# Questions tagged [fourier-transform]

The Fourier transform is a mathematical operation that decomposes a function into its constituent frequencies, known as a frequency spectrum.

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### Removing values from FFT result same as filtering?

I don't quite understand why the textbooks say it is impossible to implement an ideal low pass filter. If I was to take the FFT of a discrete signal x[n], with Matlab's fft function I'd be returned ...
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### Difference between Convolution and multiplication [duplicate]

I read that multiplication is convolution in frequency domain. I also understand that convolution is just polynomial multiplication. Can somebody explain what are the advantages of doing convolution ...
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### Compressive Sensing Incoherence Principle

As people acquainted with Compressive Sensing would know, incoherence and sparsity are two main principles. I've been reading about compressive sampling and developed an interest into the topic. What ...
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### Determining the period of a discontinuous function

I'm new to the field of DSP. I'm trying to determine the period and shift of the function. I've tried using FFT, but haven't had much luck. Seems like it should be simple. Signal (pastebin of ...
724 views

### Chop out frequencies outside human hearing range

I have a bunch of audio files all sampled at 44100 Hz sample frequency. I am trying to remove all the frequencies which are outside the human hearing range (I use the following as reference: Frequency ...
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### Convolution in frequency domain

Simple math question. The convolution theorem states that multiplication in time domain is equal to convolution in frequency domain and vice versa. There is a condition that the signal has to be ...
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### Can you decimate / downsample a signal in frequency domain just like you can interpolate / upsample it?

To interpolate a signal I can just zero pad it in the frequency domain. If I want to decimate the signal, can I just discard some part of the frequency domain? So in MATLAB this works: ...
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### What features describe audio signals? (Besides frequency and amplitude)

I recorded sounds with a microphone and I try to distinguish them in my Java program. The frequency works quite good, but if I look at the fourier transforms it seems like there should be more ...
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### Fourier Decomposition

Hello everyone have a look at this video of Fourier Decomposition of an image(otherwise you can also refer the image which shows few plots of different extracted waves from an image) . We also know ...
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### Infinite extent of spectrum, but also in time in Oppenheim's Discrete Time Signal Processing?

In Oppenheim's Discrete Time Signal Processing there's on p. 323 no limited band in both time and frequency - wouldn't that violate the Heisenberg Principle?
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### Can realizations of a filtered Gaussian white noise process be represented as a Fourier transform?

Suppose we have a noise process $V(t)$ which is the result of passing Gaussian white noise through a filter with frequency response function $H(\omega)$. Can we represent realizations of this process ...
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### Hartley Transform vs Fourier Transform

Can you explain to me in what way Hartley Transform differs from Fourier Transform? Is it even used today or is it some mostly forgotten, obsolete archaic thing? Please don't use equations - I dont ...
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### Implementation of the constant Q transform + property questions

I'm reading up on fourier theory, especially the transforms. I implement the math as spectrograms in C++ to get a better understanding of what is going on. I've made an implementation of the short ...
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### Fourier descriptors: trying to classify objects

Describing my background: I have around 33 items labeled. For example, 3 pictures of the contour of a basil plant, 4 pictures of the contour of earphones, 7 of a mug, etcetera. I'm trying to ...
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### How to recover $f(t)$ from Fourier Transform of its absolute value $\mathcal{F}|f(t)|$?

Let the Fourier Transform of a real signal, $f(t)$, be $\mathcal{F}(\omega)$. And the FT of the absolute value of the same signal, $|f(t)|$, be $\mathcal{F}(u)$. Can $\mathcal{F}(w)$ be recovered ...
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### Testing discrete data for periodicity

I have some data which looks roughly periodic - is there a nice way to measure this? This is an example I'm working on and I'd like a metric that I will be able to just threshold to give a decision ...
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### Why do we need the power spectral density?

Since the power spectral density is just the squared of the fourier transform, why is it useful ? Can't I just replace every solution that requires the psd with the fourier transform ?
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### What is the time-integration property in the Fourier series analysis?

In the continuous Fourier series properties for a periodic continuous-time signal, we have time-integration property: $$\int_{-\infty}^t x(\alpha)d\alpha \leftrightarrow \frac{a_k}{jk\omega_0}$$ ...
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### Cross-correlation, sharp peak at 0?

First of all, I have to stress that I am not a professional of coding, no more than a professional of signal processing. I am a chemist that happen to be working on a project involving both. So in ...
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### Significance of modular arithmetic in DFT?

In what ways does modular arithmetic plays a part in DFT? Why is it a so integral part of DFT?
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### What is the role of complex exponential?

What is the role of complex exponential $e^{jθ}$ in Fourier Transform? Is it different in the continuous and in discrete time domain?
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### Fourier transform with periodicity at the harmonic frequency

Let's suppose I have a signal F(t) that is periodic, with two periodicities P1 and P2, with P1>P2. Suppose that I know the values of the two periodicities. Using the Fast Fourier transform I can show ...
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### Can I study continuous time Fourier Transform and treat the rest as special cases

Say I learned the theoretical result of continuous time Fourier transform. And I want to extends some results(say "convolution rule") to Lapace transform, Z transform, DTFT, DFT, Fourier sequence ...
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### Relationship Between Sampled Continuous and Discrete Time Signals

Consider the sketched system below. $x_c(t)$ is an arbitrary, continuous-time signal at the input and $s(t)$ is an impulse train, defined as $s(t)=\sum_{n=-\infty}^{\infty} \delta(t-nT)$, where T is ...
I have a question regarding an alternating pulse train signal, $p(t)$, and a system which looks like this: Immediately, I'm supposed to be able to extrapolate that $$P_t = P_1(t)-P_1(t-\Delta)$$ ...
The unit step signal defined as $$u[n]= \lbrace 1; n>=0; \\ \qquad0; n<0 \rbrace$$ has three possible solutions for its Fourier domain representation depending on the type of ...