Questions tagged [fourier]
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346 questions
-3 votes
2 answers
162 views
Orthogonal signal of u(t) and how they are related in the s domain
I am disatisfied with why we have to pick cosine and sine when doing Fourier analysis of a signal.So I decided that one of my orthogonal signals will be $u(t)$.However what is the orthogonal signal of ...
- 135
3 votes
1 answer
285 views
Time reversal flips the Fourier coefficients
Given a periodic signal $x(t)$, with period $T = \frac{2\pi}{\omega_0}$ so that $$ x(t+T) = x(t) \qquad \qquad \forall t \in \mathbb{R} $$ $$ x(t) = \sum\limits_{k=-\infty}^{\infty} c_k \, e^{j k \...
- 187
1 vote
1 answer
74 views
what is the link between the spatial frequency in vision processing and the frequencies we see in signal processing?
(sorry, I am a bit confused), but what is the meaning behind the 'spatial frequencies'. In signal processing frequencies are expressed in Hertz, and in vision science in cycle per degree (cpd). Why ...
- 13
0 votes
4 answers
121 views
Can frequency $f$ be negative, or is it always a non-negative quantity like the mass of an object? [duplicate]
My question is: is frequency more like time (where time can be positive or negative), or more like mass (always non-negative in classical mechanics)? I know that in Fourier analysis, people talk about ...
1 vote
1 answer
75 views
Fourier Transform of a squared sinc function in R^d
Is it possible to find the Fourier Transform of $\textrm{sinc}^{2}$ in $\mathbb{R}^{\textrm{d}}$ if we use the distribution sense?
0 votes
0 answers
81 views
How to calculate the phase response?
Good afternoon. I was advised to go here after asking a similar question on Stackoverflow (https://stackoverflow.com/posts/79494905/edit). I want to write a code to output experimental frequency ...
0 votes
1 answer
273 views
FFT audio and get back original audio with IFFT
Let's say I have an digital audio signal that is very short (only a few seconds). This signal is kind of simple (can't come up with a good example, but something like mobile phone notification, or ...
0 votes
1 answer
56 views
fftshift when applying filters in frequency domain
As a part of a signal processing course, I was asked if the use of the fftshift operator necessary when applying filters in the frequency? We've been told that it is not necessery but I can't ...
- 11
-2 votes
1 answer
67 views
Can I apply the modulation property of Fourier Transform on sine?
Modulation property of Fourier Transform: \begin{align} x(t) \cos(\omega_0 t) \longrightarrow \frac{1}{2} \left[ X(\omega - \omega_0) + X(\omega + \omega_0) \right] \end{align} Can I not apply it if ...
2 votes
1 answer
118 views
Why does the Fourier integral $\frac{1}{2 \pi} \int_{-\infty}^{\infty} X(\omega) d \omega$ for a causal exponential signal yield 1 instead of 0.5?
I'm working on a problem where I am asked to evaluate the Fourier integral: $$ \frac{1}{2 \pi} \int_{-\infty}^{\infty} X(\omega) d \omega $$ where $X(\omega)$ is the Fourier transform of the signal $x(...
- 35
0 votes
0 answers
47 views
Gibbs phenomenon in sensor data
I’ve been thinking about the Gibbs phenomenon lately, and I wonder if it is more of a mathematical nuisance than a real life issue. Gibbs describes the approximation error of a discontinuous function. ...
- 413
1 vote
0 answers
79 views
Fourier uncertainty principle
When working on DSP of audio signals, I personnaly "experience" the Fourier uncertainty principle in this way: When doing a STFT / a spectrogram, you have to choose a tradeoff between time-...
- 549
0 votes
1 answer
64 views
Discrete-Fourier transform of $$u[-n+2]$$
I'm Trying to Find the fourier transform in discrete time for $$u[-n+2]$$ . My steps : Time-Reversal Property : $$ u[(-n+2)] \{\omega\} = u[-(-n+2)] \{-\omega\} = u[n-2] \{-\omega\} $$ Time-Shifting ...
- 75
2 votes
2 answers
209 views
How do you interpret the sign (positive, negative or zero) of the phase spectrum?
How do you interpret the sign (positive, negative or zero) of the phase spectrum of: 1)a digital filter (the phase spectrum of its frequency response aka phase response of the filter). 2)a signal in ...
0 votes
1 answer
64 views
Morlet wavelet convolution
I use a simple formula (without normalization) from Mike Cohen's "Analzying neural time series data" book. \begin{align} \psi \left( t \right) &= e^{-\frac{t^2}{2 s^2}} \cdot e^{2 \...
- 13