Questions tagged [fft]

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

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Why is it a bad idea to filter by zeroing out FFT bins?

It's very easy to filter a signal by performing an FFT on it, zeroing out some of the bins, and then performing an IFFT. For instance: ...
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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 <...
aha's user avatar
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Why should I zero-pad a signal before taking the discrete Fourier transform?

In an answer to a previous question, it was stated that one should zero-pad the input signals (add zeros to the end so that at least half of the wave is "blank") What's the reason for this?...
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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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50 votes
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Why is the FFT "mirrored"?

If you do an FFT plot of a simple signal, like: t = 0:0.01:1 ; N = max(size(t)); x = 1 + sin( 2*pi*t ) ; y = abs( fft( x ) ) ; stem( N*t, y ) 1Hz sinusoid + DC ...
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How do I implement cross-correlation to prove two audio files are similar?

I have to do cross correlation of two audio file to prove they are similar. I have taken the FFT of the two audio files and have their power spectrum values in separate arrays. How should I proceed ...
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8 votes
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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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What determines the accuracy of the phase result in a DFT bin?

What are the factors that affect the accuracy and precision for the phase that is given by the DFT? Just thinking medium-hard about this, it occurs to me that it must have something to do with the ...
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Find the Equivalent Noise Bandwidth

I have already asked (in another thread) how to quantify (specify) the window function I have created. One figure I need it seems is the Equivalent Noise Bandwidth (ENBW) Or Noise Equivalent Bandwidth....
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Is there a technical term for this simple method of smoothing out a signal?

Firstly, I am new to DSP and have no real education in it, but I am developing an audio visualization program and I am representing an FFT array as vertical bars as in a typical frequency spectrum ...
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29 votes
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Which time-frequency coefficients does the Wavelet transform compute?

The Fast Fourier Transform takes $\mathcal O(N \log N)$ operations, while the Fast Wavelet Transform takes $\mathcal O(N)$. But what, specifically, does the FWT compute? Although they are often ...
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Fast Cosine Transform via FFT

I want to implement the Fast Cosine Transform. I read on wikipedia, that there is a fast version of the DCT which is similarly computed to the FFT. I tried to read the cited Makhoul* paper, for the ...
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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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3 answers
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2D Cross-Correlation using 1D FFT

I need to calculate cross correlation between 2 images which I read in 2 vectors, both of them uni-dimensional. As per my understanding I need to do the following operations: FFT(1D) on vector 1 and ...
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How can I plot the frequency response on a bode diagram with Fast Fourier Transform?

Assume that we have an unknow dynamical system and we only want to estimate its parameters. The system can be discribed as: Continous time: $$G(s) = \frac{3s + 5} {5s^2 + 3s + 2}$$ Discrete time ...
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Why does spectral leakage arise in an FFT?

I've tried googling and wikipedia-ing it, but I haven't gotten any answers beyond 'it's because the frequency of the input signal is sitting between two bins'. I understand that this is the reason, ...
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Using fourier coefficients to reconstruct data in matlab

When doing a discrete fourier transform on some data using matlab's fft function, its output is a set of fourier coefficients but I was wondering how do I go about converting these into an and bn so I ...
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26 votes
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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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Strategy / Method for Implementation of the Fastest 1D Linear Convolution / Correlation

I am after the method and its implementation of the fastest convolution of 1d signals: $$ y \left[ n \right] = \left( x \ast h \right) \left[ n \right] $$ Where $ \ast $ is the linear convolution ...
Shkodrani's user avatar
3 votes
2 answers
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Can anyone explain how dft works as a filter bank?

When we take the fft of input signal, the fft formulas say us to down convert the 2pik/N frequency content of input signal and sum one period interval. This gives us a just one complex number,not an ...
Ahmet Serdar's user avatar
27 votes
1 answer
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What is the difference between PSD and squared magnitude of frequency spectrum?

The power spectrum of a signal can be calculated by taking the magnitude squared of its Fourier transform. Being an audio person, the signal of interest for me would be a time series. How does this ...
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Applying 2D Image Convolution in Frequency Domain with Replicate Border Conditions in MATLAB

I have created a function that filters an image (250x250) with a gaussian blur kernel (5x5) using FFT and IFFT. I am trying to get my filtered image to equal exactly the filtered image created by the '...
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Specific Frequency Resolution

I have an audio signal SampleRate Fs: 44100 Hz TotalSamples: 94144 samples Duration t: 2.1348 s The frequency resolution is given by ...
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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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Zero Padding of FFT

There are many question related to the zero padding a time domain signal to get more frequency bins after performing Fourier transform. As I understand this process is equivalent to trigonometric ...
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Estimation of Amplitude, Frequency and Phase of Linear Combination of Harmonic Signal Beyond the Leakage Resolution of DFT

How can I find a rough ( as accurate as possible) Amplitude of each frequency when there is spectral leakage. Currently, I am dealing with a system that contains special leakage which seems ...
Jacob wood's user avatar
4 votes
2 answers
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FFT analysis for Vibration Signal

I am working on balancing an air-spindle. For the unbalance analysis I use an accelerometer (NI device). I have the voltage signal from the accelerometer corresponding to the vibration of spindle at a ...
Deep Shah's user avatar
4 votes
1 answer
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How can I get the power of a specific frequency band after FFT?

I need help with my matlab code. I have recorded EEG data and now I want to analyse it in matlab. I want to find the mean power of specific frequency ranges (theta: 4-8 Hz,alpha: 8-12Hz etc.). For ...
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Is there an algorithm to compute the phase for a single frequecy?

