Questions tagged [frequency-domain]

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24
votes
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 ...
12
votes
2answers
13k views

When should I calculate PSD instead of plain FFT magnitude spectrum?

I have a thirty-second speech signal that was sampled at 44.1 kHz. Now, I would like to show what frequencies the speech has. However, I'm not sure what would be the best way to do that. It seems ...
11
votes
2answers
12k views

Determining the noise floor of a signal in the frequency domain

Is there an accepted way of determining the noise floor of a signal by looking at it in the frequency domain? Is it a matter of averaging all the bins, or median, or some more complex calculation ...
9
votes
4answers
257 views

What is the type of noise in this image?

what reason could make the noise/effect in this image? Below is the original Thanks!
8
votes
3answers
26k 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 ...
8
votes
5answers
4k views

What's the meaning of a complex zero/pole?

I have been studying signal processing and control for a while now, and I use Laplace and Fourier transforms almost everyday. Also another tools such as Nyquist or Bode plots. However, I had never ...
7
votes
2answers
28k views

Amplitude of the Signal in Frequency Domain different from Time Domain

How does the Amplitude of the Signal is changed when taking the FFT of a Signal, Have a look, The amplitude had changed from 2 to 30, and Here is my code for generating the above output, ...
7
votes
1answer
2k views

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 ...
6
votes
1answer
4k views

How do real-time convolution plugins process audio so quickly

Okay, so in Logic Pro I can load up a Space Designer plugin (convolution reverb) with an impulse that's 9.1 seconds long, turn my mic on, and get real-time convolution reverb as the mic records ...
6
votes
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 ...
6
votes
1answer
976 views

What is difference between terms $X(j \omega) ,X(\ e^{j \omega })$ and $ X(\omega)$?

While studying frequency transforms ,I get confused with the terms like $X(j \omega) ,X(\ e^{j \omega })$ and $ X(\omega)$ ,where $ \omega = 2 \pi f $. So what is the difference between them ?
6
votes
4answers
2k views

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 ...
6
votes
3answers
9k views

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 ...
5
votes
5answers
3k views

Why audio clipping produces harmonics?

Today I was talking to my collegue about clipping and he said that clipping produces harmonics in frequency domain as he showed me the clipped signal frequency response. However when I asked him why ...
5
votes
2answers
2k views

Frequency Domain Filtering

Can you create a zero phase IIR filter by transforming its impulse response into frequency domain and only taking the magnitude of that frequency repsone? I have seen this in an open source project ...
5
votes
2answers
1k views

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 ...
5
votes
1answer
379 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 ...
5
votes
1answer
5k views

Estimate the Filter Coefficients of 1D Filtration (Convolution)

I have an output signal $y$ which is an input signal $x$ convolved $\star$ with an impulse response function $h$ with some added noise $n$ : $$y(t) = h(t) \star x(t) + n(t)$$ I know the input signal ...
4
votes
3answers
926 views

Chop out frequencies outside human hearing range

I have a bunch of audio files all sampled at 44100 Hz sample frequency. I am trying to remove all the frequencies which are outside the human hearing range (I use the following as reference: Frequency ...
4
votes
4answers
183 views

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 ...
4
votes
2answers
103 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!
4
votes
1answer
2k views

Which information do we get from magnitude and phase spectrum?

I am learning image processing. I want to ask very basic question related to FFT topic Which information do we actually get from "phase spectrum" and "magnitude spectrum" about an image?
4
votes
1answer
286 views

Convolution Theorem using DCT

I am trying to digest this paper. [2002] Anna Usakova. Using Of Discrete Orthogonal Transforms For Convolution So far, I've been successful with DFT and DHT. Could someone give a hand with DCT? I am ...
4
votes
2answers
107 views

Idea for Noise Level Estimation / Automatic Thresholding in the Presence of Peaks

I have the fft of some signal, and want a rough estimate of the noise level in order to choose an appropriate threshold for our peak detection algorithm. In general, the fft contains mostly noise with ...
4
votes
3answers
723 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?
4
votes
1answer
940 views

Image 2D Real Cepstrum with DFT, Is `ifftshift` Needed?

This is my testing image,it is taken from this paper: I tried to transform it into its real cepstrum domain with this simple MATLAB code: ...
4
votes
1answer
70 views

Finding the Transfer Function of a Multiplicative Distortion in MATLAB

I have the frequency response of two signals shown above. One is uncontaminated, and the other is the same signal contaminated by a multiplicative distortion with two poles and two zeros. I need to ...
4
votes
1answer
111 views

Amplitude Estimating Using a Windowed DFT

Let's say we want to estimate the amplitude A of a mono-frequent signal using a windowed DFT. The frequency of the signal is unknown, and the frequency resolution of the DFT is limited, thus it cannot ...
4
votes
2answers
6k views

Why Frequency Domain conversion is Important in Digital Image Processing?

