TEST BANK FOR Digital Signal Processing 4th Edition by J. Proakis and D. Manolakis
Exam (elaborations)
TEST BANK FOR Digital Signal Processing 4th Edition by J. Proakis and D. Manolakis (Instructor Solution Manual)
11 views 0 purchase
Course
TEST BANK FOR Digital Signal Processing 4th Edition by J. Proakis and D. Manolakis
Institution
Harvard University
Exam (elaborations) TEST BANK FOR Digital Signal Processing 4th Edition by J. Proakis and D. Manolakis (Instructor Solution Manual)
Chapter 1
1.1
(a) One dimensional, multichannel, discrete time, and digital.
(b) Multi dimensional, single channel, continuous-time, analog.
(c) One dimensional,...
TEST BANK FOR Digital Signal Processing 4th Edition by J. Proakis and D. Manolakis
All documents for this subject (2)
Seller
Follow
Exceldemics
Reviews received
Content preview
,Chapter 1
1.1
(a) One dimensional, multichannel, discrete time, and digital.
(b) Multi dimensional, single channel, continuous-time, analog.
(c) One dimensional, single channel, continuous-time, analog.
(d) One dimensional, single channel, continuous-time, analog.
(e) One dimensional, multichannel, discrete-time, digital.
1.2
(a) f = 0.01π 1
2π = 200 ⇒ periodic with Np = 200.
(b) f = 105 ( 2π ) = 17 ⇒ periodic with Np = 7.
30π 1
3π
(c) f = 2π = 32 ⇒ periodic with Np = 2.
3
(d) f = 2π ⇒ non-periodic.
(e) f = 62π 1 31
10 ( 2π ) = 10 ⇒ periodic with Np = 10.
1.3
(a) Periodic with period Tp = 2π 5 .
5
(b) f = 2π ⇒ non-periodic.
1
(c) f = 12π ⇒ non-periodic.
n
(d) cos( 8 ) is non-periodic; cos( πn 8 ) is periodic; Their product is non-periodic.
(e) cos( πn
2 ) is periodic with period Np =4
sin( πn
8 ) is periodic with period N p =16
cos( πn
4 + π
3 ) is periodic with period Np =8
Therefore, x(n) is periodic with period Np =16. (16 is the least common multiple of 4,8,16).
1.4
2πk k
(a) w = N implies that f = N. Let
α = GCD of (k, N ), i.e.,
k = k ′ α, N = N ′ α.
Then,
k′
f= , which implies that
N′
N
N′ = .
α
3
,(b)
N = 7
k = 01234567
GCD(k, N ) = 71111117
Np = 17777771
1.6
(a)
x(n) = Acos(2πF0 n/Fs + θ)
= Acos(2π(T /Tp )n + θ)
But T /Tp = f ⇒ x(n) is periodic if f is rational.
(b) If x(n) is periodic, then f=k/N where N is the period. Then,
k Tp
Td = ( T ) = k( )T = kTp .
f T
Thus, it takes k periods (kTp ) of the analog signal to make 1 period (Td ) of the discrete signal.
(c) Td = kTp ⇒ N T = kTp ⇒ f = k/N = T /Tp ⇒ f is rational ⇒ x(n) is periodic.
1.7
(a) Fmax = 10kHz ⇒ Fs ≥ 2Fmax = 20kHz.
(b) For Fs = 8kHz, Ffold = Fs /2 = 4kHz ⇒ 5kHz will alias to 3kHz.
(c) F=9kHz will alias to 1kHz.
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller Exceldemics. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $17.49. You're not tied to anything after your purchase.
