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Why do we do the zero padding of sequence x n in DFT?
A common tool in frequency analysis of sampled signals is to use zero-padding to increase the frequency resolution of the discrete Fourier transform (DFT). By appending artificial zeros to the signal, we obtain a denser frequency grid when applying the DFT. but apart from this the signal is unknown.
What does zero padding do FFT?
Zero-padding a Fast Fourier Transform (FFT) can increase the resolution of the frequency domain results (see FFT Zero Padding). This is useful when you are looking to determine something like a dominant frequency over a narrow band with limited data.
What is leakage in DSP?
Leakage, more explicitly called spectral leakage, is a smearing of power across a frequency spectrum that occurs when the signal being measured is not periodic in the sample interval.
What does the length n of the DFT mean?
The length N of the DFT is the number of frequency points that will result in the DFT output. Zero padding will result in more frequency samples, however this does not increase frequency resolution, it just interpolates samples in the DTFT.
How does zero padding affect the frequency resolution?
Zero padding will result in more frequency samples, however this does not increase frequency resolution, it just interpolates samples in the DTFT. The frequency resolution is given by 1 / T where T is the time length of your data (regardless of sampling rate).
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.