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Is it possible to have a negative frequency?
If frequency is defined as an absolute number then there can be no negative frequencies, but if it is a real number negative frequencies can exist. You do need two signals to distinguish between positive and negative frequencies, the same as you need two numbers to define a complex number.
Why negative frequency is used in Fourier transform?
Negative frequency doesn’t make much sense for sinusoids, but the Fourier transform doesn’t break up a signal into sinusoids, it breaks it up into complex exponentials. The meaning of negative frequencies is just mathematical(not physical) similarly to the imaginary part of a complex signal.
Why is there negative frequency in Fourier transform?
But since any real signal is made of lots of sinusoids then in each one there is a pair of opposite sign frequencies of the same magnitude and voila you have both positive and negative spectral (i.e., frequencies) content.
Which is the correct formula for DTFT and DFT?
The DTFT formula is X(!) = P1 n=1 x[n]e. |!n whereas the DFT analysis formula is X[k] = PN 1 n=0 x[n]e |. 2ˇ N kn : If x[n]is a L-point signal, i.e., it is nonzero only for n = 0;1;:::;L 1, then the DTFT fisimpliesfl to X(!) = PL 1 n=0 x[n]e |!n : Comparing these two formulas leads to the following conclusion.
Why is DTFT not suitable for DSP applications?
Discrete Fourier Transform (DFT) Recall the DTFT: X(ω) = X∞ n=−∞ x(n)e−jωn. DTFT is not suitable for DSP applications because •In DSP, we are able to compute the spectrum only at specific discrete values of ω, •Any signal in any DSP application can be measured only in a finite number of points. A finite signal measured at N points: x(n) =
Is the DFT spectrum periodic with period N?
the DFT spectrum is periodic with period N (which is expected, since the DTFT spectrum is periodic as well, but with period 2π). Example: DFT of a rectangular pulse: x(n) = ˆ 1, 0 ≤n ≤(N −1), 0, otherwise. X(k) = NX−1 n=0 e−j2πkn N = Nδ(k) =⇒ the rectangular pulse is “interpreted” by the DFT as a spectral line at frequency ω = 0.