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# Lab 2: Prelab (part 1)

Summary: 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

พิจารณา sampled signal ที่มี DTFT Xω X ω แสดงใน รูป 1.

สมมติว่าAssuming U=D=3 U D 3 , ใช้ความสัมพันธ์ดังกล่าว ระหว่าง DTFT ของ signal ก่อนและหลัง sample-rate compression และ expansion (สมการ 1 and สมการ 2) เพื่อร่างค่า DTFT response ของ signal ที่ผ่านเข้าระบบ multirate ของ รูป 2 (โดยปราศจากการ filtering). รวมทั้ง intermediate response Wω W ω และ final response Yω Y ω . ให้ระวังว่าการแปลงค่าจาก digital frequency ω ω เป็น analog frequency ขึ้นอยู่กับค่า sampling rate. ฉะนั้นการแปลงค่า จึงแตกต่างกันสำหรั Xω X ω และ Wω W ω .

Wω=1D k =0D1Xω+2πkD W ω 1 D k 0 D 1 X ω 2 k D
(1)
Yω=WUω Y ω W U ω
(2)

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