Fourier Transform: Frequency Response vs Signal X

In summary, the conversation is about a homework question regarding the difference between Frequency Response of a system H(jw) and the Fourier Transform of a signal X(jw). The person is seeking guidance on this topic and is referred to the Convolution theorem for assistance.
  • #1
feely
24
0
Hello.

I have a homework question here that I just can't seem to answer, and I am hoping if I can get pointed in the correct direction.

The question asks
"What is the difference between Frequency Responce of a system H(jw) and the Fourier Transform of a signal X(jw)?"

It would be great if someone could point me in the right direction with this one. I have been thinking about it for a bit and have checked through my notes, but just can't seem to find anything.

Aagin, thanks.

Sean
 
Physics news on Phys.org
  • #2
  • #3
Hey,

Thanks for your help :)

Sean.
 

FAQ: Fourier Transform: Frequency Response vs Signal X

What is the Fourier Transform?

The Fourier Transform is a mathematical tool used to decompose a signal into its individual frequency components. It converts a signal from its original time domain representation into the frequency domain, where the amplitude and phase of each frequency component can be analyzed.

What is the difference between Frequency Response and Signal X?

Frequency Response refers to the output of a system when a specific input signal is applied. It is a measure of how a system responds to different frequencies. On the other hand, Signal X is the specific input signal used to analyze the frequency response of a system.

How is Frequency Response related to Signal X in the Fourier Transform?

In the Fourier Transform, the frequency response of a system is obtained by taking the Fourier Transform of the impulse response of the system. The impulse response is the output of the system when an impulse signal (represented by the Dirac delta function) is applied as the input. Signal X can be any input signal, but the impulse response is often used for analysis because it contains information about the system's behavior for all frequencies.

What is the significance of the Frequency Response in signal processing?

The Frequency Response is an important tool in signal processing as it allows us to understand how a system responds to different frequency components. It is used to design filters, equalizers, and other signal processing systems to achieve desired frequency characteristics. It also helps in identifying and removing unwanted frequency components from a signal.

Are there any limitations to using the Fourier Transform for frequency analysis?

While the Fourier Transform is a powerful tool, it does have limitations in certain cases. It assumes that the signal is periodic and infinite, which may not always be the case. Also, the Fourier Transform cannot capture sudden changes or discontinuities in a signal. In such cases, other techniques such as the Short-time Fourier Transform or Wavelet Transform may be more suitable.

Similar threads

Question regarding Fourier Transform duality
Replies
2
Views
2K
Question about Fourier Series/Transform
Replies
2
Views
2K
Simple Fourier transform problem
Replies
3
Views
1K
Engineering I/Q of Signals and Hilbert Transform
Replies
1
Views
1K
Help with DC in fourier transform please
Replies
1
Views
1K
Mathematically solving fourier transform
Replies
1
Views
2K
Convolution - Fourier Transform
Replies
6
Views
2K
Engineering Fourier Transform: best window to represent function
Replies
3
Views
2K
I New frequency generation in AM signal
2
Replies
47
Views
3K
Inverse Fourier Transform and Power Signals
Replies
1
Views
3K

Hot Threads

Recent Insights

Back
Top