Howtosignalprocessing
Yes, for time-limited functions it is possible to obtain the Fourier series coefficients by sampling the Fourier transform.
- Is Fourier transform and Fourier series Same?
- What is sampled Fourier transform?
- What is the Fourier transform of sampling function?
Is Fourier transform and Fourier series Same?
The Fourier transform is also known as a generalisation of the Fourier series. The term can also be applied to both the mathematical function used and the frequency domain representation. The Fourier transform enables the Fourier series to extend to non-periodic functions.
What is sampled Fourier transform?
The above equation relates the Fourier Transform of the sampled signal to that of the original signal. As seen clearly, Xs(ω) is obtained by replicating X(ω) infinite number of times in frequency domain. This is often quoted as Sampling in time domain replicates the spectrum in frequency domain.
What is the Fourier transform of sampling function?
The Fourier transform of the sampled signal fs=f(t)∞∑−∞δ(t−kT)
