Homework 3 - EE 4541 Digital Signal Processing Fall 2007...

Info icon This preview shows page 1. Sign up to view the full content.

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

Unformatted text preview: EE 4541 Digital Signal Processing Fall 2007 Problem Set 3 Due September 27, 2007 1. Consider the filter with transfer function given by: 1 + z -1 H ( z) = 1 - 0.9 z -1 Determine the impulse response for a causal implementation. Is the filter stable or unstable? ii. Sketch the magnitude response of the filter. Is the filter Lowpass, Highpass, Bandpass, Bandstop, or allpass? n iii. Sketch the magnitude response for the filter g[n] = (- 1) h[ n] . Comment on your result. 2. Let x[n] be a purely real sequence. You are given the following information about x[n] and must determine what it is. Even if you are unable to specify x[n] fully, you may receive partial credit by describing which features of x[n] are determined by each clue. i. x[n] is a causal sequence. ii. iii. iv. v. vi. Let v[ n] = x[n + 2] . Its DTFT, V e j , is purely real. lim X ( z ) = 2 z i. ( ) 1 2 1 2 - X (e ) e d = 0 j j x[ 2] > 0 - X (e ) j 2 d = 9 3. The magnitude responses of 4 LTI systems are given in the figure: (a) 30 40 30 20 10 10 0 -4 8 6 4 2 2 0 -4 1 -2 0 2 Frequency, radians 4 0 -4 -2 0 2 Frequency, radians 4 0 -4 5 4 3 (b) 20 -2 0 2 Frequency, radians (c) 4 -2 0 2 Frequency, radians (d) 4 EE 4541 Digital Signal Processing Fall 2007 Problem Set 3 Due September 27, 2007 i. State whether these filters act as LPF, BPF, or HPF. Also, which filter has the lowest cutoff frequency and which one has the highest. Which of the 4 magnitude responses matches: Filter 1 represented by the difference equation: y[n] = x[n] + x[ n - 1] + x[n - 2] + x[n - 3] + x[ n - 4] Filter 2 represented by the difference equation: y[ n] = 1.6 y[ n - 1] - 0.64 y[n - 1] + x[n] Filter 3 represented by the difference equation: y[n] = x[n] + x[n - 1] + x[n - 2] + x[ n - 3] + x[ n - 4] + x[ n - 5] + x[n - 6] + x[n - 7] Filter 4 represented by the difference equation: y[ n] = 1.4 y[ n - 1] - 0.49 y[ n - 1] + x[ n] + x[n - 1] + x[n - 2] ii. iii. iv. In each case, explain clearly the basis of your choice, i.e., no credit for mere guessing. 4. 5. 6. 7. 8. Problem 3.41 P&M. Problem 4.17 P&M. Problem 4.18 P&M (Grad Students only). Problem 4.22 P&M. Use Assignment3.m to generate the figures below and answer the following questions: i. What is the 90% bandwidth (in Hz) of the aortic pressure waveform? See Section 4.2.9 P&M for definition. You may have to use the zoom and the Datatip. You can also use the MATLAB command find, but this will require a little work. ii. What is the 90% bandwidth (in Hz) of the filtered waveform? iii. What is the 6dB bandwidth of the MA filter used? iv. Describe the effects of the filter on the PSD of the signal. In particular, what frequency components are affected (if any)? v. Can you estimate the SNR for both signals? vi. Repeat (i. v.) the above for the ecg waveform. EE 4541 Digital Signal Processing Fall 2007 Problem Set 3 Due September 27, 2007 ...
View Full Document

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern