Tagged Questions

The Fourier transform is a mathematical operation that decomposes a function into its constituent frequencies, known as a frequency spectrum.

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DSP interview question: use of the identity in development of a significant transform

I'm preparing interview and found this question. But I don't really understand what is the question. Does it ask about Fourier transform or Z transform? How the simple identity $$xy=\frac{1}{2}x^2 ...
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1answer
24 views

Why doesn't JPEG use 1D DCT for image compression?

I know that JPEG uses 2D dct and splits the images in 8x8 blocks. Why doesn't it simply split the image in one-dimensional vectors in $\mathbb{R}^{64}$? Wouldn't it simplify the math? My guess is that ...
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2answers
41 views

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

I have a frequency-domain representation $F[n]$ of the complex discrete one-dimensional signal $x[n]$: $F=\mathcal{F}(x)$. Is there a frequency-domain transformation of $F$ into $F'=\mathcal{F}(|x|)$? ...
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0answers
63 views

Realization of IIR resonator

The measure of a given frequency $\omega$ in a signal $x(t)$ is: $\frac{1}{N}\sum\limits^N_{t=0}x\left(t\right)e^{^{-i \omega t}}$ This is basically an average of the correlation between the signal ...
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2answers
49 views

Find the frequency response of the system

How can I find the frequency response of the following linear system
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30 views

DFT of a pressure signal from space domain to wavenumber domain

When I do the DFT of the following signal: I get the following DFT which doesn't capture any peaks at all: Why is this? I'm not really able to identify what the error is?
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1answer
35 views

Spacing between gaussian windows for STFT

I'm computing discrete short time Fourier transform. Data is split into overlapping chunks and gaussian window is used for each chunk. However, I'm not sure how much overlap there should be between ...
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2answers
110 views

[2D fourier transform]: Most people can't explain this

I am confuse of 2d magnitude plot of the spectrum frequency. So we have 2 images, the first one is shown at the top, and the expand version of the white box is shown at the second row. For the ...
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1answer
44 views

Comparing the FFT to numerical integration in Matlab

The result of calculating the fourier transform using numerical integration is: the result of using Matlab's FFT is: So where did I go wrong here? I know the FT of a Gaussian should be ...
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1answer
25 views

What is the best Algorithm to estimate the frequency for Almost-Periodic Data or complex periodic data?

I’ve got what it looks like a periodic signal but the periods seem not equally repeated, I want to estimate the PSD, particularly I need to obtain the dominant frequency of this data. I’ve estimated ...
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2answers
59 views

Purpose of Phase Information

I am learning Fourier Transform from many days but till now I am not able to understand what does phase angle image show us or tell us? They say that MAGNITUDE tells "how much" of a certain frequency ...
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1answer
30 views

Frequency of the wave in frequency domain

If we have a 1-dimensional wave in time domain, it can be represented in frequency domain with x axis indicating the frequency of the wave and y axis indicating amplitude/magnitude of the wave. But ...
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1answer
42 views

Frequency Spectrum of an image

I have been studying about Frequency Domain from many days but still i am not able to clear one of the confusion. We say that in frequency domain an image is represented as waves. What I am able to ...
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2answers
122 views

Discrete Fourier Transform by hand

I have an assignment where I'm given the DFT of a sequence $x[n]$ as $X[k]=\{4,3,2,1,0,1,2,3\}$ and also $$y[n] = \left\{ \begin{array}[cc] xx[n/2] & \text{if n is even} \\ 0 & ...
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1answer
24 views

Audio noise detection with python

Have many audio files 1 minute long. Some of them are normal. Some of them are noise. Here is a normal file: This is a noise: And this is noise too: How do auto detect noise using python? ...
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0answers
19 views

Python implementation of multidimensional power spectral density with Welch method

I have done my best to write Welch method implementation for python for multidimensional time series and still in the case of one dimensional time series I am getting inconsistent response compared to ...
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2answers
37 views

What is a translation property in DFT

Hi someone please explain me the translation property of DFT. I am not able to understand it neither from Gonzalez nor from internet. I have done extensive study on this but not able to get it. Really ...
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1answer
55 views

What part of complex number of inverse discrete Fourier transform?

