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Results tagged with fft
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user 41674
The fast Fourier transform is an efficient algorithm to compute the discrete Fourier transform (DFT) and its inverse.
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Correction of amplitude after zero padding for upsampling purposes
FFT_S=fft(Signal); % FFT of Signal of Interest
FFT_ZP=[FFT_S(1:length(t)/2,1); zeros(1000,1); FFT_S(length(t)/2+1:end,1)]; % Zero padding with 1000 zeros. … Qualitatively, in order to keep the amplitude the same, I found that if we double the sampling rate, the amplitude after inverse fft had to be multiplied by 2, if we triple the sampling rate by zero padding …
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Predicting the "amplitude" of a damped sine wave from FFT
For a sine wave, $A \sin(\omega_0 t)$, with an amplitude $A$, after FFT and calculating the magnitude spectrum we can get a single peak with a height also equal to $A$. This requires proper scaling. … Visually, the peak amplitude after FFT is the average amplitude of the damped sine wave in the time domain. …
- 666
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Definition of the DFT / FFT Bin Size
Your confusion is very much understandable because it took me a while to understand the frequency axis spacing issue. Finally after digging for years, I found that your question is answered by the the …
- 666
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Why Is the Total Time Equal to $ N \cdot {T}_{s} $ and Not $ \left( N - 1 \right) \cdot {T}_...
In the definitions of the DFT
DFT
$$
X(j)=\sum_{k=0}^{N-1} x(k) \exp \left(-i 2 \pi\left(\frac{j}{N}\right) k\right)
$$
Let us say, if we have $10$ points, $N=10$, each sampled at $0.2$ seconds, why i …
- 666
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Interpreting N in DFT as the Number of Points vs. Number of Intervals
The "N" is DFT is understood to be the number of data points in a given sequence or in other words the length of the sequence. We recently have had discussions here Indexing in DFT (from an old paper) …
- 666
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In the context of DFT, Where Does the Nyquist Frequency Sample Belong In a Double Sided Freq...
If we have an even number of data points $N$, after DFT in MATLAB, the output has the order:
$$(\text{DC}, f_1, f_2, \ldots, f_{N/2-1}, f_\text{Nyq}, -f_{N/2-1}, -f_{N/2-2}, \ldots, -f_1)$$
For real s …
- 666