Questions tagged [frequency-domain]

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DFT and Inverse DFT in Image Processing

I have implemented DFT from this link. 1) Tried taking dft for the three Channels(R, G and B) and reconstructed the original image by taking inverse dft for all three channels and merged them ...
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2answers
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Why do frequencies of analog signals range from $-\infty$ to $\infty$ while frequencies of digital signals are restricted to $[0,2\pi]$?

In Fourier analysis while dealing with discrete-time signals, frequencies range from $0$ to $2\pi$ why? Intuitively how can i understand it?
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2answers
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Perform Convolution in Frequency Domain Using FFTW?

I'm trying to convolve two signals $x(n)$ and $h(n)$ in C by using the FFTW library's functions to perform a Fourier transform on each, multiply the appropriate complex components together, and take ...
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2answers
2k views

How to Apply Window Functions in Frequency Domain?

I am trying to apply a window function to smooth my signal and finally obtain the peaks of the signal. Yet, for spectral leakage I apply window function in time domain. After taking the Fourier ...
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4answers
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Continuous Time Signal and Discrete Time Signal - Connection Between Periodicity and Discretness

I know that all periodic continuous time signal have discrete spectral representations, but are all discrete spectral representations periodic in continuous time? Also, can all periodic signals be ...
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1answer
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Computation of the Inverse DCT (IDCT) Using DCT Or IFFT

Is there a way to compute the inverse discrete cosine transform (type-2) by leveraging either a DCT, FFT, or IFFT algorithm? I have seen ways to compute the DCT using FFTs, and I've seen ways to ...
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2answers
6k views

Understanding the frequency domain [duplicate]

I'm trying to understand what frequency domain is. I found general explanations on the Internet, for example: frequency-domain graph shows how much of the signal lies within each given frequency band ...
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1answer
1k views

Applying Gaussian Blur in Frequency Domain

Please see second update I'm trying to implement gaussian blur in frequency domain using c#. Those are steps that I'm doing: Load bitmap. Split bitmap into separate color channels. Convert every ...
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1answer
179 views

Bilateral Laplace transform and existence of Fourier transform

I was reading from Athanosios Papoulis' "The Fourier integral and its applications." and they referenced the bilateral Laplace transform and Fourier Transform as: $$F(p)=\int_{-\infty}^{\infty}e^{-pt}...
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1answer
82 views

Complex FFT reversing

I've succeeded to compute complex FFT of a data array of interleaved values using the arm_cfft_f32() API of the CMSIS DSP library for Cortex-M4, and got in the same array the FFT results as frequency ...
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0answers
23 views

Is there a criterion that says at what point you can distinguish 2 partially overlapping Lorentzian peaks?

If you have 2 Lorentzian peaks that partially overlap and you have some frequency resolution df (your points in frequency space are separated by df) and both Lorentzian peaks have FWHM $\Gamma$ is ...
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4answers
2k views

Why does the frequency in the DFT have to be an integer?

I don't know why the result of DFT and FFT in MATLAB like below images.. fs=128; t=0:1/fs:1-1/fs; x=cos(2*pi*3.5*t); X=fft(x); N=length(x); n=0:N-1; f=fs*n/N; plot(f,abs(X)/N); If I set the ...
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Does the number of samples matter for FFT, and how to get a specific frequency visible?

If I have a signal that has 740 samples, the sampling frequency is 1000 Hz, and I take an FFT of length 1024, are the frequencies I get now 0, fs/1024, 2*fs/1000, ..., 511*fs/1024? I mean, do I get ...
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Plot Background Noise

I am a total newbie in signal processing. I have been trying to plot on simulink a time/frequency domain noise in PLC (Powerline Communication) that matches a real-world research "...
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1answer
888 views

How to calculate a delay between two signals in frequency domain?

Calculation of a delay between two signals is generally done by finding the maximum in the cross-correlation of the two signals (in time domain): $$ \tau_{delay} = \arg\max_\limits{t}(f(t) \star g(t)) ...
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What is the best spline to interpolate freq analiser graph

the question is as it is in the topic: What is the best spline to interpolate freq analiser graph? I am looking something simply and fast to implement. I read about catmull-rom it looks it could be ...
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2answers
102 views

Why are LTI filters not able to output frequencies not present at the input?

