Assignment1
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School
Hollywood High School**We aren't endorsed by this school
Course
KID LZXJCL
Subject
Electrical Engineering
Date
Jan 14, 2025
Pages
1
Uploaded by ProfessorSteel7125
Sinai University Faculty of Information Technology & Computer ScienceINT421-Digital Signal Processing Fall 2023 Assignment 1INT 421-DSP (Dr. M. El-Telbany) Page 1 of 1 1.Sketch the following sequences: a)?(?) = 3𝛿(? + 2) − 0.5𝛿(?) + 5𝛿(? − 1) − 4𝛿(? − 5)b)?(?) = 𝛿(? + 1) − 2𝛿(? − 1) + 5𝑢(? − 4)2.Determine which of the following is a linear system: a)?(?) = 5?(?) + 2?2(?)b)?(?) = ?(? − 1) + 4?(?)c)?(?) = 4?3(? − 1) − 2?(?)3.Given the following linear systems, find which one is time invariant: a)?(?) = −5?(? − 10)b)?(?) = 4?(?2)4.Determine which of the following linear systems is causal: a.?(?) = 0.5?(?) + 100?(? − 2) − 20?(? − 10)b.?(?) = ?(? + 4) + 0.5?(?) − 2?(? − 2)5.Determine whether the following systems are causal or not. a)?(?) = 0.5?(?) + 0.25?(? − 2), ??? ? ≥ 0b)?(?) = 0.25?(? − 1) + 0.25?(? + 2) + 0.4?(? − 1), ??? ? ≥ 06.Determine causality for each of the following linear systems: a)?(?) = 0.5?(?) + 20?(? − 2) − 0.1?(? − 1)b)?(?) = ?(? + 2) − 0.4?(? − 1)c)?(?) = ?(? − 1) + 0.5?(? + 2)7.Given the sequence definitions ?(?) = {−2,? = 0,1,21,? = 3,40?????ℎ???and ℎ(?) = {2,? = 0,−1,? = 1,20?????ℎ???Evaluate the digital convolution ?(?) = ∑ℎ(?)?(? − ?)∞𝑘=−∞a)Using the graphical method; b)Using the table method; c)Applying the convolution formula directly. 8.Given the sequence ℎ(?) = {2,? = 0,1,21,? = 3,40?????ℎ???where?is the time index or sample number. a)Sketch the sequenceℎ(?)and the reverse sequenceℎ(−?). b)Sketch the shifted sequencesℎ(−? + 2)andℎ(−? − 3). 9.Check the following for linearity, time-invariance, and causality. a)y(n)=5nx2b)y(n)= ?(?)?𝑖?2?c)?(?) = ?−𝑛?(? + 3)10.Given the input ?(?) = 𝑢(?)and the output ?(?) = (12)𝑛−1𝑢(? − 1) of a system. a)Determine the impulse response ℎ(?)b)Is the system stable? c)Is the system causal?
