barcode generator for ssrs Thus, by inspection, we see that in Software

Encoder Code 128 Code Set A in Software Thus, by inspection, we see that

Thus, by inspection, we see that
ANSI/AIM Code 128 Scanner In None
Using Barcode Control SDK for Software Control to generate, create, read, scan barcode image in Software applications.
Generating ANSI/AIM Code 128 In None
Using Barcode generation for Software Control to generate, create ANSI/AIM Code 128 image in Software applications.
with the other DFS coefficients from k = 0 to k = 19 equal to zero.
Reading Code 128 In None
Using Barcode decoder for Software Control to read, scan read, scan image in Software applications.
Code 128 Code Set B Creator In Visual C#
Using Barcode drawer for .NET Control to generate, create Code 128 Code Set C image in Visual Studio .NET applications.
The Discrete Fourier 'Ikansform
USS Code 128 Creator In VS .NET
Using Barcode drawer for ASP.NET Control to generate, create ANSI/AIM Code 128 image in ASP.NET applications.
Code-128 Generation In VS .NET
Using Barcode drawer for .NET Control to generate, create Code 128A image in VS .NET applications.
Compute the N-point DFT of each of the following sequences:
Creating USS Code 128 In VB.NET
Using Barcode encoder for VS .NET Control to generate, create Code 128 Code Set A image in VS .NET applications.
Barcode Generator In None
Using Barcode encoder for Software Control to generate, create bar code image in Software applications.
xl(n) = &n)
Making EAN-13 In None
Using Barcode creation for Software Control to generate, create EAN13 image in Software applications.
Generating GTIN - 128 In None
Using Barcode drawer for Software Control to generate, create EAN128 image in Software applications.
(b) x2(n) = S(n - no), where 0 < no
DataMatrix Printer In None
Using Barcode encoder for Software Control to generate, create Data Matrix 2d barcode image in Software applications.
Print Code128 In None
Using Barcode creator for Software Control to generate, create Code128 image in Software applications.
THE DFT (c) x 3 ( n ) = c r n
Painting USPS Intelligent Mail In None
Using Barcode printer for Software Control to generate, create 4-State Customer Barcode image in Software applications.
Encoding Barcode In .NET Framework
Using Barcode maker for .NET Control to generate, create barcode image in VS .NET applications.
[CHAP. 6
Creating Data Matrix ECC200 In Objective-C
Using Barcode creator for iPad Control to generate, create DataMatrix image in iPad applications.
ANSI/AIM Code 39 Generation In Visual Studio .NET
Using Barcode generator for .NET framework Control to generate, create ANSI/AIM Code 39 image in VS .NET applications.
O s n c N
Paint Data Matrix ECC200 In None
Using Barcode printer for Font Control to generate, create DataMatrix image in Font applications.
GS1 - 13 Encoder In .NET
Using Barcode generator for ASP.NET Control to generate, create EAN-13 image in ASP.NET applications.
( d ) x&)
Make Matrix 2D Barcode In C#
Using Barcode creator for Visual Studio .NET Control to generate, create Matrix Barcode image in Visual Studio .NET applications.
Read EAN-13 Supplement 5 In Java
Using Barcode reader for Java Control to read, scan read, scan image in Java applications.
= u(n) - u(n - no),where 0 < no < N
(a) The DFT of the unit sample may be easily evaluated from the definition of the DFT:
Another approach, however, is to recall that the DFT corresponds to samples of the z-transform X l ( z ) at N equally spaced points around the unit circle. Because X I ( z ) = I, i t follows that X l ( k ) = I .
(h) For the second sequence, we may again evaluate the DFT directly from the definition of the DFT. Let us instead, however, sample the z-transform. We know that X 2 ( z ) = z - " U . Therefore, sampling X 2 ( z )at the points z = ~ , o r k = O , I ...., N-1,wefind
( c ) For x 3 ( n ) ,the DFT may be found directly as follows:
iV-I
(d) The DFT of the pulse. x 4 ( n ) = u ( n ) - u ( n - no), may be evaluated directly as follows:
Factoring out a complex exponential w l2 denominator, the DFT may be written as
from the numerator and a complex exponential w;l2 from the
Find the 10-point inverse DFT of
To find the inverse DFT, note that X ( k ) may be expressed as follows:
Written in this way, the inverse DFT may be easily determined. Specifically, note that the inverse DFT of a constant is a unit sample: x l ( n )= S ( n ) Similarly. the DFT of a constant is a unit sample:
x l ( k )= 1
Therefore, i t follows that
x(n) =
+6(n)
CHAP. 61
THE DFT
Find the N -point DFT of the sequence
Compare the values of the DFT coefficients X ( k ) when wo = 2 n k o l N to those when wo # 2 r r k o l N . Explain the difference.
To find the N-point DFT of this sequence, it is easier if we write the cosine in terms of complex exponentials:
Evaluating the DFT of each of these terms, we find
~ ( k= C x ( n ) e - i % n i = )
At this point, note that if 9 = 2 r r k o / N ,
N- I e - ~ n ( % ~ - r n+ ~
rV - I
e-~nliJi+ul)
Because the first term is a sum of a complex exponential of frequency wo = 2 z ( k - k o ) / N , the sum will be equal to i zero unless k = ko, in which case the sum is equal to N . Similarly, the second sum is equal to zero unless != N - k,,, in which case the sum is equal to N . Therefore. if on= 2 z k o / N . the DFT coefficients are
X(k) =
k = ko and k == N - ko
otherwise
In the general case, when wo # 2 n k n / N , we must use the geometric series to evaluate Eq. (6.18):
Factoring out a complex exponential from the numerator and one from the denominator, we have
Note that. unless % is an integer multiple of 2 n / N , X ( k ) is, in general, nonzero for each k . The reason for this difference belween these two cases comes from the fact that X ( k ) corresponds to samples of the DTFT of x ( n ) , which is
When sampled at N equally spaced points over the interval [ O , 2 n ] , the sample values will, in general, be nonzero. However, if wo = 2 z k o / N , all of the samples except those at k = kc and k = N - ko occur at the zeros of the sine function.
Find the N -point DFT of the sequence
THE DFT The DFT of this sequence may be evaluated by expanding the cosine as a sum of complex exponentials:
=4 +
[CHAP. 6
[ej2nnlN
+e-j2~nlN
]2 = 4 + ;+ $ p ~ 4 n " l N + ,e - j 4 ~ n l N I
Using the periodicity of the complex exponentials, we may write x ( n ) as follows:
Copyright © OnBarcode.com . All rights reserved.