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Why is the DFT periodic?
In the frequency domain, the DFT is periodic because the time domain signal being analyzed is sampled. Recall that any periodic sequence cannot be uniquely represented for frequencies above fs/2 where fs is the sampling frequency of the sequence (also known as the nyquist frequency).
What makes a signal periodic?
A periodic signal is one that repeats the sequence of values exactly after a fixed length of time, known as the period. In mathematical terms a signal x(t) is periodic if there is a number T such that for all t Equation 10.10 holds.
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.
How does the DFT view the frequency spectrum as periodic?
The lower two figures show how the DFT views this frequency spectrum as being periodic. The key feature is that the frequency spectrum between 0 and 0.5 appears to have a mirror image of frequencies that run between 0 and -0.5. This mirror image of negative frequencies is slightly different for the magnitude and the phase signals.
Why do we need DFT when we already have DTFT?
We already have DTFT so why do we need DFT? Please don’t write DTFT is used for discrete, aperiodic signal which transfers in the frequency domain to periodic and continuous, but in DFT is discrete periodic transfer in discrete periodic, these things I already know.
How are the 128 points of the DFT connected?
Unfortunately, the DFT doesn’t see things this way. As shown in the lower figure, the DFT views these 128 points to be a single period of an infinitely long periodic signal. This means that the left side of the acquired signal is connected to the right side of a duplicate signal.