Ok, so we have an image that is a Fourier inverse of the original picture. We want to get the original picture back. We use Matlab to get that job done. We import the image and then we invert it with ...
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1answer
139 views

Is there a way to further optimise my FFT?

I've written my own FFT but wanted to know if there was perhaps a way to combine the Cooley and Turkey methods. So far I've got N/2 log N real multiplies for transforming a real signal. My current ...
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2answers
54 views

intuitive interpretation Fourier Transform of two different Rectangular pulses

From my understanding of Fourier transform, a Fourier transform of a signal in time domain will give the different frequency components of the signal in frequency domain, specified by their ...
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3answers
95 views

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 ...
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2answers
72 views

Best method to do piano key pitch detection?

For example, when playing piano, at the same time, print out the key notes by analyzing the signal of piano sound. How to do some pre-processing to remove the noise? When calculate with FFT, noise ...
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1answer
95 views

Fourier transform properties. Spectral density function [closed]

I have the following signal for which amplitude and phase spectrums have to be computed: This exercise also has a solution which begins by deriving the signal twice. Next, they say the spectral ...
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0answers
59 views

Why is level of power spectrum dependent on FFT resolution?

I created a sinusoidal wave in some noise, and plotted the power spectrum of the signal using two periodogram estimates (welch procedure). One estimate is 'high resolution' - i.e. it uses a longer ...
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1answer
43 views

How to obtain mean Power Spectrum from two audio channels?

I have a source of noise in a duct, on either side of the noise source I have a microphone, which register the pressure, so that I get two pressure signals: $p_1$ and $p_2$. I want to get the acoustic ...
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2answers
111 views

How to compute the Fourier Transform of this ramp-like signal?

I have the following signal: and this as the solution to the problem: $$\begin{align} X(j\omega) &= \int_{-\infty}^{+\infty}x(t)e^{-j\omega t}dt \\ &= \int_0^\tau \frac{E}{\tau}t\; ...
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0answers
41 views

Implementation of the constant Q transform + property questions

I'm reading up on fourier theory, especially the transforms. I implement the math as spectrograms in C++ to get a better understanding of what is going on. I've made an implementation of the short ...
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0answers
36 views

What are the differences between STFT in time and frequency domain?

For a signal f(t), we can do a short-time Fourier transform in time domain to get the time-frequency information. However, we can also to a "short-frequency inverse Fourier transform" in frequency ...
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1answer
52 views

Basics of waveform, how to define the zero point

Audio is a sequence of waveforms which have peaks, troughs, 0, just like below. How to define the x axis (y = 0) in the picture, how to choose the 0 point in the waveform since there are so many ...
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1answer
24 views

Signal Plus Weakly Stationary Noise

I was reading the book "Spectral Analysis of Time Series" By Herman Koopmans. On Page 55, he explains that a specific type of non-stationary signal which is the result of adding weakly stationary ...
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3answers
480 views

disadvantages of FFT, it can not extract enough frequencies without enough samples

Let's say sampling rate is $Fs = 44\mathtt{kHz}$, now I have $N = 2048$ samples, then I can get $N/2 + 1 = 1025$ frequencies. I'm confused by Matlab's FFT documentation that says the frequencies are ...
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0answers
53 views

How do I construct input to neural network from audio signals?

