Questions tagged [frequency-domain]

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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 ...
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 ...
13k 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 ...
271 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!
28k 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 ...
5k 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 ...
29k 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, ...
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 ...
2k views

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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 ...
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 ...
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 ...
10k 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 ...
482 views

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

Given a discrete signal $\left\{ x [ 0 ], x [ 1 ], \ldots, x [ N - 1 ] \right\}$ what would be the correct way to downsample it in the frequency domain (Sinc interpolation)?
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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 ...
1k 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 ?
4k 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 ...
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 ...
308 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 ...
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 ...
403 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 ...
1k 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: ...
35 views

The Proper Way to Do Sinc Upsampling (DFT Upsampling) 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 upsample it in the frequency domain (Sinc interpolation)? Note: Added as a request by the answer ...
131 views

Explain the Process of Spectral Pooling and Spectral Activation in the Context of CNN in Frequency Domain

I am reading the paper Design of an energy efficient accelerator for training of convolutional neural networks using frequency Domain Computation: which uses Frequency Pooling, from Spectral ...
90 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 ...
1k 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 ...
592 views

Convolution Theorem using DCT

I am trying to digest this paper.  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 ...
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!
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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?
844 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?
482 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 ...
139 views

Frequency-domain deconvolution: "Direct" filtering vs "Wiener" filtering

Can someone help with clarifying the difference between two approaches to frequency domain "deconvolution: For the frequency domain problem: We want to find a filter $F(\omega)$ which will ...
483 views

Circular Convolution Matrix of ${H}^{H} {H}$

We all know that Discrete Fourier Transform (DFT) corresponds to circular (not linear) convolution. That is to say, if $x(n),h(n)$ and $y(n)$ is the original signal, the filter and output signal in ...
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 ...
710 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,...
158 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 ...
182 views

Frequency Spectrum Analysis

How do you find the phase and inverse Fourier transform of this frequency spectrum?
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Constructing frequency domain filter from a 2d spatial kernel

Given a 2d spatial kernel $h$, I want to construct the corresponding frequency filter $H$. In theory, $H$ is simply obtained by calculating the DFT of $h$ using a FFT algorithm. But in practice, there ...
7k 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 ...
246 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 ...
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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 $X(... 6answers 3k views Definition of the DFT / FFT Bin Size When reconstructing the frequency domain for an FFT, what is the most self-consistent way to do this -- i.e. how is it best to define the bin width,$\Delta f$? For example, previously I thought it a ... 3answers 4k views How to compute fundamental frequency from a list of overtones? Given a list of overtones (F1, F2, F3, etc), how do I compute the fundamental frequency? Can I do something like F2/F1=F1/F0? Is it the correct method to use? 4answers 3k views Why does the frequency in the DFT have to be an integer? I don't know why the result of DFT and FFT in MATLAB like below images.. fs=128; t=0:1/fs:1-1/fs; x=cos(2*pi*3.5*t); X=fft(x); N=length(x); n=0:N-1; f=fs*n/N; plot(f,abs(X)/N); If I set the ... 3answers 5k views Impulse Response to Frequency Response in Octave Having an impulse response of an audio system recorded as a wav file, how to calculate the frequency response of the system with octave? 1answer 2k views How does the number of frequency-domain sampling points influence the outcome of an inverse FFT? Given some frequency-domain representation of an impulse response. How does the number of frequency-domain sampling points influence the outcome of an inverse FFT, if I keep the sampling frequency ... 2answers 91 views Sampling Theorem: T-Sampled Signal I am stuck in a small question which I am trying to solve. The signal$f$defined by$f(t) := \text{sinc}(t)$is to be sampled. How should I draw the illustrations of the$T$-sampled signal$f_{T} = (...
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 ...