=impseq(n0,n1,n2) % n=[n1:n2]; x=[(n-n0)==0]; >>[x,n]=impseq(0,-3,9); >>stem(n,x); grid >>axis([ ])

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Sinusoidal Sequence » n=[0:9]; » h=sin(0.503*n); » stem(n,h),grid

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Convolution » [x,n]=impseq(0,-3,9); » h=sin(0.503*n); » y=conv(x,h) y = Columns 1 through Columns 8 through Columns 15 through Columns 22 through

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y MATLAB ={0,0.4821,0.8447,0.9981,0.9042,0.5864,0.1233, , , } y HAND ={0,0.4821,0.8443,0.9980,0.9048,0.5878,0.1253, , , }

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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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>> [x,n]=impseq(0,-3,25); >> h=sin(0.628*n); >> y=conv(x,h); >> t=[-6:1:length(y)-7]; >> stem(t,y),grid MATLAB Implementation

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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.

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