New answers tagged dft
0
votes
Can time aliasing cause peaks?
Here I answer the question, "Can time aliasing in convolution cause peaks?". It showed up in a recent question, Random Peak at the end Impulse Response, where users suggested time aliasing ...
- 8,141
0
votes
What is the reason my DFT of a convolution of signals with disjoint spectrums is not zero everywhere?
Disjoint spectra do produce a zero result, but the convolution is circular. However, I encourage against thinking that FFT-based and "direct" (np.convolve)...
- 8,141
2
votes
What is the reason my DFT of a convolution of signals with disjoint spectrums is not zero everywhere?
In short:
As corrected by @Matt, the DFT pair convolution-product refers to a circular convolution, not to a linear one.
For Fourier transform, the property convolution FT is the product of individual ...
- 375
0
votes
Finding maximum using DFT
The maximum of $x[n]$, where $X[k] = \texttt{DFT}\{x\}$, is
$$
\begin{align}
& \texttt{max}\{x\} =
\frac{1}{N}\underset{s\in[0, N-1]}{\texttt{max}}\left\{
\sum_{l=0}^{N-1} (X[k] \cdot e^{-...
- 8,141
0
votes
Can we do down sampling by taking fft, omitting samples on the ends of the spectrum, and then taking inverse fft?
Suppose that the the maximum frequency content of the signal is low enough that we do not have any concern about aliasing. ... Can we take the FFT of signal, then omit samples from 1023-th index up to ...
- 8,141
1
vote
The difference between DFT and DFS
This answer documents an important exchange in the periodicity and DFT-DFS debate, for "meta reasons". Comments are from under the accepted answer, with my votes removed:
- 8,141
2
votes
DFT of a sine, closed form solution
The length $N$ DFT of the discrete-time sinusoid
$$x[n]=\cos(\omega_0n+\phi),\qquad n=0,1,\ldots,N-1\tag{1}$$
is given by
$$X[k]=\sum_{n=0}^{N-1}\cos(\omega_0n+\phi)e^{-j2\pi nk/N},\qquad k=0,1,\ldots,...
- 85.8k
0
votes
Is it true that the “DFT can only deal with causal signals"?
I cannot speak for the source, but with much due clarification, it's correct in an important sense: "DFT is a sampling of DTFT" assumes we're taking $\texttt{DFT}$ of $x[n]$, where $x[n] \...
- 8,141
4
votes
Accepted
How does the effect of windowing change with the phase of the input signal?
Summary
The problem is caused by detrend='constant' in the call to periodogram, which subtracts the mean of the input before ...
- 8,141
-2
votes
DFT of a sine, closed form solution
Planning
We seek something like
$$
\texttt{DFT}\{x[n]\} = \texttt{DFT}\{\cos[2\pi f_0 n + \phi]\}
$$
To tackle this, I begin by reformulating the problem in terms of a time shift, which will be more ...
- 8,141
1
vote
The difference between DFT and DFS
So @OverLordDragon found a way to see one of the old comp.dsp discussions about this and reminded me of something.
So the Discrete Fourier Transform (DFT) is being defined as:
$$ X[k] = \begin{cases}
\...
- 18.9k
0
votes
The difference between DFT and DFS
Conceptually, DFS $\neq$ DFT.
DFS is, by definition, the Fourier transform of discrete-time, infinite-length, and periodic signals, which are denoted as $\tilde{x}[n]$. Therefore, DFS is given by
$$
\...
- 293
4
votes
Accepted
Gaussian filter: Plotting DTFT and DFT (by hand) from the continuous-time impulsive response
Before anything, let me just rewrite your TF from linear frequency ($f$, in Hertz) to angular frequency ($\Omega = 2\pi f$, in rad/sec). The notation $\Omega$ is usually adopted in the field of DSP to ...
- 293
2
votes
Accepted
FFT of complex signal (I/Q), what do the bins N/2..N-1 represent?
It may be useful to go through an example of how the complex-valued I/Q data is produced from real-valued signals and then explore how that relates to DFT bins.
Down-conversion example
In ...
- 244
0
votes
FFT of complex signal (I/Q), what do the bins N/2..N-1 represent?
For the DFT of a real-valued signal the second half of the bins is just conjugates of the first half
Correct
and can/should be ignored.
Wrong. They need to be included in any calculation (inverse ...
- 39.2k
0
votes
Is 2D circular cross-correlation with FFT done as described in this source?
OP's approach follows three basic premises:
Output at i, j corresponds to similarity of kernel with input, with kernel centered at ...
- 8,141
5
votes
Is 2D circular cross-correlation with FFT done as described in this source?
For the question's approach of shifting the h input image spatially using ifftshift before frequency-domain complex-conjugation, ...
- 13.2k
1
vote
Accepted
2D FFT Cross-Correlation in Python
I've replicated scipy.signal.correlate2d for all mode - 'full', ...
- 8,141
0
votes
Why are the negative frequencies of the DFT symmetrically reflected at the nyquist to the positive frequencies?
I wrote my own DFT in C++ (plotted in python) and tested 7.5*cos(5*2πt)+2.5*cos(8*2πt) with a sample rate of 1000Hz and a 2 second duration. t is then the array([0.,...
- 11
6
votes
How does the effect of windowing change with the phase of the input signal?
What's going on?
I think the main issue is the use of detrend='constant' in the calls to signal.periodogram. If I change that to ...
- 244
1
vote
How to measure aliasing?
Where it matters to explicitly account for aliasing, my approach (that for context I have often used in the area of wireless communications) is using the correlation coefficient with a reference copy ...
- 45.8k
0
votes
Use of DFT for Decimating Channelizers
This is only a partial answer focused on the title, illustrating the failure of a DFT channelizer in decimation, per one reasonable interpretation of "decimation".
The magnitude of frequency ...
- 8,141
5
votes
How to measure aliasing?
Note: it's "Work In Progress", I intend to address some limitations, including "time aliasing". Interested hot visitors may wish to "Follow" the answer.
Motivating the ...
- 8,141
2
votes
Accepted
Use of DFT for Decimating Channelizers
As explained in detail at this post, an N-point DFT is functionally a bank of $N$ unity gain coefficient filters ("moving average" filters), each centered on $f_s/N$ where $f_s$ is the ...
- 45.8k
Top 50 recent answers are included