# Homework 2, ECE438, Fall 2014, Prof. Boutin

Hard copy due in class, Monday September 15, 2014.

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.