I know this a very basic question but I'm just having troubles understanding why. Thanks in advance!
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1answer
108 views

FFT radix-2 in audio - resolution issues - logarithmic scale - sample rate VS buffer size

I would like to ask how to deal with audio DSP. Is FFT good at all to deal with audio? I am working on an app, that generates a single impulse, rout it to an EQ plugin, and the output of the plugin is ...
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1answer
346 views

characterization of DC component

Consider the following two statements: In time axis: A signal without a DC component is a signal which doesn't have the zero frequency (the DC frequency) A signal without a DC component is averaged ...
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Discontinuities in the FFT

So I am taking the Fast Fourier Transform of the following function: $$ x[n] = \displaystyle\sum\limits_{i=0}^{5} A_{i} \cos\left(\frac{\omega_{i}}{\omega_{s}} n + \phi_{i}\right) $$ Where the ...
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1answer
370 views

How to do image reconstruction from array data?

i have 15 set of data which is the s-parameter, consist of 2 column (1001x2) each set. The first column is frequency and the second column is magnitude in dB. I have transform the magnitude from (dB) ...
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3answers
3k views

Comparison between 2 images in Frequency domain

As you can see there are 2 images from the Tom and Jerry cartoon program. In the 1st image both Tom and Jerry are present. But in the 2nd one,only Tom is present.Now,we can clearly see this ...
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2answers
619 views

Convolution and Modulation Theorem with Octave Example

As far as I know, convolution theorem stated that $$ x[n] * y[n] = X(e^{j \omega}) Y(e^{j \omega}) $$ $$ X(e^{j \omega}) * Y(e^{j \omega}) = x[n] y[n] $$ I tried a simple experiment using GNU Octave ...
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Convolution of BPSK signal in frequency domain implementation

Here is the simplified version of code which implement convolution of BPSK-signal in frequency domain: ...
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1answer
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Doppler shift in time domain?

I have some clarifications required in this topic So initially I know that to shift a signal $X(f)$ by $f_0$ we need to take its inverse fourier transform and multiply it with a factor of $\exp(−j2\pi ...
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2answers
418 views

Averaging over bins in frequency domain

I have a sound file with a computed spectrogram from 0 to 8000 Hz (spanning about 5 octaves). The spectrogram has 128 logarithmically spaced frequency bins. How can I reduce the number of bins so that ...
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1answer
870 views

Meaning and unit of frequency in Laplace (Fourier) transform

Imagine transfer function obtained by Laplace transform, for example: $G(s) = \dfrac{1}{s+1}$ Now, I would like to do some frequency analysis, so I replace the $s$ with $\omega i$ (let's consider ...
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1answer
43 views

Does each pixel of the original image has a corresponding coefficient for every scale and every direction calculated by the DWT?

I want to take a pixel and find its coefficients calculated by the discrete wavelet transform for every scale and every direction. But as the DWT subsamples images, I don't see how to do that. Do I ...
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1answer
7k views

How to circularly shift a signal by a fraction of a sample?

The shift theorem says: Multiplying $x_n$ by a linear phase $e^{\frac{2\pi i}{N}n m}$ for some integer m corresponds to a circular shift of the output $X_k$: $X_k$ is replaced by $X_{k-m}$, where ...
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2answers
2k views

Is it possible to apply a frequency filter a time domain signal?

Is it possible to frequency filter a time domain signal, without converting the signal to a frequency domain.. My question comes in regards how MFCC according to wiki and other pages describe the ...
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2answers
166 views

Fourier transform

Fourier transform of a DC signal is an impulse at the origin. Now if the spectrum of a signal is the plot of the amplitudes of the respective frequencies of each harmonic, then the Fourier transform ...
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2answers
474 views

Closest two frequencies that can be resolved

Forgive me if I misuse the terminology. I wish to transmit two slowly changing analogue signals by amplitude modulating two higher frequency sinusoidal carrier waves. I will superimpose the two AM ...
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2answers
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Determine Phase Difference and Time Delay Between Two Pulsed Sinusoidal Signals

I am working on a code that generates two signals: A pulsed sinusoidal signal ($1\textrm{ MHz}$) beginning at $0$ phase, and lasts for say $5\ \mu\text{s}$, then trails zeros. The other signal has the ...
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2answers
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Implementing a Band-Pass Filter from Scratch

