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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71 views

How do you sub-sample an FFT?

I'm currently trying to understand this paper on a Sparse Fourier Transform. On page four, there is a section on a sub-sampled FFT. The purpose of this section is to show that you can compute a sub-...
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38 views

On the channel estimation based on vector

I have a matrix $X$ of size .i.e $(8,8)$ with $M$ columns and $N$ rows. Suppose I took it's $iFFT$ column wise resulting matrix $x$ of size $(8,8)$ too, $x = F^HX_{(:,m)}, $ ...... (1), where ...
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3answers
50 views

Simplifying frequency response equation

I am trying to to find a magnitude and phase response of a FIR filter as in problem 5.18 Digital Signal Processing 4th Edition by John Proakis. I got the frequency response as: $$ H(\omega ) = 1 - e^{...
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1answer
51 views

What is the difference between time complexity and sample complexity?

What is the the difference between time complexity and sample complexity in the context of algorithm development? I'm currently studying the sparse Fourier transform and this idea of sample ...
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2answers
35 views

non-consistent normalization problem in fft

I have a csv file of data sampled with Ts=1ns which looks like this: This signal is a step response of some system which responds to a step of value 1. I'm trying to get the impedance profile of the ...
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1answer
46 views

How to Find spectral Peaks from 2D array of Spectrogram? [closed]

I have computed a Spectrogram 2D array as : How to develop a spectrogram (2D array) from audio signal? Now, I want to find spectral peaks to find the respective temporal displacement. In python using ...
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2answers
51 views

Are there any difference between the FFT magnitude of a signal and average FFT magnitudes of the signal broken into multiple frames?

Suppose I calculate the FFT of a 5 seconds sound wave. If I'm only interested in the FFT magnitudes across frequencies, I should obtain the same result if I segmented the sound wave into five 1-second ...
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1answer
32 views

IFFT and sample count issue in OFDM

I wrote a python program to generate OFDM packets (i.e. the IQ samples) with a custom payload to, for example, be transmitted via an SDR. After mapping the chunk of bits corresponding to one ofdm ...
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1answer
27 views

What is spectrum permutation?

This paper refers to the concept of "spectrum perumutation" on page 4. I'm having a difficult time understanding what it means to permuate a signal. This is mainly due to the fact I don't understand ...
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0answers
17 views

obtain envelope of spectrum

To extract a 2001-sampled envelope of magnitude of the spectrum of a signal, I have divided the frequency axis into 2001 intervals. In each interval, I find the 3 largest spectrum magnitude values ...
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1answer
32 views

Shifting a fourier spectrum by subpixel amount in python

I am working on a Fourier Ptychography problem. My research problem requires me to shift the Fourier spectrum of an image by a floating-point value. For a real-valued image, we can simply use ...
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1answer
41 views

FMCW radar: Linear phase change determination with sinusoidal decomposition

I am struggling to understand how linear phase shift can be determined with a transform whose main purpose is to determine frequencies rather than rate of change of a function. In FMCW radar, ...
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0answers
23 views

Compute $d^2$ entries of a 3D convolution faster than $O(d^3)$

Let $A,B\in \mathbb{R}^{d\times d\times d}$. The 3D circular convolution $\text{conv}(A,B)$ can then be computed as $F^{-1}(F(A)\odot F(B))$ where $F(\cdot)$ denotes the 3D discrete Fourier transform ...
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0answers
39 views

On the performance of DCT-based OFDM

I am trying to understand the OFDM based on DCT instead of DFT in order to compare between their performance. In case of AWGN, the performance is logic, but when I perform channel equalization in DCT-...
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0answers
21 views

Difference between these two Continuous Wavelet Transforms?

