# 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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### WAV encoding problem

When processing wav files, I encounter this problem: the what I extract PCM from a 8-bit encoded .wav file, I got a sequence of integers. However, when verifying my implementation with ...
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### What is the Fourier Transform of a constant signal?

I am trying to figure out what the fourier transform of a constant signal is and for some reason i am coming to the conclusion that the answer is 1. Or better yet a step function.
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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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### Why the unilateral Laplace transform?

Why is the Laplace transform commonly taught as the unilateral Laplace transform? I mean, for the Fourier transform, we commonly have the bilateral transform... if the signal is 0 for $t<0$, then ...
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### Fourier Transform with both Time Delay and Frequency Shift

I know that the Fourier transform of a function with time delay can be written as: $$\mathscr{F}\big\{x(t-t_0)\big\}=X(f)e^{-j2\pi f t_0}$$ The Fourier transform of a function with frequency shift ...
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### How do I convert a real baseband signal to a complex baseband signal?

I have radio telescope observations that have resulted in two real-valued signals (corresponding to the right- and left-handed circular polarizations). The signals are sampled at rate $2B$, and ...
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### Is sampling a Fourier transformed signal and fourier transforming a sampled signal the same?

I'm having a hard time understanding an assignment that states: Draw the complex spectrum of the sampled signal $f(t)$ (periodic and continuous). Do this, by first calculating the Fourier ...
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### Is interpolation of an audio signal to increase frequency resolution possible?

I apologize if some of what I ask is not entirely correct, I'm new to this field, but extremely interested. I have an Audio signal of sample rate 44.1 kHz that I want to segment into 30 frames, and ...
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### Implementing Convolution in Frequency Domain?

Suppose, we have a bitmap image represented as a 2D integer array, int [,] image2D; whose FFT is Complex[,] fftImage2D; ...
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### 2-d circularly symmetric low-pass filter

For a square pixel grid, the ideal 2-d low-pass filter with a horizontal and a vertical cut-off angular frequency $\omega_c$ in radians has an impulse response (kernel) $h_{\small\square}(x, y)$ that ...
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### Discrete Time Fourier Transform (DTFT) for an unstable system (Ideal Low Pass Filter)

The Dirchlet conditions state that if the signal is absolutely summable then it the DTFT of the signal definitely exists. This is a sufficient condition but not necessary condition. There are ...
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### Window functions with rippleless spectra

On Wikipedia I found the Hann-Poisson window, and the article claims the spectrum is smooth, but it isn't theoretically smooth, as it turns out. In practice you achieve partial smoothness by jacking ...
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### What are the uses of those three types of wavelet transformations?

In my studies of wavelets, there appear to be 3 different families of them: The Continuous wavelet transform The Discrete wavelet transform The Redundant wavelet transform They are all based on the ...
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### How to combine bins of my DFT

I have a time series and apply the FFT to get a spectrum. Let's assume that my sampling frequency and the length of the time sample are chosen such that I end up with a $\Delta f = 0.1$ Hz. As this ...
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### Why do we discard imaginary part of the phase spectrum?

Suppose I compute phase spectrum from the fftn function in MATLAB as ...
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### Kernel Convolution in Frequency Domain - Cyclic Padding

I don't know whether this is the right place to post this, but I suppose it is. I know that frequency multiplication = circular convolution in time space for discrete signals (vectors). I also know ...
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### Correlation filter output range normalization

I'm developing correlation filters based image recognition. I implemented MACE correlation filter in matlab: training code: ...
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### redundancy of sin and cos waves with real data

I have the following question. Isn't it true that when applying a fourier transform to a real function (i.e. computing a characteristic function for a density), we only ever need one of the two waves: ...
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### Transfer function and deconvolution

Forewords This question is about methodology references and numerical application. I am posting on Signal Processing because I think this question belong to this place. I am new to the stack, feel ...
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### Fourier domain: temporal versus spatial

I am little bit confused over these two. As per my understanding, spatial domain is the usual method we did in matlab by using the function fft2, which will return ...
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### Is Gabor uncertainty a feature of the Fourier transform, or of nature?

By Gabor uncertainty, I mean the principle of uncertainty as applied to signals — with the result that you can't have arbitrary time and frequency localization. By way of background to my question, ...
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### Minimum statistics noise estimate - how to calculate the underestimation factor?

I have implemented a basic noise estimator using the minimum statistics method. Noise power estimate is obtained as a minimum of the short time power estimate within a window of subband power samples. ...
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### Impulse Response / Frequency response Question [closed]

I have a major question. Please take a look. I have this differential equation (DE): $$\frac{d^2y(t)}{dt} +\frac{dy(t)}{dt} +4y(t)= \frac{dx(t)}{dt} +2x(t)$$ And I have to find impulse response (...
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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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### Is Fourier series a sampled version of Fourier transform?

I recently learned about dtft and how dft/dfs is the sampled version of dtft. I was wondering if Fourier series is also obtainable by sampling Fourier transform? I am a noob in the subject so sorry if ...
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### FFT of input length 1536

Does anyone knows can i find a FFT of 1536 length input. Its a specification given in 3gpp Lte and we need a transform of 1536 input size which is neither a power of any number i would say. I just ...
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### About Discrete Fourier Transform vs. Discrete Fourier Series

I am new to the field of signal processing. I am wondering what is the difference between DFS(Fourier Series) vs. DFT(Fourier Transform). For common applications, usually we get a segment(length <...