What is the full Fourier transform?
Thus the full Fourier transform is As mentioned before, the spectrum plotted for an audio signal is usuallyf˜(?)2. Let’s see whatthis looks like. We’ll take?0=10 and?= 2. The function and the modulussquaredf˜(?) its Fourier transform are then:2of Figure 2.
What are Fourier series coefficients?
•The Fourier Series coefficients can be expressed in terms of magnitude and phase –Magnitude is independent of time (phase) shifts of x(t) –The magnitude squared of a given Fourier Series coefficient corresponds to the power present at the corresponding frequency
Is f(t) a real function?
For a real function f(t), the Fourier transform will usually not be real. Indeed, theimaginarypart of the Fourier transform of a real function is This is a Fourier sine transform. Thus the imaginary part vanishes only if the function has nosine components which happens if and only if the function is even.
Does a cat have a Fourier transform?
Fourier transform of a cat. The magnitude is concentrated near kx?ky?0, but maybe not asmuch as the panda, since that cat has smaller wavelength features. Phase still looks random. Now let’s Fourier transform back. Of course for the cat and panda we get back the orignalimage.
Continuous Time Signals (Part - II) - Fourier Transform