
Study with the several resources on Docsity
Earn points by helping other students or get them with a premium plan
Prepare for your exams
Study with the several resources on Docsity
Earn points to download
Earn points by helping other students or get them with a premium plan
Community
Ask the community for help and clear up your study doubts
Discover the best universities in your country according to Docsity users
Free resources
Download our free guides on studying techniques, anxiety management strategies, and thesis advice from Docsity tutors
Questions get repeated sometimes from previous year papers or similar sort of questions are given.This could be helpful.
Typology: Assignments
1 / 1
This page cannot be seen from the preview
Don't miss anything!
( (^) π 3 n^ +^
π 4
ii) 2 + cos
( (^) π 6 n^ +^
π 8
3
)n u[n] is connected in parallel with another causal LTI system with impulse response h 2 [n]. The resulting parallel interconnection has the frequency response:
ejω^
= −12+5e
−jω 12 − 7 e−jω^ +e−j^2 ω^.
Determine h 2 [n].
i) x[n] =
3
)|n| u[−n−2] ii) x[n] =
2
)|n| cos
( (^) π 8 (n^ −^ 1)
iii) x[n] = sin( πnπn/ 5)cos
( (^7) π 2 n
iv) x(t) = 1 + cos πt, |t| ≤ 1 0 , |t| > 1 v) x(t) =
n=−∞ e
−|t− 2 n| (^) vi) d dt {u(−^2 −^ t) +^ u(t^ − 2)}.
ejω^
= cos^2 ω + sin^2 3 ω (discrete) ii) X
ejω^
k=−∞(−1) kδ (ω − π 2 k
(discrete) iii) X(jω) = 2 sin3((ω−ω 2 −π)^2 π) iv) X(jω) = 2[δ(ω − 1) − δ(ω + 1)] + 3[δ(ω − 2 π) + δ(ω + 2π)] (continuous) v) X(jω) = (sin^2 (3ω)) cos^ ω ω^2 (continuous).
dy(t) dt + 8y(t) = 2x(t) i) Find the impulse response of the system. ii) What is the response of this system if x(t) = te−^2 tu(t)?
k=−∞ x[n]δ[n^ −^ kN^ ]. If X(ejω^ ) = 0 for 3π/ 7 ≤ |ω| ≤ π, determine the largest value for the sampling interval N which ensures that no aliasing takes place while sampling x[n].