Truncated Fourier series analysis in Matlab

In summary, a Matlab function should be written to accept a finite set of Fourier series coefficients, the fundamental period T of the signal, and a vector t representing the times for reconstruction. The output should be a vector x of length equal to t, containing values of xn at the times indicated by t. The code provided so far uses the imaginary operator and 3.14159 for pi.
  • #1
d2009
2
0
a) Write a Matlab function, which accepts the following inputs

-a finite set of Fourier series coefficients

-the fundamental period T of the signal to be reconstructed

-a vector t representing the times for which the signal will be reconstructed.

This function should produce an output x[t][/n]( should be a vector x with length equal to the length of t containing values of xn at the times indicated by t.

this is the code i have come up with so far.

function fourier1=f(a,T,t)
fourier1=zeros(length(a),1);
for n=1:length(a)
fourier1(n)=(a(n)*exp((i*(2*pi/T)*n*t)));
end;
 
Last edited:
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  • #2
What language is that? Unless the language recognizes i as the imaginary operator, and "pi" as 3.14159, it won't work.
 

Related to Truncated Fourier series analysis in Matlab

1. What is "Truncated Fourier series analysis"?

Truncated Fourier series analysis is a mathematical technique used to approximate a periodic function with a finite number of sine and cosine terms. It involves decomposing a function into a sum of sinusoidal functions with different frequencies and amplitudes.

2. How is "Truncated Fourier series analysis" used in Matlab?

In Matlab, the Fourier series analysis is performed using the "fft" function. This function computes the discrete Fourier transform of a given sequence of data points. The "ifft" function can then be used to reconstruct the original signal from the Fourier coefficients.

3. What is the significance of truncating the Fourier series?

Truncating the Fourier series means using a finite number of terms to approximate an infinite series. This is important because it allows us to simplify complex functions and make calculations more manageable. Additionally, truncating the series can help reduce computational time and resources.

4. How do I determine the number of terms to use in a truncated Fourier series?

The number of terms to use in a truncated Fourier series depends on the desired level of accuracy. Generally, the more terms used, the more accurate the approximation will be. However, using too many terms can also lead to overfitting. It is important to consider the trade-off between accuracy and computational complexity.

5. Can "Truncated Fourier series analysis" be applied to non-periodic functions?

No, "Truncated Fourier series analysis" is only applicable to periodic functions. Non-periodic functions do not have a repeating pattern and therefore cannot be decomposed into a sum of sinusoidal functions. However, there are other mathematical techniques that can be used to analyze non-periodic functions.

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