CH6_Problems

# CH6_Problems - Problems Section 6.1 Fourier Analysis...

This preview shows pages 1–3. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Problems Section 6.1: Fourier Analysis, Filters, and Transfer Functions P6.1. What is the fundamental concept of Fourier theory? P6.2. The triangular waveform shown in Figure P6.2 can be written as the infinite sum 8 Vt(t) = 1 + rr 2 cos (2000rrt) 8 + 2 cos ( 6000rrt) + ... (3rr) 8 + 2 cos (2000nrrt) + (nrr) in which n takes odd integer values only. Use MATLAB to compute and plot the sum through n = 19 for 0 :::: t :::: 2 ms. Com- pare your plot with the waveform s hown in Figure P6 .2. 1 Figure P6.2 2 t (ms) P6.3. The full-wave rectified cosine wave shown in Figure P6.3 can be written as 2 4 Vfw = - + cos(4000rrt) rr n(1)(3) 4 - cos(8000rrt) + n (3) (5) 4(-1) (n /2 +1 ) + n(n _ 1 )(n + 1 ) cos(2000nrrt) + in which n assumes even integer values. Use MATLAB to compute and plot the sum Problems 341 through n = 60 for 0 &amp;lt; t &amp;lt; 2 ms. Com- pare your plot with the waveform s hown in Figure P6.3. Vr wCt) = Ieos (20001Tt) l 1 0.5 1.0 Figure P6.3 t (ms) P6.4. The Fourier series for the half-wave rectified cosine shown in Figure P6.4 is 1 1 2 vhw(t) = rr + 2 cos(2rrt) + rr( 1 )( 3 ) cos(4rrt) 2 --- cos(8rrt) + n(3)(5) 2(-1) (n / 2+1) + cos(2nnt) + n(n- 1)(n + 1) in which n = 2, 4, 6, etc. Use MATLAB to compute and plot the sum through n = 4 for -0.5 :::: t :::: 1.5 s. Then plot the s um through n = 50. Compare your plots with the waveform in Figure P6.4. 0.5 1.0 Figure P6.4 t (s) * Denotes that answers are contained in the Student Solutions fi les. See Appendix F for more information about accessing the Student Solutions. 342 Chapter 6 Frequency Response, Bode Plots, and Resonance P6.5. Fourier analysis shows that the sawtooth waveform of Fig ure P6.5 can be written as Vs t(l) = 1 - ~ sin(2000rrt) 7f - 2 sin( 4000nt) - 2 sin(6000rrt) 2rr 3rr 2 . - - sm (2000nnt) - nn Use MATLAB to compute and plot the sum through n = 3 for 0 &amp;lt; t &amp;lt; 2 ms. Repeat for the sum through n = 50. 2 1 2 Figure P6.5 3 t (ms) P6.6. What is the transfer function of a filter? De scribe how the transfer function of a filter can be determined using laborator y method s. P6.7. How do es a filter process an input signal to produce the output signal in te rm s of sinusoidal components? *P6.8. The transfer function H (f) = V out!Vin of a filter is shown in Figure P6.8. The input signal is given by IH (f) I 2 1 Vin (t) = 5 + 2 cos(5000rrt + 30) + 2 cos(15000nt) Find an expression (as a function of time) for the steady-state output of the filter. 5 10 5 10 f -~.::--------.----.---- (kHz) f -180 ( kH z) Figure P6.8 P6.9. Repeat Problem P6.8 for the input voltage given by Vin (t) = 4+ 5 cos(10 4 rrt-30 ) + 2 sin(24000nt) P6.10. Repeat Problem P6.8 for the input voltage given by Vi n (t) = 6 + 2 cos(6000nt) - 4 cos(12000nt) *P6.11. Th e input to a certain filter is given by and the steady-state output is given by Determine the (complex) value of the tran s- fer function of the filter for f = 5000Hz....
View Full Document

{[ snackBarMessage ]}

### Page1 / 13

CH6_Problems - Problems Section 6.1 Fourier Analysis...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online