Fourier transform for Discrete signal

In summary, the conversation discusses a discrete signal defined as f(n)=a^n * u(n), where u(n) is the unit step function and a is a constant between 0 and 1. The Fourier transform for discrete signals is also defined and the conversation explores why F(i)=sum(1/(1-a*e^-j2*pi*n/N). The hint provided suggests considering the infinite geometric series and the common ratio r.
  • #1
electronic engineer
145
3
let us asuume this discrete signal:

f(n)=a^n * u(n) ; where u(n) is unit step function
; u(n)=1 where n>=0
u(n)=0 where n<0
;0=<a<1
and the foruier transform for discrete signals is defined as :
F(i)=sum ( f(n)*e^(-j2*pi*n/N) ;n=0 to inifinity

i know that the sum is equal to:

F(i)=sum(1/(1-a*e^-j2*pi*n/N)

but actually i don't know why! could anyone help!


thanks in advance!
 
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  • #2
Hint: think infinite geometric series. In this example, what is the common ratio r?

Regards,
George
 
  • #3
what do you mean by common ratio r?
 

1. What is the Fourier transform for discrete signals?

The Fourier transform for discrete signals is a mathematical technique that decomposes a discrete signal into its constituent frequencies. It is a way to analyze the frequency components of a signal and is commonly used in signal processing and data analysis.

2. How is the Fourier transform for discrete signals different from the continuous Fourier transform?

The main difference between the Fourier transform for discrete signals and the continuous Fourier transform is that the discrete transform is used for signals that are sampled at discrete time intervals, whereas the continuous transform is used for signals that are continuous in time. The discrete transform is also typically computed using algorithms, while the continuous transform is calculated using mathematical integrals.

3. What is the purpose of using the Fourier transform for discrete signals?

The Fourier transform for discrete signals is used to analyze the frequency components of a signal. This allows for the identification of specific frequencies and their amplitudes, which can provide insight into the behavior and characteristics of the signal. It is also used for filtering, compression, and other signal processing techniques.

4. What are some common applications of the Fourier transform for discrete signals?

The Fourier transform for discrete signals has many applications, including audio and image processing, data compression, and filtering in communication systems. It is also used in fields such as physics, engineering, and economics for data analysis and pattern recognition.

5. Are there any limitations to using the Fourier transform for discrete signals?

One limitation of the Fourier transform for discrete signals is that it assumes the signal is periodic, meaning it repeats itself infinitely. This may not always be the case in real-world signals. Additionally, the accuracy of the transform can be affected by the sampling rate and the length of the signal being analyzed.

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