FFT? Digital Filter? Problem Exactly Defined

In summary, the conversation is about applying a lowpass filter to a measured signal in order to smooth it. The signal is available as measured data and needs to be applied in C or C++. The filter frequency is known and the signal has a constant delta t. The conversation also mentions converting the signal using a kernel, such as Butterworth, and calculating the coefficients for this conversion. Finally, the conversation asks for recommendations for a free C/C++ library that can help with this problem. The person later mentions finding a useful website for solving this issue.
  • #1
jensel
22
0
Hello,

Please help me with the following problem.

Given a measured signal which has to be smoothed. A lowpass filter has to be applied. The signal is available as measured data (a data file on the hard disk, numerical, not real-time) ( it has to be applied in C or C++). The filter frequency where "the cut-off" should apply is well-known. It is a real signal and has constant delta t.
I have no serious background in frequency data analysis so I will order my questions in a way of most urgency (sorry if one of the points is "easy to see" or wrong):

- if the signal is given as a series f(n), the converted signal is (depending from the order of the filter)
f_filtered(n)=f(n-k)*a_(-k)+f(n-k+1)*a_(-k+1)+...+f(n)*a_0+...+f(n+k)*a_(k+1)
under the condition that we have a kernel in the integration which is, let us say Butterworth (as far I understand the problem).
If this is right, how are the coefficients calculated? (for example with Matlab or in a different way)
- which free C/C++ library can be included to be more flexible to exactly solve this problem (it is not needed to be the universal library with all sorts of filtering - easy to use is priority)

Thanks a lot for helping me with this issue.


Jens
 
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  • #2
Hi,

Problem seems to be solved. I found this brilliant website (rest in peace Tony, you genius, you helped me a lot!):
http://www-users.cs.york.ac.uk/~fisher/mkfilter/

So great...


Jens
 

FAQ: FFT? Digital Filter? Problem Exactly Defined

1. What is FFT and how does it work?

FFT, or Fast Fourier Transform, is a mathematical algorithm used for efficiently calculating the discrete Fourier transform of a sequence. It breaks down a complex signal into its individual frequency components, allowing for analysis and filtering. It works by dividing the original signal into smaller segments, performing the Fourier transform on each segment, and then combining the results.

2. How is FFT used in digital filters?

FFT is used in digital filters to analyze and manipulate signals in the frequency domain. By identifying and isolating certain frequency components, digital filters can be used to remove unwanted noise or distortions from a signal. FFT is also used in designing and implementing different types of digital filters, such as low-pass, high-pass, and band-pass filters.

3. Can FFT be used for any type of signal?

Yes, FFT can be used for any type of signal, including audio, video, and even images. It is commonly used in signal processing applications, such as audio and video editing software, as well as in scientific and engineering fields for analyzing and filtering data.

4. What is the problem exactly defined in FFT and digital filter applications?

The problem that is exactly defined in FFT and digital filter applications is the need to accurately analyze and manipulate signals in the frequency domain. This requires precise mathematical algorithms and techniques, such as the FFT, to efficiently calculate and manipulate the discrete Fourier transform of a signal.

5. How does FFT compare to other methods of calculating the Fourier transform?

FFT is significantly faster and more efficient than other methods of calculating the Fourier transform, such as the discrete cosine transform or the discrete sine transform. This is because FFT takes advantage of symmetry and repeating patterns in the signal, resulting in a much faster calculation time. It is also more accurate and less prone to errors compared to other methods.

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