I am trying to implement a band-pass filter from scratch. Here is an article which I thought explained the nuts and bolts of how to build one; the author combines a low-pass with a high-pass filter (...
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2answers
286 views

Interpretation of a sampled signal in the frequency domain

Suppose we have a signal $y(t)$. For sampling we use a Dirac $\delta$ function. The sampled function is $\widetilde{y}(t)$. So $$\widetilde{y}(t) = y(t)\cdot\sum_{n=-\infty}^{\infty}\delta(t-nT).$$ ...
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1answer
877 views

Corresponding frequency domain filter of spatial domain filter in image processing?

My question is: Suppose that we have low pass spatial domain filter that averages 4-connected neighbors of that pixel and it doesn't consider its pixel in averaging. Find its corresponding filter in ...
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1answer
122 views

Convert fixed frequency bandwidth samples to time domain

I'm trying to convert signal (bandwidth 1400 MHz, start freq 9300 MHz, stop freq 10700 MHz, step 3.5 MHz) from frequency domain to time domain. Signal data in frequency domain, as well as signal data ...
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1answer
375 views

Stationary signal: time-domain vs frequency domain

If I understand correctly, a signal is stationary if: time domain: it's generated from the same distribution at each instant time. frequency domain: its frequency content does not change in time. ...
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Operations applied to functions in time domain and frequency domain

I am trying to make a succinct summary of how algebraic operations in the time domain translate in the frequency domain (via the use of Fourrier/Laplace transforms). Here is what I have derived so far:...
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2answers
441 views

Smallest FFT buffer size given zero-padding

I am currently working on a project that involves processing an audio signal by dividing it into chunks of size B. The buffer is then zero padded to have a size of 44100 points, after which FFT is ...
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3answers
648 views

Time domain maximum from frequency domain data?

Is it possible to calculate the maximum value of a time-domain signal from frequency-domain representation without performing an inverse transform?
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2answers
160 views

How to discard coefficients in the frequency domain without losing too much quality?

I was reading a text that shows that one can throw away 66% of the coefficients and gets an image that is still acceptable. I tried to replicate it using python (last example) and selectively ...
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2answers
644 views

What proportion of a padded FFT should be actual values

For a given signal, I've been told that you can pad the vector with $0$s at the end to get a larger DFT, and as a result get more precision in frequency bins. What are the limits to this approach? ...
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4answers
161 views

Why does changing the frequency of a single component change total sum of amplitudes in my FFT?

I have the following code which generates a single simple sine wave with amplitude $1$ and then calculates the Fourier transform, normalises it, and finally takes the sum of all the components. ...
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3answers
636 views

How should this fft output be intepreted?

I am currently reading some code, so I can understand how this FFT output is actually been stored. I have a function which computes FFT of audio file, and stores is in the format. ...
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1answer
390 views

Time-Frequency Analysis of Big Data - Data Size Reduction: averaging the most appropriate method?

Explanation: I would like to analyse the data from an experiment, which investigates the performance of a mechanical component using sensors, that has generated 2000 CSV files. Each file contains 513 ...
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$\tt ifft()$ function - absolute vs real form

I have multiple files from an experiment in frequency-domain that I would like to use ifft() function to convert to the time domain in R to apply signal processing ...
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2answers
119 views

Fourier transform of $ne^{-an}u[n]$

I need to find the Fourier transform of the following signal: $$ne^{-an}u[n]$$ The answers start by using the rule of the basic signal: $$a^nu[n] \rightarrow \frac{1}{1-ae^{-j\omega}} $$ and then ...
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1answer
369 views

Understanding the $\mathcal Z$-transform

I was studying $\mathcal Z$-transforms and found pretty good material on the topic, though I feel I do not have a proper understanding of the concept. Could someone help me clarify this? I know that ...
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0answers
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How to conserve symmetry of discrete spectrum after applying fractional delay in the frequency-domain? [duplicate]

Imagine a real-valued, discrete-time signal $h[n]$ with $N$ samples and a sampling period of $T_s = 1/f_s$. We know that the DFT of the signal $H[k]$ is conjugate symmetric because the signal is real-...