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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2answers
28 views

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,...
2
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1answer
29 views

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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0answers
20 views

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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24 views

How to normalize $\tt numpy.ifft$ results

I have a function $V_{\rm in}(t) = \cos(t)$ and I've used it to calculate $V_{\rm out}(t)$, now I want to regain $V_{\rm in}$ from $V_{\rm out}$ using $$V_{\rm in}(t)=\mathcal{F}^{-1}\left[\frac{\...
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14 views

R, Fourier transform, signal and noise

I have a set of time series data that contains a background noise, one short frequency signal and one occasional signal. I am trying to use R with Fourier transform to separate them and plot these ...
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0answers
11 views

Correlograms using FFT in 2D in R - how do I shift the image? [closed]

I have the following correlogram as a result of applying fft to the following image How do I shift it, in other words which function or how do I move the values of the corners to the correlogram'...
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0answers
22 views

What is the correct way to perform FFT-based convolution?

As far as I know, Obtain the input image whose width/height are power of 2. Obtain the mask/kernel whose width/height are power of 2. The width/height of the mask/kernel must be larger than 3 and ...
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1answer
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SNR problem with different sampling rates using innerproduct

I'm trying to measure the amplitude of a sinusoidal component in a noisy signal. Since the signal frequency is known beforehand, I'm calculating scalar product with a sine and cosine base function ...
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1answer
45 views

Generating blue/violet noise without FFT

I need noise with a high frequency bias for a realtime audio application, so I'm interested in things like blue noise or violet noise. Is there a way to generate such noise without using a FFT or an ...
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0answers
11 views

Is it possible compare 'the shape' of audio(voice) signal?

Here is an example: Record very low-tone voice guy saying, "Nice to meet you" Record very high-tone voice girl saying, "Nice to meet you" (they are saying almost same speed, it's like the second ...
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0answers
19 views

can I compensate for hann-window preceding fft? [duplicate]

To reduce spectral leakage, I have created a hann window going from almost 0 to 1 to almost 0 across 128 time points. I multiply that with my 128-point time series data, then feed the result to FFT. ...
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2answers
64 views

What should be the correct scaling for PSD calculation using $\tt fft$

I would to calculate the PSD of a signal using FFT however the result do not match with periodogram command. What did was as follow : ...
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3answers
235 views

Why do I have frequency leakage in DFT after zero padding if frequency resolution is fine?

Let's consider this example: Fs=1000; Ns=500; t=0:1/Fs:(Ns-1)*1/Fs; f1=10; f2=400; x=5+5*sin(2*pi*f1*t)+2*sin(2*pi*f2*t); X=fft(x); In this scenario, frequency ...
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0answers
38 views

Polyphase Analysis Channelizer in MATLAB

I am attempting to reproduce results for both polyphase analysis and synthesis channelizers found in "Non-Maximally Decimated Filter Bank and Its Applications in Wideband Signal Processing". Detailed ...
0
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1answer
35 views

Frequency analysis of a signal with not constant sampling frequency

I'm a stack exchange user for some time and now I'm registering to ask a simple question (I think!). I have a vibration signal with an amplitude and time (sampling frequency not constant) in a $...
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2answers
34 views

What should be the dimensions of a Fourier Transformed image?

I have applied Fourier Transform to the following image. I have downloaded this image from the Internet. I re-sized (without maintaining the aspect ratio) it using MS Paint application of Win7 to ...
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1answer
32 views

Summation of audio tone

Suppose you transmit at a single tone $\omega\textrm{ rad/sec}$ and you have two receiving microphones $i=1,2$ which sample at $r$ samples per second. Assume you have a direct path with coefficients $...
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1answer
57 views

Detection of low frequency signal

I have a strong primary signal with frequency range between 100–200 kHz. This signal has very low frequency and lower SNR secondary signal phase modulated to it. The modulated signal is around 10-30 ...
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1answer
40 views

Calculating phase response of filter with latency

I have an LTI filter that I want to treat like a black box. It has a latency of 24 samples. This is what I'm doing (which works for a filter with no latency): Send unit impulse through my filter ...
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votes
3answers
115 views

FFT to spectrum in decibel

Here is a 10 seconds-long 440hz sine wave normalized at $0\textrm{ dBFS}$. When computing the STFT (with the code below) of this audio file, I noticed that ...
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4answers
129 views

Intuition for sidelobes in FFT

I was wondering if there's a intuitive way to understand why sidelobes appear when performing an FFT on a signal of fixed length?
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3answers
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MATLAB: $\tt fft$ and $\tt ifft$ scaling

In MATLAB, the outputs of the fft and/or ifft functions often require additional processing before being considered for analysis....
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19 views

When to use raw signal strength, vs. when to filter first

I am collecting I/Q samples from an RTL SDR dongle. I notice the rtl_power utility provided for Linux filters and does other processing, before reporting signal ...
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1answer
40 views

How can I transform this FFT into real FFT ($\tt rfft$)?

I'm using Python numpy.fft.rfft (real FFT) that produces an output of length n / 2 + 1. It works. Now I'm rewriting my algorithm ...
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26 views

Real-time STFT masking

When doing offline audio processing (example : template-based noise reduction) I can use this classic method : $$\boxed{\textrm{Input}}\longrightarrow\boxed{\textrm{STFT matrix}}\longrightarrow \...
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1answer
24 views

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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1answer
52 views

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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0answers
20 views

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 ...
3
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1answer
52 views

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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28 views

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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2answers
68 views

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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0answers
35 views

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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1answer
40 views

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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1answer
34 views

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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1answer
52 views

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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1answer
56 views

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 ...
3
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2answers
52 views

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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0answers
58 views

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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0answers
32 views

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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1answer
39 views

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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1answer
92 views

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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1answer
46 views

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 ...
1
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1answer
39 views

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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28 views

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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2answers
62 views

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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0answers
19 views

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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40 views

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 ...
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13 views

Windowing the sequence to compute Correlation

I want to compute the Correlation Functions of the input and output time-domain sequence, ...
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0answers
22 views

amplitude of FFT analysis rotor encoder

I have 2 motors turning at the same speed (rotor encoder). I want to analyze their movement (rotation) in fft . If their axis of rotation was exactly at the center the FFT result should have been a ...