I am porting Synchrosqueezing to Python, and came across an implementation difference on CWT between mine and PyWavelets' - details below. The idea is to merge this implementation to PyWavelets if ...
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1answer
55 views

Ideal low-pass filter in the Frequency Domain

I try to create a low-pass filter to apply it for an image. $$H(U, V)=1 \text{, if }D(U,V) ≤ D_0 \text{, and } 0 \text{ otherwise}$$ and $D(U, V) = \sqrt{U^2 + V^2}$ ...
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1answer
30 views

Recover Weak Modulated Signal

I have two signals. F1 and F2. F1 is changing over time slowly. It is in 5-10kHz range. (Change is nonlinear but very slow, a drop of 1-2KHz in one second would be typical) F2, for sake of argument ...
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0answers
53 views

True Envelope algorithm: how to speed it up?

Premise (since somebody may ask about the background): I am the author of the spectral modules for SynthEdit, a modular framework for realtime STFT audio processing, currently struggling since ...
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4answers
371 views

Why do we have to rearrange a vector and shift the zero point to the first index, in preparation for an FFT?

I am trying to learn how to implement the FFT as a way to approximate the continuous-time Fourier transform, and as a "nice easy example" I have chosen to test it with a simple Gaussian pulse in the ...
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2answers
43 views

OFDM symbol synchronization

In an OFDM receiver, how could we find the start of the symbol for FFT operation. I know the CP-based method to find the start of symbol. However, what if the sampling is off by some duration. We ...
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0answers
30 views

DFT vs DCT Discrete transform

The discrete Fourier transform transforms a sequence of $N$ complex numbers $x_n := x_0, x_1, . . . . x_{N-1}$ into another sequence of complex numbers $X_k := X_0, X_1, . . . . X_{N-1}$ , which is ...
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2answers
68 views

DC and Nyquist values are higher than all other bins

I am using a mean centered signal and applying fft to it, however the dc and nyquist values are a lot higher than all other values. Wondering if I am doing anything wrong or need to add anything else. ...
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3answers
325 views

Fast phase calculation

I need to detect the PSK modulation posted on my previous post(phase difference detection) with 8 to 16 phase constellations (depending on selected baud rate) over a max 60 degree PSK phase range.For ...
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1answer
61 views

A filter with low phase shift or no phase shift at all? Which one? [duplicate]

I'm seeking a good advice for a filter. Can you help me? Right now I made my own simple filter. Not sure what I'm doing, but it seems to work. ...
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1answer
44 views

What is the best way to detect rectangular pulse for AFSK demodulation?

I've got a WAV file with a rectangular pulses coding zeros and ones. By specification, a 1 bit is a 320 microseconds wide rectangle, and a 0 bit is a 640 microseconds. So basically the idea is to ...
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0answers
32 views

How Can I Add noise to a Frequency Domain Input Signal?

I am new with Matlab and doing some work on Amplifier and Bipolar Shappers Amplifiers. Adding Noise to a Time Domain Signal is quite easy and I have done it multiple time as: ...
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1answer
39 views

Calculating PSD, Cross PSD by using FFT outputs

I am having the FFT results of two distinct voice signals. Let's say the FFT results of these two signals are of the form (a+ib) and (c+id). Now, I want to calculate the PSD of each signal and also ...
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1answer
33 views

Calculating Cross Power Spectral density between two complex signals

I have a small misunderstanding of cross power spectral density between two complex signals. I know that it is the Fourier transform of cross correlation between two signals. Let's say the complex ...
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2answers
196 views

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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1answer
112 views

2D DFT in image processing in python

I try to compute 2D DFT in a greyscale image with this formula: I write the code bellow with python ...
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2answers
124 views

How to develop a spectrogram (2D array) from audio signal?

I have developed a spectrogram in Python using Scipy.Signal.Spectrogram. But I need a complete understanding of data. Here I am not asking about plotting and color ...
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3answers
841 views

Understanding FFTs for simple Sin / Cos

this is my first question in this forum, and although I read several threads on this side and googled a lot I could not find the answer to my question (maybe it is too basic)? For anyone reading this ...
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0answers
59 views

Handling stride>1 in FFT-based convolution

The Fourier transform of the convolution of two signals with stride 1 is equivalent to point-wise multiplication of their individual Fourier transforms. I need to perform stride-'n' convolution using ...
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2answers
58 views

How to get coordinates(x(time),y(frequency)) of spectral peaks from spectrogram?

