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Results tagged with dft
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user 41674
The Discrete Fourier Transform (DFT) is a mapping between a finite set of discrete points in a (primal) domain (time, space) and the dual frequency domain. DFT requires an input sequence which is discrete, such as a sampling from an analogue audio signal.
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What is the correct length for obtaining a true linear convolution from DFT?
Suppose, one does not want to do zero padding in DFT to obtain linear convolution.
b) Secondly, if we wish to do true linear convolution via DFT, should we use zero padding up to length(M)+length(N)-1. … This is a figure from a PhD thesis obtainable from ResearchGate pg 18, why does it say if the length of DFT >length(M)+length(N)-1, then results are valid. …
- 666
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Indexing in DFT (from an old paper)
There is a nice paper on explaining DFT from the 1960s in IEEE A guided tour of the fast Fourier transform. … The author uses the following definitions of DFT
DFT
$$
X(j)=\sum_{k=0}^{N-1} x(k) \exp \left(-i 2 \pi\left(\frac{j}{N}\right) k\right)
$$
Inverse
$$
x(k)=\frac{1}{N} \sum_{j=0}^{N-1} X(j) \exp \left(i …
- 666
3
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2
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492
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Multiplying the imaginary part of DFT with a linear ramp to get a derivative
I am trying to understand the statement in a relatively old publication from 1970s, when Fourier transforms found applications in chemical analysis. The author quotes the derivative theorem citing Bra …
- 666
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Definition of the DFT / FFT Bin Size
Cooley & Tukey are the key persons who made Discrete Fourier Transform (DFT) possible by computers for lowly mortals like us, otherwise it was an elitist subject among the mathematicians. …
- 666
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Constraints on choosing the frequency axis when Fourier transforming non-uniformly sampled d...
The uniform DFT will convert a sequence of $N$ numbers $x[n]$, where $n=0,1, \ldots, N-1$, into another sequence of $N$ complex numbers $X[k]$, where $k=0,1, \ldots, N-1$. … I cannot find selection of the frequency scale in nonuniform DFT discussed in detail anywhere. …
- 666
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Why Is the Total Time Equal to $ N \cdot {T}_{s} $ and Not $ \left( N - 1 \right) \cdot {T}_...
In the definitions of the DFT
DFT
$$
X(j)=\sum_{k=0}^{N-1} x(k) \exp \left(-i 2 \pi\left(\frac{j}{N}\right) k\right)
$$
Let us say, if we have $10$ points, $N=10$, each sampled at $0.2$ seconds, why is …
- 666
4
votes
4
answers
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Interpreting N in DFT as the Number of Points vs. Number of Intervals
The "N" is DFT is understood to be the number of data points in a given sequence or in other words the length of the sequence. … We recently have had discussions here Indexing in DFT (from an old paper) and someone's old question How do I measure the time duration of a finite-length discrete sequence?. …
- 666
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In the context of DFT, Where Does the Nyquist Frequency Sample Belong In a Double Sided Freq...
If we have an even number of data points $N$, after DFT in MATLAB, the output has the order:
$$(\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)$$
For real signals … \frac{N}{2}, \ldots,-1,0,1, \ldots, \frac{N}{2}-1
$$
Alternatively,
$$
\text { If } N \text { is even, } \quad k \text { takes: } -\frac{N}{2}-1, \ldots,-1,0,1, \ldots, \frac{N}{2}$$
where $k$ is the DFT …
- 666