Solving FFT Signal Processing Problem for Complex Time Signal

In summary, the conversation discusses a complex time signal x(t) and its conversion to frequency domain using FFT. The desired frequencies are obtained, but the amplitudes do not correspond to the original values due to the phase difference between signals. The question is how to retrieve the correct amplitudes when multiple frequency components are present. The conversation also mentions that when only one frequency component is present, the correct amplitude can be obtained. The question of sampling rate and number of samples compared to ω is not addressed.
  • #1
shravz
2
0
Hi, I have a complex time signal x(t)=X1*exp(i*∅)+X2*exp(i*2*∅). On converting to frequency domain, i expect frequency components at ω and twice of ω (when ∅=ω*t). FFT gives the desired frequencies, but the amplitudes don't correspond to X1 and X2. I understand that this is due to the phase difference between the signals X1*exp(i*∅1) and X2*exp(i*2*∅). My question is how should i get back the amplitudes X1,X2,... when multiple frequency components exist in the signal.

P.S: when only x(t)=X1*exp(i*∅1);am able to get back X1 in the fft.

Thanks in advance.
 
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  • #2
It is not a question of phase. If you did everything correctly, you should get X1 and X2 back.

What is the sampling rate and number of samples compared to w?
 

What is FFT signal processing?

FFT (Fast Fourier Transform) signal processing is a mathematical algorithm used to convert a time-based signal into its frequency components. It is commonly used in digital signal processing to analyze and manipulate signals in various applications such as audio and image processing.

Why is FFT signal processing important?

FFT signal processing allows us to analyze signals in the frequency domain, which can provide valuable insights into their characteristics and properties. This can be useful in a wide range of applications, including noise reduction, filtering, and pattern recognition.

How does FFT signal processing work?

The FFT algorithm works by breaking down a signal into smaller segments and performing mathematical operations on these segments to determine their frequency components. These components are then combined to reconstruct the signal in the frequency domain.

What are the advantages of using FFT signal processing?

One of the main advantages of FFT signal processing is its speed. It can process signals much faster than traditional methods, making it ideal for real-time applications. Additionally, it allows for more accurate and detailed analysis of signals, making it a valuable tool in many fields.

What are some common challenges in solving FFT signal processing problems for complex time signals?

Some common challenges in solving FFT signal processing problems for complex time signals include understanding the underlying mathematical principles, selecting the appropriate windowing and scaling techniques, and dealing with noise and artifacts in the signal. Additionally, properly interpreting and analyzing the results can also be a challenge.

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