ELEC 353 Signal Analysis and Filtering HW 1 2025 PDF
Document Details
Uploaded by Deleted User
2025
Dr Muhammad Salman Khan
Tags
Summary
This document contains a homework assignment for the ELEC 353 Signal Analysis and Filtering class, Spring 2025. The assignment includes five problems related to sketching spectra of signals, calculating sampling rates and the maximum amount of quantization error. The problems cover the concepts of signal processing, filtering and quantization.
Full Transcript
Homework # 1 ELEC 353 Signal analysis and filtering, spring 2025 Student name: ________________________ ID number: ___________________ Instructor: Dr Muhammad Salman Khan Problem: The signal 𝑥(𝑡) = 2 cos(10𝜋𝑡) + 4cos(20𝜋𝑡) is passed through an ideal low-pass f...
Homework # 1 ELEC 353 Signal analysis and filtering, spring 2025 Student name: ________________________ ID number: ___________________ Instructor: Dr Muhammad Salman Khan Problem: The signal 𝑥(𝑡) = 2 cos(10𝜋𝑡) + 4cos(20𝜋𝑡) is passed through an ideal low-pass filter with cutoff frequency 𝜔𝑐 = 15𝜋. The output of the filter is denoted 𝑦(𝑡) with corresponding spectrum 𝑌(𝜔). 𝑦(𝑡) is then sampled at twice its Nyquist rate to yield the sampled signal 𝑦̅(𝑡), with corresponding spectrum 𝑌̅(𝜔). 1. Sketch 𝑋(𝜔), the spectrum of 𝑥(𝑡). 2. Sketch 𝑌(𝜔), the spectrum of the filtered signal. 3. Given that sampling is performed at twice the Nyquist rate, what is the sampling rate in Hz. 4. Sketch 𝑌̅(𝜔) the spectrum of the sampled signal. 5. Each sample of 𝑦(𝑡) is quantized using a 8-bit quantizer. Assume the quantizer limit (i.e. 𝑚𝑝 ) is set to the peak signal value of 𝑦(𝑡). What is the maximum amount of error introduced by the quantization process?
