# Tagged Questions

The fast Fourier transform is an efficient algorithm to compute the discrete Fourier transform (DFT) and its inverse.

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### How to show Image FFT with origin as DC?

The page Here explains how to do the discrete fourier transform on a 2d image. It mentions this: In most implementations the Fourier image is shifted in such a way that the DC-value (i.e. the ...
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### Power spectrum of a pure sine problems

I am writing a C++ program to use to analyse oscillations and create a power spectrum. I am using FFTW3. To test the system, I am using a perfect sine function. But no matter what parameters I try,...
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### Could there be any reason to prefer convolution-based calculation of autocorrelation?

Theoretically both of ways of calculating autocorrelation function are identical: strightforward convolution and Fourier-based method where we use FFT/iFFT in practice. And as it is well known, the ...
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### How can I remove noise in these strain data? (New to data processing and MatLab)

I am fairly new to data processing and currently was assigned a task to remove noise in these data (strain). Without previous knowledge of data processing and couldn't get much help/guidance out of ...
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### Sampling theory and frequency spacing

If a CT signal $x(t)$ is sampled for one ($1$) second and $4096$ samples are generated: Isn't the highest frequency that can be sampled without aliasing ($4096/2$) $2048\textrm{ Hz}$? If a $4096$...
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### How to perform an FFT on a signal with a sampling rate of 44100?

This is probably a very simple Signal Processing question but I can't quite work it out. I'm currently writing an android app which needs to perform an fft on audio data taken from the phone's ...
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### How to find frequences domains in a 2D FFT (or DFT)?

I try to understand the FFT (and 2D FFT) with some basic R functions. x=1:10 plot(Re(fft(x))/length(x)) For the signal x, we ...
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### Define comb function in terms of exponential function

I have one signal with $N$ samples and I want to downsample it by factor of $M$. Essentially my downsampler is comb function which takes every M$^{th}$ sample while others are set to zero, i.e.,  \...
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### Comb function and downsampling [duplicate]

I understand role of Dirac comb function in downsampling in theory but I have problem with showing it mathematically. Let me start with time domain representation of the $2N$ periodic original signal ...
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### Mathematical justification for zero padding?

This question asks what's the point of zero padding. The accepted answer is certainly very insightful, but I don't understand a big chunk of it: Zero padding allows one to use a longer FFT, which ...
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### Calculating Phase Response for 2 microphones given the input

I want to measure and compare the phase response of two identical microphones. To do this, I have a pressure chamber, which allows to apply the same pressure to both microphones. I apply a sweeped ...
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### Fourier transform of moving image sensor

Consider an image sensor that is moving with some velocity $\mathbf{v}(t) \in \mathbb{R^3}$, and an orientation $\mathbf{R}(t) \in SO(3)$. Treat those vectors as fixed. At a specific time $t$ the ...
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### Why can FFT only operate on images with specific properties?

Can FFT only operate on Grayscale images? If Yes, why? Can FFT only operate on images with dimensions of power of two? If Yes, why?
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### MATLAB center frequency shift

I am wondering how to shift the center frequency of the below complex data from 0, to say 20 MHz (10 MHz to 30 MHz- 20 MHz bandwidth). I tried to change the indexing of the bins but I could not get ...
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### The frequency response function (FRF) fails to detect the antiresonance of a system

I am trying to identify a vibrational systems by computing the frequency response function (FRF) of the system when a chirp signal is applied to its input. After comparing the FRF computed and the ...
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### Butterworth filtering behaving unexpectedly -MATLAB

I'm new to signal processing but I'm trying to understand how the Butterworth filter works. To do so, I did the following: I assumed a sampling frequency of 100Hz and wanted to attentuate everything ...
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### remove static noise from audio

I have a recording with a static noise added throughout the audio. the longest silence period I could extract was this: audio_file however, it contains some moments of new sounds of flipping pages. ...
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### Is my approach for Splitting a magnitude across multiple bins correct?

I'm trying to synthesise a sine wave whose frequency is between bin centre frequencies per this post: Splitting a magnitude across multiple bins in an IFFT I'm trying to split my sine's magnitude ...
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### What factors go into choosing DCT type 1 over type 2 or type 3 etc?

I'm a newcomer to the DCT, DFT etc. I understand that they're intrinsically related, I understand that the DCT tends to "compress" the information in a signal towards the first few bins, leaving the ...
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### Splitting a magnitude across multiple bins in an IFFT

By Georg-Johann own work, CC BY-SA 3.0. I’m trying to synthesise a sine wave using an IFFT at a frequency between bin centre frequencies. Here are the details ...
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### Finding the maximum and minimum frequency of a 2D image

Suppose I transform the image into frequency domain and obtain a 2D array of complex numbers. How can I determine the minimum and maximum frequency from that array? By finding magnitude of each ...
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### PSD looks to clean/continuous

I generated an signal with a base frequency of $50\textrm{ Hz}$ and its harmonics and quantization noise in it (as an array in MATLAB). It's sampled fast enough to make sure there is no aliasing etc. ...
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### When doing Fourier extrapolation how can I adjust the projection to give correct results?

In the answer to http://stackoverflow.com/questions/4479463/using-fourier-analysis-for-time-series-prediction there is a snippet of code for doing Fourier extrapolation. However, it only works ...
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### How can I implement 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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### Quantifying patterns in the time-domain of a signal

I have a rather general question. Supposing I have 2 audio signals as seen in images 1 & 2 below, and when analyzing the power spectrum density of both signals, they are equal (i.e. the rms power ...
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### Efficient computation of Chirp Z Transform

Chirp Z Transform (1, 2, 3) is more powerful than zooming techniques (I use it to actually trace non-stationary chirp signals) and very usable in signal processing, but it's flexibility comes at price ...