If you have a function $f(t)=A \cdot \sin(\omega t+\phi)$, and reference sin wave $\sin(\omega x)$ what would be a fast algorithm to compute $\phi$? I was looking at Goertzel algorithm, but it doesn'...
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18 votes
1 answer
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What is the phase and magnitude response of white noise?

I would like to create white noise in the frequency domain, and then transform it to the time domain using python. To understand the problem, I simply generated white noise in the time domain, and ...
Uffe's user avatar
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16 votes
2 answers
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Image Reconstruction:Phase vs. Magnitude

Figure 1.(c) shows the Test image reconstructed from MAGNITUDE spectrum only. We can say that the intensity values of LOW frequency pixels are comparatively more than HIGH frequency pixels. Figure 1.(...
sagar's user avatar
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14 votes
7 answers
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The difference between DFT and DFS

In the literature, I've found that DFS and DFT are one and the same. If they are one and the same why to use two different names for them? If there is really a difference what is it and what is the ...
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FFT frequency resolution

I'm having some problems understanding the FFT. Is the frequency resolution in the spectrum calculated as $\frac{\textrm{sampling rate}}{\textrm{number of FFT points}}$ or $\frac{\textrm{sampling ...
argh's user avatar
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13 votes
4 answers
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Efficiently calculating autocorrelation using FFTs

I'm trying to calculate an autocorrelation on a platform where the only accelerated primitive I have available is the (I)FFT. I'm having a problem though. I prototyped it in MATLAB. I am, however, ...
Goz's user avatar
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3 answers
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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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12 votes
2 answers
4k views

What statistic is used to determine presence of a signal in noise?

This is a detector problem I believe: I am being stumped by what appears to be a simple problem. Basically, I have a band of interest. If signal energies exist within this band of interest, then I ...
Spacey's user avatar
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For 2D signals can it be said that the frequency response is the same as the Fourier transform?

Say I have a signal: [1, 1 , 1; 1 100 1; 1 1 1];, I wanted its frequency response, then can I take its FFT? Why does MATLAB have two functions to do the same ...
user26763's user avatar
1 vote
2 answers
733 views

FFT Phase interpretation of input signal with non-integer number of cycles in FFT window

It is known that if we take the FFT of a signal at such a frequency which has non-integer number of cycles in the sample window we get different value of phase even if the original signal was at phase ...
malik12's user avatar
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2 answers
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What is the advantage of overlapping windows while evaluating Spectrogram?

I've seen many documents that refer to calculate spectrogram through overlapping windows but haven't found clear documents on why this is done and how to calculate the number of points that need to be ...
Sadat Rafi's user avatar
36 votes
9 answers
14k views

Is there an algorithm for finding a frequency without DFT or FFT?

I was looking in the Android app store for a guitar tuner. I found a tuner app that claimed it was faster than other apps. It claimed it could find the frequency without using the DFT (I wish I still ...
Slamice's user avatar
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22 votes
4 answers
7k views

How to distinguish voice from snoring?

Background: I'm working on an iPhone application (alluded to in several other posts) that "listens to" snoring/breathing while one is asleep and determines if there are signs of sleep apnea (as a pre-...
Daniel R Hicks's user avatar
22 votes
2 answers
78k views

Power spectral density vs. FFT bin magnitude

What's the difference between these? Both are measurements of some form of signal power, but surely there's some difference between the power they are measuring?
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20 votes
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How do you calculate spectral flatness from an FFT?

Ok, the spectral flatness (also called Wiener entropy) is defined as the ratio of the geometric mean of a spectrum to its arithmetic mean. Wikipedia and other references say the power spectrum. Isn'...
endolith's user avatar
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19 votes
2 answers
18k views

Why do we say that "zero-padding doesn't really increase frequency resolution"

Here is a sinusoid of frequency f = 236.4 Hz (it is 10 milliseconds long; it has N=441 points at sampling rate ...
Basj's user avatar
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17 votes
5 answers
14k views

FFT of sine wave not coming as expected i.e single point

The cyan plot is a spectrum of 50 Hz, and the magenta one is a 50.1 Hz sine wave (having amplitude 0.7). Both are sampled at 1024 samples/s. I performed a 1024 point FFT to get this spectrum. Why is ...
gpuguy's user avatar
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15 votes
1 answer
29k views

What are the units of my data after an FFT?

Magnetometer measures the derivative of the magnetic field, or dB/dt, with an output in microvolts (mV). The Sampling rate is 128 Hz, so if we collect data for 2 minutes, $2 \times 60 \times 128=...
MikiBelavista's user avatar
9 votes
3 answers
32k views

Number of DFT (FFT) Points Required for a Specific Frequency Resolution for an Oversampled Signal

I have a bandpass signal centered at 2 MHz and bandwidth of 50 kHz (the signal frequency varies from 2 MHz - 25 kHz to 2 MHz + 25 kHz). This signal is being sampled at 10 MHz. I want a frequency ...
Vinod's user avatar
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9 votes
1 answer
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Non Uniform FFT / DFT with FFTW?

Can FFTW perform the FFT on data which is not uniform in time? I can't seem to find a straight-forward answer to this question anywhere online.
John's user avatar
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7 answers
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Qualitative Explanation of Fourier Transform

I am reading the book Fundamentals of Music Processing by M.Muller and I am close to understanding the idea behind the decomposition of a signal into basic frequencies, and would appreciate some help ...
nikos's user avatar
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7 votes
1 answer
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The necessity of null subcarrier in OFDM?

In looking to LTE specifications, with the subcarrier spacing $\Delta f = 15 \textrm{kHz}$, for bandwidth $10 \textrm{MHz}$, fft size $N_{fft} = 1024$ that needs a sampling rate $F_s \geq 1024 \times ...
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