Lab 2: Prelab (Part 1) 1.1 2006/07/26 10:59:03.192 GMT-5 2006/08/20 21:37:13.733 GMT-5 Thomas Shen tbshen@uiuc.edu Douglas L. Jones dl-jones@uiuc.edu Thomas Shen tbshen@uiuc.edu aliasing downsampling DSP imaging multirate sample-rate compressor sample-rate expander upsampling You will work through an example problem that explores the effects of sample-rate compression and expansion on the spectrum of a signal.

Multirate Theory Exercise Consider a sampled signal with the DTFT X ω shown in .

DTFT of the input signal.

Assuming U D 3 , use the relations between the DTFT of a signal before and after sample-rate compression and expansion ( and ) to sketch the DTFT response of the signal as it passes through the multirate system of (without any filtering). Include both the intermediate response W ω and the final response Y ω . It is important to be aware that the translation from digital frequency ω to analog frequency depends on the sampling rate. Therefore, the conversion is different for X ω and W ω . W ω 1 D k 0 D 1 X ω 2 k D Y ω W U ω

Multirate System