Calculate Sum of Fourier Transform | N = 7 Vector

  • Thread starter Thread starter bodensee9
  • Start date Start date
  • Tags Tags
    Fourier
Click For Summary
SUMMARY

The discussion focuses on calculating the sum of a modified sequence derived from a Discrete Fourier Transform (DFT) of a real signal represented by an N = 7 vector. The user seeks to compute the expression x[1] - x[2] + x[3] - x[4] + x[5] - x[6], noting that the odd value of N prevents the use of standard frequency tricks. A suggested approach involves expressing the modified sequence as x'_n = (-1)^n x_n and exploring the Fourier transform properties of the product of two functions.

PREREQUISITES
  • Understanding of Discrete Fourier Transform (DFT)
  • Familiarity with Fourier transform properties
  • Knowledge of signal processing concepts, particularly real signals
  • Basic understanding of square wave functions and their mathematical representation
NEXT STEPS
  • Study the properties of the Fourier transform of products of functions
  • Learn about the implications of odd N in DFT calculations
  • Explore the concept of square waves and their role in signal modulation
  • Investigate techniques for manipulating sequences in signal processing
USEFUL FOR

This discussion is beneficial for signal processing students, engineers working with Fourier analysis, and anyone interested in advanced mathematical techniques for analyzing real-valued signals.

bodensee9
Messages
166
Reaction score
0

Homework Statement


Hello: I have a say N = 7 vector. Say I know that it's DFT is X = [X[0] X[1] ... X[6]]
I am wondering if there is any way that I can find the sum of:
x[1] - x[2] + x[3] - x[4] + x[5] - x[6]?
Since N = odd, I can't use the trick with N/2 = pi as a frequency. Thanks so much.
My signal x{n] is real, but I really can't see any relation between the entries of X and x.
 
Physics news on Phys.org
You could express your modified sequence as the product of the sequence x times a square wave:

[tex]x'_n=(-1)^n x_n,[/tex] with n=0, 1, ...

Try taking it from there. Hint: what is the Fourier transform of a product of two functions?
 

Similar threads

Replies
1
Views
3K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 5 ·
Replies
5
Views
2K
  • · Replies 14 ·
Replies
14
Views
2K
  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 7 ·
Replies
7
Views
2K
  • · Replies 2 ·
Replies
2
Views
1K
Replies
3
Views
2K
  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 16 ·
Replies
16
Views
2K