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# Lesson_9 - Lesson9 Challenge8 Lesson9 FIRfilters Challenge9...

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Lesson 09 Lesson 9 Challenge 8 Lesson 9 FIR filters Challenge 9

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Lesson 09 Challenge 8 A sinusoid x(t)=cos(2 π 100t), for t 0, 0 otherwise, is sampled at a rate  f s =1000 Sa/s (oversampled).  The sample values are: x[k]={1.0, 0.809, 0.309, -0.309, -0.809, -1.0, -0.809, -0.309, 0.309, 0.809, 1.0} The sampled signal x[k] is sent to a discrete-to-continuous-time (D to C)  converter which produces a continuous time output signal using linear  interpolation given by:  ( 29 - - = otherwise T t T for T t t p s s s 0 1 -T s 0 T s 1
Lesson 09 Challenge 8 x[k]= {1.0, 0.809, 0.309, -0.309, -0.809, -1.0, -0.809, -0.309, 0.309,                           0.809, 1.0} -.001 0 .001 .002 .003 .004 .005 .006 .007 .008. .009 .010 0.809 0.309 -0.309 -0.809 -1.000 1.0

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Lesson 09 Challenge 8 Interpolated signal -.001 0 .001 .002 .003 .004 .005 .006 .007 .008. .009 .010 1.000 0.809 0.309 -0.309 -0.809 -1.000 Maximum approximation error for all time  is at t=0 - , is unity but this error is outside  the analysis 10ms window.
Lesson 09 Challenge 8 Machine interpolation Error min(err)= -0.046561 max(err)= 0.0465711 worst case error ~ 0.0465 Error e(t)=x(t)-x interpolated (t)

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Lesson 09 Lesson 9 FIR filters (digital filters) General Purpose Graphics Filtering (Convolution) Rotation Detection (Correlation) Image transmission and compression Spectral analysis (Fourier transforms) Image recognition Adaptive filtering Image enhancement Instrumentation Control Waveform generation Servo control Transient analysis Disk control Steady-state analysis Printer control Biomedical instrumentation Engine control Information systems Guidance and navigation Speech processing Vibration (modal) control
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Lesson_9 - Lesson9 Challenge8 Lesson9 FIRfilters Challenge9...

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