Input: Microphone recordings of digits from 0 to 9 from different speakers. Output: The digit from 0 to 9. I am doing this for fun. So first I will train my neural network using some samples and ...
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1answer
56 views

Unit Impulse funciton FT

How is FT of $ \delta $(t) equal to 1 ? Normal FT gives the result $\infty$. Can someone please explain? I did the normal integration and substituted the limits. Is it because $ \delta $(t) is a ...
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1answer
105 views

FFT Matlab - Meaning of Frequency Vector

I'm following a tutorial about the FFT. It's well explained but I don't understand the meaning of the frequency vector: ...
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2answers
140 views

Using Goertzel Algorithm in under-sampling

I plan to calculate a signal's phase using Goertzel Algorithm. I have 2 signals coming to microcontroller's ADC. Need to measure the phase difference between them. Signals are 15MHz sinusoids. Sample ...
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1answer
146 views

How to compute the main lobe width of generalized Hamming windows (i.e. Hann, Hamming, etc.)?

Is there a way to compute the main lobe width of windows of the generalized Hamming window family (i.e. Hann, Hamming, etc.)? By main lobe I mean the first zeros left and right of the center of the ...
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1answer
83 views

Power Spectrum: Defnition

I am new to the study of time series. Recently I have asked a question about the covariance of real and imaginary part of a real(in time domain) stochastic time series and I have received an answer ...
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1answer
45 views

UWB radar to find heartbeat

I have a UWB radar that Im playing with. The problem is that my algorithms at the moment can clearly, reliably and validly pick up 1-2mm movements of a pendulum i've set up. However, when I use it on ...
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4answers
152 views

Is there any alternative basis for a fourier-like transform?

Fourier transform of a continuous signal is just the projection of the signal on the sinusoidal family for imaginary part and the same family with phase offseted by a quarter of period for the real ...
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2answers
164 views

Covariance between real and imaginary parts of Fourier transform of a stationary time series

Since Fourier transform of a random stationary process in time (in the case of existence) is not necessarily real, my question is what is the relation between the covariance of real and imaginary ...
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1answer
65 views

how to get the phasor(frequency domain) representation of a digitalized signal?

I know that we can get the phasor representation(frequency domain) of a signal through Fourier transform, but the picture above gives a method that can get the phasor representation of a signal in a ...
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1answer
59 views

Discrete Fourier Transform and Opposite Convolution Theorem

I am reading the Wiki for DFT. There is a part for circular convolution theorem which sounds a bit odd saying: $$ \mathcal{F} \left \{ \mathbf{x\cdot y} \right \}_k \ \stackrel{\mathrm{def}}{=} ...
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0answers
41 views

How to get the quaternionic analytic signal of a image?

The 2D discrete image signal's quaternionic fourier transform can be described as F(u,v), and its 2D analytic signal often be described as: $$ F_q(u,v) = (1 + \mbox{sgn}(u))(1 + \mbox{sgn}(v)) F(u,v) ...
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1answer
41 views

Why does the periodic signal in time always give a discrete frequency spectrum

I would like to know, why does the periodic signal in time always give a discrete frequency spectrum in FT? I know the equations, but I simply dont understand why is it so. Thanks!
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3answers
74 views

What happens with signal in frequency spectrum when it is time shifted in time spectrum?

I have some trouble to understand what is going on with signal in frequency spectrum when it is time shifted in time spectrum. I am hoping that somebody will help me to understand that. Thanks you ...
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2answers
293 views

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 ...
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2answers
120 views

Intuitive explanation of the Fourier Transform for some of the functions

Does anyone have a mechanism to understand intuitively (and automatically) why the Fourier Transform of certain functions have certain shapes (at least for some functions, not necessarily for all)? I ...
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2answers
74 views

Frequency spectrum of a sinc function

I am doing one example from my book as a preparation for exam. The assignment is: It is given that: $$\mathbb{rect}(t)=pf(t) \leftrightarrow PF(f)=2AT_0 \cdot \mathbb{sinc}(2\pi fT_0)$$ you ...
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1answer
13 views

Filtered backprojection implementatoin

I am wondering the detail of the filtered backprojection. Suppose I have a projection file: $p(s,\theta)$=[1 2 3 1 2] Then to get its filtered backprojection ...
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1answer
35 views

How are phase values able to capture motion from video?

I know that the phase spectrum contains most of the structural information about the image importance of phase. But I want to know more about importance of phase spectrum related to video signals. I ...