Contents
Can a Fourier transform be applied to a discrete signal?
Continuous-time Fourier Transform (CTFT) We can apply Fourier series analysis to a non-periodic signal and the spectrum will now have a continuous distribution instead of the discrete one we get for periodic signals. This idea of extending the period which results in this change is our segway into the concept of Fourier transform.
Is the Fourier transform of an EKG periodic?
Fourier series discussions however always assume that the signal under our microscope is periodic. But a majority of signals we encounter in signal processing are not periodic. Even those that we think are periodic, such as an EKG which looks periodic, are not really so. Each period is slightly different.
What are the formulas for the Fourier transform?
The respective formulas are (a) the Fourier series integral and (b) the DFT summation. Its similarities to the original transform, S (f), and its relative computational ease are often the motivation for computing a DFT sequence.
Why is the basis set for Fourier analysis discrete?
Because the basis set for Fourier analysis is discrete, the spectrums computed are also discrete. Fourier series discussions however always assume that the signal under our microscope is periodic. But a majority of signals we encounter in signal processing are not periodic.
How is the Fourier transform of a pulse train?
Take a look at signal in Fig. 4.2. In the first figure we show a pulse train and its CTFS in (a), (b) and (c) as we push the signal period out. Note that as the pulses move further apart, the harmonics begin to move closer together, i.e. there is more of them in each lobe.
Can a Fourier transform tell you the amplitude of a superposition?
The answer is clear: The Fourier transform / spectrum of frequencies does not give you any information about the amplitude of the superposition. Side note: At the same time keep into mind that the first example is the buttom line or callibration of the second example.