Topmusicanswers
The DFT is the discrete-time equivalent of the (continuous-time) Fourier transforms. As with the discrete Fourier series, the DFT produces a set of coefficients, which are sampled values of the frequency spectrum at regular intervals. The number of samples obtained depends on the number of samples in the time sequence.
- Why is Fourier transform continuous?
- What is continuous time Fourier series?
- What is the difference between discrete and continuous Fourier transform?
- Is a Fourier series discrete or continuous?
Why is Fourier transform continuous?
The Fourier transform of an integrable function is continuous and the restriction of this function to any set is defined. ... For n = 1 and 1 < p < ∞, if one takes ER = (−R, R), then fR converges to f in Lp as R tends to infinity, by the boundedness of the Hilbert transform.
What is continuous time Fourier series?
The continuous-time Fourier series expresses a periodic signal as a lin- ear combination of harmonically related complex exponentials. Alternatively, it can be expressed in the form of a linear combination of sines and cosines or sinusoids of different phase angles.
What is the difference between discrete and continuous Fourier transform?
The difference is pretty quickly explained: the CTFT is for continuous-time signals, i.e., for functions x(t) with a continuous variable t∈R, whereas the DTFT is for discrete-time signals, i.e., for sequences x[n] with n∈Z.
Is a Fourier series discrete or continuous?
The Fourier series represents periodic, continuous-time signals as a weighted sum of continuous-time sinusoids. It is widely used to analyze and synthesize periodic signals.
