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# 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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### How to generalise the Fourier transform?

The Fourier transform takes a signal and splits it into a series of sine and cosine waves. I am told that it's supposed to be possible to split a signal into some other set of functions. My question ...
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### How to calculate the gain in a bivariate fft in R?

In Statistica gain is defined as follows: Gain. The gain value is computed by dividing the cross-amplitude value by the spectrum density estimates for one of the two series in the analysis. ...
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### Solving a Convolution Problem of a 1D Signal

I'm finding in trouble trying to resolve this exercise. I have to calculate the convolution of this signal: $$y(t)=e^{-kt}u(t)\frac{\sin\left(\dfrac{{\pi}t}{10}\right)}{({\pi}t)}$$ where $u(t)$ is ...
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### Real-Time Human Pitch Detection

I'm trying to implement a singing game that will analise raw mic input and tell the player how good is he singing. That needs to be done in real-time. I've come across a lot of threads asking the ...
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### plotting phase of a signal adding delay

I'm trying to plot the phase of this signal $s(f)=A^2T^2sinc^2(Tf)e^{-(j\pi Tf)}$ How can I plot manually this signal?I have to follow some particular rules?I have problems with the delay. Edit ...
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### How to combine a rotation matrix and a stretch matrix into a single matrix for easy Fourier Transform

For full disclosure, this is related to homework. I have to find the Fourier Transform of a function that I've boiled down to the following. I have a function $f(x,y)$ that I can think of as another ...
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### What is the most lucid, intuitive explanation for the various FTs - CFT, DFT, DTFT and the Fourier Series?

Even after having studied these for quite sometime, I tend to forget (if I'm out of touch for a while) how they are related to each other and what each stands for (since they have such similar ...
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### Deriving 2-D discrete Fourier transforms

I have a problem in DFT. It was one of my past-year exam papers questions. Question: Let $F(u,v)$ be the 2-D Fourier transform of a 2-D continuous function $f(x,y)$. Derive in terms of $F(:,:)$ ...
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### Whats the optimal window function to use for analyzing real-time data samples?

Say you wanted to run a X point FFT on the last X audio samples that were played. The problem being, using a normal hann window function would place emphasis on the "middle" of the audio sample. ...
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### Harmonic Product Spectrum limitations in pitch detection

I've made a pitch detection algorithm using HPS and I'm facing a problem. I'm a beginner with signal processing and this site helped me before, so I though I should ask. For higher pitches ( ...
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### Choices of convention and notation for the Fourier transform?

The definitions of the Fourier transform and inverse Fourier transform I learned in college were $$F(j\omega) = \int_{-\infty}^{\infty} f(t) e^{-j\omega t}\ dt$$  f(t)=\frac{1}{2\pi}\int_{-\...
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### Using the Inverse Filter to Correct a Spatially Convolved Image (Deconvolution)

As part of a homework assignment, we are implementing the Inverse Filter. Degrade an image then recover with an Inverse Filter. I convolve the image in the spatial domain with a 5x5 box filter. I FFT ...
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### How to get coefficients for sine/cosine function from complex FFT?

I'm working on a control system that measures the movement of a vibrating robot arm. Because there is some deadtime, I need to look into the future of the somewhat noisy signal. My idea was to use the ...
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### What effect does a delay in the time domain have in the frequency domain?

If I have a signal that is time limited, say a sinusoid that only lasts for $T$ seconds, and I take the FFT of that signal, I see the frequency response. In the example this would be a spike at the ...
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### What is the physical significance of negative frequencies?

This has been one of the holes in my cheddar cheese block of understanding DSP, so what is the physical interpretation of having a negative frequency? If you have a physical tone at some frequency ...
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### Tips for improving pitch detection

I'm working on a simple web app that allows the user to tune his/her guitar. I'm a real beginner in signal processing, so please don't judge me too harshly if my question is inappropriate. So, I ...
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### RMS calculation in frequency domain after windowing

I can calculate RMS in frequency domain as derived from Parseval's Theorem. But what if I have applied a windowing function before doing the FFT (in my case a Hann window)?. Now the RMS values are ...
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### Am I handling offline FFT correctly?

I need some help clarifying FFTs and what they represent. I have a buffer containing compressed audio. Due to limitations, I can't handle the full uncompressed audio but can decompress small segments ...
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### Recognizing math functions within songs

I'm new to DSP, and just discovered this StackExchange, so apologies if this isn't the right place to post this question. Is there a resource that describes genres in a more mathematical terms? For ...
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### Complex conjugate and IFFT

I asked a question over on stack overflow. I'm having a slight problem however. As suggested by Paul R I am mirroring my lower $n/2$ bins into the upper $n/2$ bins. I have a few questions however. ...
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### How do I optimize the window lengths in STFT?

I have many EEG signals and I want to analyze them using linear methods such as STFT (Short Time Fourier Transform). In STFT , How can I optimize the analysis window length, to reflect the frequency ...
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### Is it possible for a signal to be represented by *both* sinusoidal *and* rectangular/triangular Fourier transforms?

A signal might have both continuous and discrete parts (where the "discrete" parts are regions where a sinusoidal Fourier transform would be subject to unnecessary Gibbs Noise). So I would think that ...
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### In Fourier transforms, can momentum space be analogized to frequency, and position space be analogized to wavelength?

We know that in quantum mechanics, momentum space is the fourier transform of position space (and vice versa) And also, in time-series analysis, that frequency (of cycles) is the fourier transform of ...
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### How do you measure "detail" of a signal?

I have an image and I would like to measure the amount of detail in it. Another way to look at it is to measure how blurry an image is. One way is to analyse the high frequency components in the ...
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