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barcode lib ssrs If y(n) = x(n), Y ( e i U )= X(eIu), and it is clear that this will be true if and only if a = in Software
If y(n) = x(n), Y ( e i U )= X(eIu), and it is clear that this will be true if and only if a = ANSI/AIM Code 128 Reader In None Using Barcode Control SDK for Software Control to generate, create, read, scan barcode image in Software applications. Code128 Generator In None Using Barcode generator for Software Control to generate, create Code 128 image in Software applications. Find the input x ( n ) that will produce a response, y ( n ) = 6 ( n ) ,for a system described by the LCCDE Code 128 Scanner In None Using Barcode decoder for Software Control to read, scan read, scan image in Software applications. Code 128 Code Set A Printer In Visual C# Using Barcode maker for VS .NET Control to generate, create Code 128B image in .NET applications. This problem is easily solved if we express this difference equation in the frequency domain. Specifically, we have Print Code 128B In .NET Framework Using Barcode drawer for ASP.NET Control to generate, create Code 128 image in ASP.NET applications. Encoding Code128 In VS .NET Using Barcode creator for .NET framework Control to generate, create USS Code 128 image in VS .NET applications. y (,jw) USS Code 128 Printer In VB.NET Using Barcode creator for .NET framework Control to generate, create Code 128 Code Set C image in VS .NET applications. Generate Code 128B In None Using Barcode printer for Software Control to generate, create Code 128B image in Software applications. ieiwy (,iw) = ~ ( ~ j ! )  i h ~ ( e " J J ) w e
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w(n) = and x(n) is given by
(y " n=0,2,4, otherwise
FOURIER ANALYSIS
[CHAP. 2
Supplementary Problems
Frequency Response
Consider a linear shiftinvariant system with a unit sample response h(n) = 6(n) Find the output of the system when the input is + 6(n
If the unit sample response of a linear shiftinvariant system is h(n) = a n u ( n ) with la1 < I, find the response of the system to the input x ( n ) = I . Repeat for x ( n ) = (1)". Find the frequency response of the system that has a unit sample response h(n)= The input to a linear shiftinvariant system is ( (nwo) o5n5N 1 otherwise
Find the output when the unit sample response is
The input to a.linear shiftinvariant system is x(n) = n(i)"u(n) and the output is y ( n ) = (;)"'u(n  2 ) Find the frequency response ~ ( e j , ) . Find the frequency response of the system described by the LCCDE ~ ( n= i y ( n ) u ( n  3) 10) + x ( n ) + j s ( n  10) Find the group delay of the system that has a frequency response
Filters
What is the unit sample response of an ideal bandstop filter with a lower cutoff frequency of o,and an upper cutoff frequency of w If h ( n ) is the unit sample response of an ideal lowpass filter with a gain of one and a cutoff frequency w , = n / 8 , what is g ( n ) = cos(nn/2)h(n) CHAP. 21
FOURIER ANALYSIS
The Interconnection of Systems
What type of filter has a unit sample response
What is the magnitude of the frequency response of the cascade of the following two systems
The DiscreteTime Fourier 'Ikansform
Find the DTFT of the sequence
x(n) = else
For each of the following systems, find the frequencies that are present in the output when the DTFT of the input x(n) is Let x(n) = ejnnI4u(n) and y(n) = 0.5ejn"/4u(n).Determine whether or not there is a linear shiftinvariant system that has the response, y(n), to the input x(n). If such a system exists, determine whether or not the system is unique, and find the frequency response of an LSI system with thedesiredbehavior. If no suchLSI system exists, explain why. Find the inverse DTFT of X(ejo) illustrated in the figure below. Find the inverse DTFT of X ( e J Willustrated in the figure below. ) 2.62 2.63 Find the inverse DTFT of X(ejo) = cos 2w Find the inverse DTFT of
+ j sin a.
otherwise
FOURIER ANALYSIS
[CHAP. 2
Find the DTFT of
If x(n) is real and causal, and
find x(n). DTFT Properties
Let x ( n ) be a sequence with a DTFT X(ejw). For each of the following sequences that are related to x(n),express the DTFT in terms of X(ejW): (4 x*(n) ( h ) x ( n )  x(n  2) ( c ) x(2n) ( d ) x ( n )* x ( n  I ) 2.67 2.68 If the DTFT of x ( n ) = ( i ) " u ( n 2) is X(ejW), the sequence that has a DTFT given by Y (ejw) X(ejzo), find = Let x ( n ) be the sequence x ( n ) = 26(n
+ 3)  26(n + I ) + 6(n
+ 36(n
If the DTFT of x ( n ) is expressed in terms of its real and imaginary parts as follows, find the sequence y(n) that has a DTFT given by
The DTFT of a sequence x ( n ) is
3 JW X ( e )  ( 1  0.Xejw)5 Evaluate the sum
The DTFT of a sequence .r(n) is
x ( e J W= cos3(3w) ) Evaluate the sum
2.71 2.72 Let C:,x(n) = A and
x : , h ( n ) = B. If y(n) = h ( n )* x(n), is it true that
C z  , y(n) = A . B
Evaluate the following integral: ,w i
 0.3ejm
Using the center o gravity (see problem 2.36), find the time delay of the sequence f
x ( n ) = anu(n) CHAP. 21
FOURIER ANALYSIS
Applications of the DTFT
A causal linear shiftinvariant system is defined by the difference equation
2y(n) y(n  2 ) = x ( n Find the frequency response, H (e'").  1) +3x(n  2) +2x(n  3) The frequency response of a linear shiftinvariant system is
I H(eJW) elw=
2 + e2iw
Find an LCCDE that relates the input to the output.
Find the inverse of the system that has a unit sample response h(n) = n(k)"u(n  3).

