How is calculated the determinant of a matrix containing a fourier transform?

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Erkan 2025-7-8

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评论： Erkan 2025-7-9

Hi everyone. Let's assume that there are two paired differential equations as shown in equations 1 and 2 and that these equations are solved, that is, the values of A and B are known. However, to find the behavior of

and

in the frequency domain, the time derivatives of these equations are taken by taking the Fourier transform to obtain equations 3 and 4. Then, when the linear equation system is formed using equations 3 and 4, how is jw calculated when finding the determinant of the coefficient matrix of the system?

Sample number: N=1024 and Sample frequency: Fs=4kHz

(1)

(2)

(3)

(4)

(5)

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Torsten 2025-7-8

编辑：Torsten 2025-7-8

I thought you want to reconstruct F_A(omega) and F_B(omega) given A(omega) and B(omega). So why do you need a determinant to do this ? You can simply solve equation (3) for F_A(omega) and equation (4) for F_B(omega) (after computing the Fourier Transforms of A(t) and B(t)).

Erkan 2025-7-8

What I want to learn is how to calculate jw? w=2*pi*Fs/1024*(0:Fs/2)?

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采纳的回答

Matt J 2025-7-8

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https://ww2.mathworks.cn/matlabcentral/answers/2178320-how-is-calculated-the-determinant-of-a-matrix-containing-a-fourier-transform#answer_1567702

编辑：Matt J 2025-7-8

在 MATLAB Online 中打开

N=1024; Fs=4000;
f=(0:(N-1-ceil((N-1)/2)))/N*Fs;
jw = 1j*2*pi*f;
determinant =  (jw-x2).*y1 - (jw-x1).*y2  ;

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Matt J 2025-7-9

编辑：Matt J 2025-7-9

在 MATLAB Online 中打开

The general formula for the (two-sided) discrete frequency axis is,

NormalizedAxis = -ceil((N-1)/2) : +floor((N-1)/2);
deltaOmega=2*pi*Fs/N; %frequency sample spacing
w=deltaOmega*NormalizedAxis;

Erkan 2025-7-9

ok. Thank you very much

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Signal Processing Signal Processing Toolbox Transforms, Correlation, and Modeling Transforms Discrete Fourier and Cosine Transforms

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