4.1 Lab 2: prelab (part 1)

Multirate theory exercise

Consider a sampled signal with the DTFT $X(\omega )$ shown in [link] .

Assuming $U=D=3$ , use the relations between the DTFT of a signal before and after sample-rate compression and expansion( [link] and [link] ) to sketch the DTFT response of the signal as it passes through themultirate system of [link] (without any filtering). Include both the intermediate response $W(\omega )$ and the final response $Y(\omega )$ . It is important to be aware that the translation from digital frequency $\omega$ to analog frequency depends on the sampling rate. Therefore, the conversion is different for $X(\omega )$ and $W(\omega )$ .