How is the following fraction split for inverse Fourier?

In summary, The conversation discusses a problem with equations and the use of partial fractions for the inverse Fourier transform. The speaker eventually figures out the solution but has another question and asks for help. In order to obtain the value of A in the second equation, the speaker mentions using the cancellation method, but notes that the denominator would equal 0.
  • #1
Jeviah
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Hi i’m having problems with the following equations:

X(w)=2/(-1+iw)(-2+iw)(-3+iw)

This then becomes the following equation according the the tutorial, although there is no explanation as to how:

X(w)=1/-1+iw, -2/-2+iw, +1/-3+iw

The commas indicated the end of each fraction to make it easier to interpret

This process is for inverse Fourier transform which i understand however to do not understand how the above step was completed
 
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  • #2
Use partial fractions.
 
  • #3
Thank you i figured it out, although i have a problem with another question if you could possibly help out please

6/(2iw-3)^2(iw+1)
I have split it and obtained B=12/5 and C=6/12 with the layout A/(2iw-3), +B/(2iw-3)^2, +C/(iw+1) cancelling them out of the original equation to obtain the respective values

How would i obtain A considering using the cancellation method above, the denominator would equal 0
 

1. What is inverse Fourier?

Inverse Fourier is the mathematical operation that allows us to convert a signal from the frequency domain to the time domain. It is the inverse of the Fourier transform and is commonly used in signal processing to analyze signals in the time domain.

2. How is the following fraction split for inverse Fourier?

The fraction for inverse Fourier is typically split into two parts: the real part and the imaginary part. This is known as the complex conjugate pair and is represented by the equation F(x) = Re(F(x)) + iIm(F(x)). The real part represents the cosine terms and the imaginary part represents the sine terms.

3. What is the significance of splitting the fraction for inverse Fourier?

Splitting the fraction for inverse Fourier allows us to separate the real and imaginary parts of the signal, making it easier to analyze and manipulate. It also allows us to easily transform the signal back to the frequency domain if needed.

4. How is the fraction split for inverse Fourier in practice?

In practice, the fraction for inverse Fourier is typically split using the Euler's formula, which states that e^ix = cos(x) + i*sin(x). This allows us to rewrite the complex conjugate pair as F(x) = e^(i*2πx) and F(x) = e^(-i*2πx), which can then be combined to form the inverse Fourier transform equation.

5. Are there any limitations to using inverse Fourier?

While inverse Fourier is a powerful tool in signal processing, it does have some limitations. One limitation is that it assumes the signal is periodic, which may not always be the case in real-world applications. Additionally, inverse Fourier may not be able to accurately represent signals with sharp changes or discontinuities. These limitations should be taken into consideration when using inverse Fourier in analysis and processing of signals.

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