Frequency Specturm and fourier transform

In summary, for those looking for a concise resource on the use of Fourier transforms with wave trains, "Arfken, Math Methods for Physicists (2nd ed.)" provides a 10-page summary and example. Additionally, "Merzbacher, QM, 2nd ed." introduces the topic in just 3 pages, making it a short and sweet option. However, prior knowledge of Fourier transforms is assumed.
  • #1
zwoodrow
34
0
Can someone recommend a good book or notes detailing the use of the Fourier transform with wave trains. Something short and sweet hopefully. thanks
 
Physics news on Phys.org
  • #2
In the future, please post these kinds of questions in the Science Book forum under Academic Guidance.

Arfken, Math Methods for Physicists (2nd ed.), summarizes Fourier transforms (FT's) and works an example on finite wave trains in just 10 pages. Books on quantum mechanics also treat this subject (assuming you already know something about the FT). Merzbacher, QM, 2nd ed., introduces the FT of wave packets in 3 pages (p. 17). You decide how sweet, but you can't get much shorter.
 

FAQ: Frequency Specturm and fourier transform

What is frequency spectrum?

Frequency spectrum refers to the representation of a signal in terms of its frequency components. It shows the amplitude of each frequency component in a signal, allowing us to analyze the signal's frequency characteristics.

What is the Fourier transform?

The Fourier transform is a mathematical tool used to convert a signal from its time domain representation to its frequency domain representation. It decomposes a signal into its individual frequency components, allowing us to analyze its frequency characteristics.

What is the relationship between frequency spectrum and Fourier transform?

Frequency spectrum and Fourier transform are closely related. The frequency spectrum is the visual representation of the Fourier transform, showing the amplitude of each frequency component in a signal. The Fourier transform is used to calculate the frequency spectrum of a signal.

Why is the Fourier transform important in signal processing?

The Fourier transform is important in signal processing because it allows us to analyze signals in the frequency domain, which can provide valuable information about a signal's characteristics. This information is useful in many applications such as filtering, noise reduction, and compression.

What is the difference between Fourier transform and inverse Fourier transform?

The Fourier transform converts a signal from its time domain representation to its frequency domain representation, while the inverse Fourier transform does the opposite and converts a signal from its frequency domain representation back to its time domain representation. Essentially, the Fourier transform analyzes a signal's frequency components, while the inverse Fourier transform reconstructs the signal using those frequency components.

Similar threads

Back
Top