Contents
What is discrete Fourier transform sample frequencies?
In mathematics, the discrete Fourier transform (DFT) converts a finite sequence of equally-spaced samples of a function into a same-length sequence of equally-spaced samples of the discrete-time Fourier transform (DTFT), which is a complex-valued function of frequency.
What is frequency spectrum in Fourier transform?
An example is the Fourier transform, which converts a time function into a sum or integral of sine waves of different frequencies, each of which represents a frequency component. The “spectrum” of frequency components is the frequency-domain representation of the signal.
What is the frequency shift property?
Modulation means multiplying a signal with a complex exponential. In the Fourier Transform, modulating a signal in time domain corresponds to shifting it in the frequency domain.
Can a Fourier transform be seen as an expansion?
Thank you for your help. Up to a factor of 2 π the Fourier transformation can be seen as an expansion in terms of e i ω t. Clearly for e i ω 0 t there is only one component in the expansion. In a discrete expansion this would mean that we have a Kronecker delta δ ω 0 ω as component.
Is the Kronecker delta a generalized function in discrete expansion?
Clearly for e i ω 0 t there is only one component in the expansion. In a discrete expansion this would mean that we have a Kronecker delta δ ω 0 ω as component. But because we are doing a continuous transformation this becomes the Dirac delta. This (generalized) function will filter out that single component e i ω 0 t.
Which is the generalized function in a discrete expansion?
In a discrete expansion this would mean that we have a Kronecker delta δ ω 0 ω as component. But because we are doing a continuous transformation this becomes the Dirac delta. This (generalized) function will filter out that single component e i ω 0 t.