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

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STFT: why overlapping the window?

For STFT, we impose window of certain size onto the original signal, then we perform fft on each window. The uncertanty about frequency and time is determined by the width of the window, however, I ...
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11 views

Short Time Fourier, What happen when window is outside the sample points

I am trying to compute STFT on the following signals..... such that they have 15 cycles of (1/50) second sine wave, with Fs=10000. The algorithm for STFT I am using is :STFT algorithm Then I set ...
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23 views

Fourier transform of triangular function

Determine $X(\omega)$. $g(t)$: I understand how to create a box from [-1,1] of amplitude 1/2. $x(t) = g(t) * g(t)$ $X(\omega) = G(\omega)G(\omega)$ the solution I am seeing says that $G(\omega) ...
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20 views

Constant-Q transform - summing complex DFT coefficients vs. summing DFT magnitudes

The constant-Q transform computes a spectrum on a logarithmic frequency axis. When analyzing music signals, this can be a more meaningful representation than the Discrete Fourier Transform (DFT), as ...
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13 views

Wiener filter of two signals of comparable magnitude

Suppose I have two signals, x(t) and y(t) (e.g. from a Lock In amplifier, such that x(t) and y(t) are 90 deg. out of phase). Assume x(t) is the clean signal, s(t), plus background noise, while y(t) is ...
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151 views

Conceptual question on FFT and chirp signal

If I take the FFT of a sinusoid I will get a plot whit all the energy of the signal concentrated at the sinusoid frequency. But what happens if I have a signal in which the frequency keeps ...
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1answer
93 views

Regarding Bode plots; $H(s)$ and $H(j\omega)$

In circuit analysis, I understand the use of Laplace Transforms to obtain the impedance of a linear RLC circuit, ie transforming from the time domain to the frequency domain. In most texts I have seen ...
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23 views

Basic Fourier Transform filtering and LTI frequency response using Matlab

Not sure if this is the right place to ask... I'm new to Matlab for LTI signal processing and wondering if anyone can help with something that I'm sure is meant to be basic. I've spent hours and hours ...
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2answers
36 views

How do I take the real part of this bandpass filter system's output?

I'm stuck on a final step in this problem. Essentially, there are the two systems above, which we'll call System 1 (Fig. 4.26, with ideal lowpass $H(jw)$) and System 2 (with $H_1(jw)$). The ...
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16 views

Motion Blur Filter

I want to implement Motion Blur Filter in C# using Emgu CV, what is the correct way to do this in fourier domain. I am currently stuck at how to perform multiply of Motion Blur filter and my Complex ...
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3answers
147 views

Why is a negative exponent present in Fourier and Laplace transform?

could anyone explain why there is a need of negative exponent in fourier and laplace transform.I looked through the web but I couldn't get anything.Does anything happen if a positive exponent is ...
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42 views

Fourier Transform Problem - absolute value, time-saving tricks, etc

I am given the following signal: $$[e^{-at}cos(w_{o}t)]u(t),\ a>0$$ Then I am told to find the Fourier Transform, which tells me I need an answer of the form: $$X(jw)=\int_{-\infty}^\infty \! ...
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81 views

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
36 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
60 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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79 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
52 views

Find the frequency response of the system

How can I find the frequency response of the following linear system
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33 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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42 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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138 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
63 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
49 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
61 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
32 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
44 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
146 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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42 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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26 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
43 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
75 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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63 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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101 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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73 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
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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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69 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
51 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
113 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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51 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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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
63 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
509 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
56 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
139 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
152 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
200 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
52 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 ...