Contents
Why discrete Fourier transform is periodic?
The term discrete-time refers to the fact that the transform operates on discrete data, often samples whose interval has units of time. From uniformly spaced samples it produces a function of frequency that is a periodic summation of the continuous Fourier transform of the original continuous function.
Can we use Fourier series for non periodic signal also?
The Fourier series for a non-periodic function will not converge at every point but will still converge in the sense of L2. Also, Fourier series are not meant to be defined on the whole line, they are indeed meant to be defined on intervals.
Is the DFT Fourier transform a periodic transform?
Periodic Nature of the DFT Unlike the other three Fourier Transforms, the DFT views both the time domain and the frequency domain as periodic. This can be confusing and inconvenient since most of the signals used in DSP are not periodic. Nevertheless, if you want to use the DFT, you must conform with the DFT’s view of the world.
Why are Fourier coefficients periodic in discrete time?
While for discrete-time signals, the model is based on the δ ( t) function, for which the changing is infinitely sharp and rapid, thus periodicity becomes possible in this case. The spectrum of any discrete signal has a period of 2*pi. Thus, the fourier coefficients occur periodically at interval of 2*pi.
When does the imaginary part of a Fourier transform vanish?
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. For an odd function, theFourier transform is purely imaginary. For a general real function, the Fourier transform willhave both real and imaginary parts. We can write
Why is the result of a DTFT periodic?
The result of a DTFT is periodic, because any discrete-time signal has a continuous spectrum. This can be e.g. explained by the following: Let x ( t) be a time-continuous signal.