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Pick a signal x(t) representing a note of the middle scale of the piano (but not the middle C we did in class) and obtain its CTFT <math>X(f)</math>. Then pick a sampling period <math>T_1</math> for which no aliasing occurs and obtain the DTFT of the sampling <math>x_1[n]=x(n T_1)</math>. More precisely, write a mathematical expression for <math>X_1(\omega)</math> and sketch its graph. Finally, pick a sampling frequency <math>T_2</math> for which aliasing occurs and obtain the DTFT of the sampling <math>x_2[n]=x(n T_2)</math> (i.e., write a mathematical expression for <math>X_2(f)</math> and sketch its graph.) Note the difference and similarities between <math>X(f)</math> and <math>X_1(\omega)</math>. Note the differences and similarities between <math>X_1(\omega)</math> and <math>X_2(\omega)</math>. | Pick a signal x(t) representing a note of the middle scale of the piano (but not the middle C we did in class) and obtain its CTFT <math>X(f)</math>. Then pick a sampling period <math>T_1</math> for which no aliasing occurs and obtain the DTFT of the sampling <math>x_1[n]=x(n T_1)</math>. More precisely, write a mathematical expression for <math>X_1(\omega)</math> and sketch its graph. Finally, pick a sampling frequency <math>T_2</math> for which aliasing occurs and obtain the DTFT of the sampling <math>x_2[n]=x(n T_2)</math> (i.e., write a mathematical expression for <math>X_2(f)</math> and sketch its graph.) Note the difference and similarities between <math>X(f)</math> and <math>X_1(\omega)</math>. Note the differences and similarities between <math>X_1(\omega)</math> and <math>X_2(\omega)</math>. | ||
| − | + | == Presentation Guidelines == | |
| + | * Write only on one side of the paper. | ||
| + | * Use a "clean" sheet of paper (e.g., not torn out of a spiral book). | ||
| + | * Staple the pages together. | ||
| + | * Include a cover page. | ||
| + | * Do not let your dog play with your homework. | ||
| + | ---- | ||
| + | == Discussion == | ||
| + | Please discuss the homework below. | ||
| + | *write comment/question here | ||
| + | **answer will go here | ||
---- | ---- | ||
[[2013_Fall_ECE_438_Boutin|Back to ECE438, Fall 2013, Prof. Boutin]] | [[2013_Fall_ECE_438_Boutin|Back to ECE438, Fall 2013, Prof. Boutin]] | ||
Latest revision as of 03:42, 31 August 2013
Contents
Homework 2, ECE438, Fall 2013, Prof. Boutin
Due Friday September 6, 2013 (in class)
Question
Pick a signal x(t) representing a note of the middle scale of the piano (but not the middle C we did in class) and obtain its CTFT $ X(f) $. Then pick a sampling period $ T_1 $ for which no aliasing occurs and obtain the DTFT of the sampling $ x_1[n]=x(n T_1) $. More precisely, write a mathematical expression for $ X_1(\omega) $ and sketch its graph. Finally, pick a sampling frequency $ T_2 $ for which aliasing occurs and obtain the DTFT of the sampling $ x_2[n]=x(n T_2) $ (i.e., write a mathematical expression for $ X_2(f) $ and sketch its graph.) Note the difference and similarities between $ X(f) $ and $ X_1(\omega) $. Note the differences and similarities between $ X_1(\omega) $ and $ X_2(\omega) $.
Presentation Guidelines
- Write only on one side of the paper.
- Use a "clean" sheet of paper (e.g., not torn out of a spiral book).
- Staple the pages together.
- Include a cover page.
- Do not let your dog play with your homework.
Discussion
Please discuss the homework below.
- write comment/question here
- answer will go here