Any Image enhancement technique can be easily applied to the normal images. Still, most of the folks say that frequency domain conversion of the images can lead to better enhancement. Why do we need ...
4
votes
1answer
236 views

What is the LOW frequency resolution rule analogous to Nyquist?

If I'm analyzing a signal in the frequency domain, I know about the well known Nyquist criteria that the sample frequency must be > 2x of the highest component present in the signal. However, there ...
4
votes
2answers
7k views

How does taking the absolute value of a complex signal reflect in the frequency domain?

I have a frequency-domain representation $X(e^{i\omega})$ of the complex discrete one-dimensional signal $x[n]$: $X(e^{i\omega})=\mathcal{F}\{x[n]\}$. Is there a frequency-domain transformation of $X(...
3
votes
6answers
2k views

Definition of the DFT / FFT Bin Size

When reconstructing the frequency domain for an FFT, what is the most self-consistent way to do this -- i.e. how is it best to define the bin width, $\Delta f$? For example, previously I thought it a ...
3
votes
3answers
4k views

How to compute fundamental frequency from a list of overtones?

Given a list of overtones (F1, F2, F3, etc), how do I compute the fundamental frequency? Can I do something like F2/F1=F1/F0? Is it the correct method to use?
3
votes
1answer
1k views

How does the number of frequency-domain sampling points influence the outcome of an inverse FFT?

Given some frequency-domain representation of an impulse response. How does the number of frequency-domain sampling points influence the outcome of an inverse FFT, if I keep the sampling frequency ...
3
votes
2answers
4k views

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 ...
3
votes
1answer
440 views

Exercise Related to Frequency Resolution and SNR

I'm studying a book about DSP and trying to make exercises. Here is one I'm interested in: A scientist acquires 65,536 samples from an experiment at a sampling rate of 1 MHz. He knows that the signal ...
3
votes
1answer
2k views

Magnitude of the Gradient in Frequency Domain

I'm learning some basics of image processing. Recently I've read about image filtering and two-dimensional Fourier transform, because I'm preparing for exam. And I have one question I don't know ...
3
votes
1answer
692 views

Spectral Leakage, Phase and other questions about FFT

I'm currently implementing a voice recognition algorithm using FFT and now some questions came up to me: Spectral Leakage: I know what it is, why it appears and how to solve it using a Windowing ...
3
votes
1answer
254 views

The Proper Way to Do Sinc Downsampling (DFT Downsampling) for Uniformly Sampled Discrete Signals with Finite Number of Samples

Given a signal $ \left\{ x [ 0 ], x [ 1 ], ..., x [ N - 1 ] \right\} $ what would be the correct way to downsample it in the frequency domain (Sinc interpolation)?
3
votes
1answer
2k views

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 ...
3
votes
1answer
2k views

Filter - Spatial Domain Versus Frequency Domain

Note: This is a followup question of How can I create a custom band-pass filter?. Can you explain the following python source code?. Bandpass filter bank. Suppose, I have an equation ...
3
votes
2answers
599 views

Color Artifacts in Fourier Transformed Image

I am working with images and Fourier transforms. I am trying to understand what might be causing some artifacts in my output image. I am starting with a 512x512, RGB image of Lenna. I FFT the image,...
3
votes
2answers
166 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 ...
3
votes
2answers
462 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 ...
3
votes
2answers
1k 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
votes
1answer
1k views

How to find phase shift and process I/Q channel

I am currently working of 24GHz FMCW radar signal processing. The Module I'm using has 2 receiving antennas and each has 2 outputs (I and Q channel). So overall I've 4 channels. I'm using combination ...
3
votes
1answer
159 views

Frequency Spectrum Analysis

How do you find the phase and inverse Fourier transform of this frequency spectrum?
2
votes
4answers
3k 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 ...
2
votes
2answers
2k views

Finite and Infinite support in time and frequency domain

It's known that signals with a finite support in time has an infinite support in frequency (talking about Fourier Transforms). A common example that is given for the claim is the triangle function ...
2
votes
3answers
2k views

What does the negative sign mean in the image frequency domain?

When I transform an image from the spatial domain to the frequency domain, some frequencies are negative. What is the meaning of the negative sign? For example:

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