I have created this spectrogram from a wav file. Please have a look: As it can be observed clearly that my somewhat spectral peaks are visible. I want to get the x = time, y= frequency of these ...
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0answers
22 views

Remove known sound from signal

I'm currently getting FFT values from the music playing from a user's PC. However, my application also generates noise which interferes with the FFT data as my app's sound is also coming out of the ...
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0answers
44 views

Pitch correction using Fast Foruier Transform [duplicate]

I am very new to digital signal processing and I have a project about audio programming. For the project, I wanted to try to make an Auto-tune like effect. I started by experimenting on the signal ...
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0answers
19 views

Noise floor flatness in IQ FFT window

I am doing a simple $P_{in}$ - $P_{out}$ linearity test for my RF generator/receiver system. The generator provides an IQ modulated CW single tone with $P = - 80dBm$ at 1 GHz. If we look at the RF ...
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1answer
64 views

creating this famous basic nyquist theory photo

Hello i ha built this code which create a only one replica of the data, how can i create the whole photo shown bellow of many cycles as shown bellow? i read in the internet that zero padding could ...
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1answer
61 views

What's wrong with my STFT implementation?

I'm studying the linear convolution for achieve more complex results in Audio FX. My main goal is to implement a realtime convolution between two stream of sound in live perfomance (for example Sound ...
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1answer
45 views

Circular convolution of real signal N by N/2 sized complex IFFT

There are two related questions with good answers; for calculating the forward FFT in N/2 values, and calculating inverse FFT from N real values, now I'm in search for the missing link of packing the ...
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0answers
13 views

2D FFT Toeplitz Matrix Indexing

I have a convolution sum_j M(x_i-x_j) v(x_j) which I would like to numerically compute using a FFT. x_i and ...
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2answers
82 views

Missing known sinusoid in FFT of sensor data

Let me ask about FFT, i have data sample from sensor, source of frequency from generator is 5 Hz, i want to extract the data with FFT but why i cannot find the 5 Hz frequency from source. This is my ...
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0answers
37 views

Is there a FFT algorithm which is both in-place and constant geometry?

I work in crypto where the NTT (Number Theoretical Transform) which is just a FFT in finite fields is used. I wanted to know if there exists an implementation of the FFT which is both in-place and ...
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1answer
21 views

DIF based FFT scaling for OFDM Input

I'm working on XILINX FFT IP(PG109) in pipeline mode, which uses radix 2 DIF Lattice to perform FFT/IFFT operation. How to perform scaling of each stage in FFT, such that the effect of saturation or ...
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1answer
47 views

How to difference a loud sound (playing notes), from a soft noise in spectrum. (Pitch detection with bass)

I'm trying a program that outputs the bass line that you are playing. I have some arrays from a big one with the sound in time domain, that are splited (Hann window). Later, I do the FFT, then I get ...
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2answers
167 views

What is the DFT of a pure cosine wave cos(θ)

I want to find a DFT of a pure cosine wave cos(θ) sampled at N equally spaced points on the interval $[0, 2\pi)$ so for our cosine wave, I put my $x$ like this $x=cos(\phi)$ then I just put it in ...
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2answers
84 views

How to get Spectrogram after fft in matlab?

I have many EEG signals which record at 100 Hz. I use FFT on them with fft Matlab toolbox. Now I wanted to get a Spectrogram. As I searched and read a lot, I figure that I should window my signal and ...
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1answer
55 views

Signal Timing Recovery, Loop Bandwidth and SNR

As explained in the answer here, for the symbol timing recovery loop we need to keep loop bandwidth sufficiently below the modulation bandwidth of the signal so as to avoid the filtering of the signal ...
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1answer
35 views

MATLAB: Generating a random bit stream in a frequency Band for PSK Modulation

I want to generate a pseudo-random bit stream in MATLAB in a given frequency band for PSK Modulation. I am using the idinput function to generate the bit stream: <...
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2answers
167 views

High Pass Filtering and Noise

I have the following code: ...

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